New Geometries for Ring Resonator Sensing

A thesis submitted to The University of Manchester for the degree

Doctor of Philosophy

in the Faculty of Science and Engineering

2017

Thomas Catherall

School of Electrical and Electronic Engineering

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List of Contents

Title Page 1 List of Contents 3 List of Figures 5 Abstract 11 Declaration 12 Copyright Statement 12 Preface 13 Acknowledgements 14 Chapter 1 - Introduction 16 1.1 Research Motivations 16 1.2 Basics of Waveguides 19 1.3 References 46 Chapter 2 – Literature Review 49 2.1 Introduction 49 2.2 Main Body 50 2.3 Summary 79 2.4 References 82 Chapter 3 – Experimental Setup 86 3.1 Introduction 86 3.2 Laser and Spectrometer Specifications 88 3.3 Standard Photonic Chip Design and Specifications 94 3.4 Optical Setups and Experimental Procedure 96 3.5 Sources of Noise and Uncertainty 98 3.6 References 101 Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems 102 4.1 Introduction 102 4.2 Un-tuned Ring Resonator Spectra 103 4.3 Single Ring Tuning 124 4.4 Thermal Calibration 132

4.5 Double Ring System Thermal Tuning 137 4.6 Y-Splitting Double Rings 142 4.7 Analysis of Double Rings 151 4.8 Conclusion 159 4.9 References 160 Chapter 5 – Modelling of Double Ring System 161 5.1 Introduction 161 5.2 Influencing Factors of Light Confined Within Ring Resonators 161 5.3 3x3 Transfer Matrix Modelling 165 5.4 Comparison Between Model and Experimental Data 173 5.5 Conclusion 201 5.6 References 202 Chapter 6 – Sensing with Ring Resonators 203 6.1 Introduction 203 6.2 Basic Ring Resonator Sensing 203 6.3 Drop Testing Streptavidin 209 6.4 Microfluidics Integration 217 6.5 Upconverting Nanoparticles 224 6.6 Conclusion 234 6.7 References 236 Chapter 7 – Conclusions and Future Outlook 237 7.1 New Contribution to Knowledge 237 7.2 Progress towards meeting the Thesis Aims 238 7.3 Future Continuation of this Research 238

Word Count: 42,334

List of Figures

1.1 Planar Waveguide Dimensions 20 1.2 Evanescent Field 22 1.3 Evanescent Field Propagation 23 1.4 Evanescent Field Biosensing 24 1.5 Light in a Waveguide 25 1.5 Common Waveguide Designs 26 1.7 Confined Waveguide Field 27 1.8 The Smart Cut Production Method 30 1.9 Mach-Zehnder Waveguide Interferometer 32 1.10 Field in Slotted Strip Waveguide 33 1.11 Evanescent Coupling Methods 35 1.12 Holographic Lens 36 1.13 Ring Resonator Analogies 37 1.14 Typical Ring Resonator Transmission Spectrum 39 1.15 Fano Resonances 42 1.16 Slotted Waveguide Setup 45 2.1 The SWG Waveguide 55 2.2 SEM Image of SWG Ring Resonator 55 2.3 Photonic Crystal Cavity 56 2.4 3-Stage Multi-ring Filter 58 2.5 Ring Resonators in Series 59 2.6 Series Resonator Transmission Spectra 60 2.7 Fano Shape Resonance System 61 2.8 RBRMZI System 62 2.9 Doped Ring Resonator 63 2.10 Thermally Controlled Doped Ring Resonator 64 2.11 Etchless Silicon Waveguide Fabrication Process 66 2.12 SEM Image of Etchless Waveguide 67 2.13 Pedestal Supported Waveguide 67

2.14 Alternative Waveguide Output Layout 73 2.15 Reaction Tube Design 74 2.16 Vertically Stacked Microfluidics 75 2.17 Mach-Zehnder Interferometer 77 3.1 Ring Resonator Functionality 87 3.2 Tuneable Laser Kit Layout 89 3.3 Tuneable Laser Power Output 90 3.4 Power Output of Broadband Superluminescent Diode 91 3.5 Optical Spectrum Analyser Resolution 92 3.6 Optical Spectrum Analyser Noise Floor 93 3.7 Microchip Architecture 95 3.8 Non-probing Optical Setup 96 3.9 Ambient Peak Position vs Time 99 3.10 Equivalent Intensity Comparisons 100 4.1 Spectral Tuning Methods 103 4.2 Transmission Spectrum Properties 104 4.3 Single Ring Resonator Layout 106 4.4 Plain Waveguide Transmission Spectrum 107 4.5 25 μm Windowless Ring Resonator with 200 nm Gap Transmission Spectrum 108 4.6 25 μm Windowed Ring Resonator with 200 nm Gap Transmission Spectrum 108 4.7 50 μm Windowless Ring Resonator with 200 nm Gap Transmission Spectrum 109 4.8 50 μm Windowed Ring Resonator with 200 nm Gap Transmission Spectrum 109 4.9 Gaussian Fit to Spectrum 111 4.10 Sine Fit to Spectrum 112 4.11 Straightened Plain Waveguide 113 4.12 Straightened 25 μm Windowed Spectra 113 4.13 Straightened 25 μm Windowless Spectra 114 4.14 Straightened 50 μm Windowed Spectra 114 4.15 Straightened 50 μm Windowless Spectra 115 4.16 Typical Lorentzian Fit 116 4.17 Q-Factor Measurements 117

4.18 GDS Single Ring Drop Port 119 4.19 Drop Port Straightened 25 μm Windowed Spectra 120 4.20 Drop Port Straightened 25 μm Windowless Spectra 120 4.21 Drop Port Straightened 50 μm Windowed Spectra 121 4.22 Drop Port Straightened 50 μm Windowless Spectra 121 4.23 Typical Lorentzian Fit Drop Port 122 4.24 Drop Port Q-Factor Measurements 123 4.25 Thermal Tuning Setup 125 4.26 Wavelength vs Time Thermal Calibration 25 μm 128 4.27 Wavelength vs Applied Power 25 μm 129 4.28 Wavelength vs Time Thermal Calibration 50 μm 130 4.29 Wavelength vs Applied Power 50 μm 131 4.30 Wavelength vs Applied Power 25 μm, 300 nm Gap 133 4.31 Hot Pad Thermal Setup 134 4.32 Thermal Heating Element Schematic 135 4.33 Wavelength vs Temperature for Hot Pad 135 4.34 Double Ring Mach-Zehnder Interferometer 138 4.35 Drop Port Intensity vs Wavelength (Full Free Spectral Range Tune) 139 4.36 Drop Port Intensity vs Wavelength (Higher Resolution Peak Overlap) 140 4.37 Drop Port Intensity vs Wavelength New Chip 141 4.38 Throughput Intensity vs Wavelength 141 4.39 Y-Splitting Double Ring Setup 143 4.40 Travelling Peak Raw Data 145 4.41 Travelling Peak Gaussian Background Removed 146 4.42 Travelling Peak Sinusoidal Background Removed 146 4.43 Travelling Peak Offset Spectra 147 4.44 Stationary Peak Raw Data 148 4.45 Stationary Peak Gaussian Background Removed 148 4.46 Travelling Peak Sinusoidal Background Removed 149 4.47 Travelling Peak Offset Spectra 150 4.48 Travelling Peak Intensity Comparison 152

4.49 Drop Port 2D Intensity Map 153 4.50 Drop Port Compared Spectra 154 4.51 Travelling Peak 2D Intensity Map 155 4.52 Travelling Peak Compared Spectra 155 4.53 Stationary Peak 2D Intensity Map 156 4.54 Stationary Peak Compared Spectra 156 4.55 Intensity vs Heater Power Comparissons 157 5.1 Generic Mathematical Ring Resonator System 162 5.2 Mathematical System for 3x3 Transfer Matrix System 165 5.3 Scattering Matrix Model Diagrams 167 5.4 Throughput Changes Due to Losses 174 5.5 Drop Port Changes Due to Losses 174 5.6 Throughput Changes Due to Coupling 175 5.7 Drop Port Changes Due to Coupling 176 5.8 Throughput Changes Due to Coupling LHS 176 5.9 Throughput Changes Due to Coupling RHS 177 5.10 Drop Port Changes Due to Coupling 177 5.11 Throughput Changes Due to Coupling LHS 178 5.12 Throughput Changes Due to Coupling RHS 179 5.13 Drop Port Changes Due to Coupling 179 5.14 Travelling Peak Relative Phase Transmission Spectra 181 5.15 Stationary Peak Relative Phase Transmission Spectra 182 5.16 Drop Port Relative Phase Transmission Spectra 183 5.17 Typical Model Results 184 5.18 Model Fitting Example 185 5.19 Transmission vs Wavelength 0.1 mA 186 5.20 Transmission vs Wavelength 1.0 mA 186 5.21 Transmission vs Wavelength 2.0 mA 187 5.22 Transmission vs Wavelength 3.0 mA 187 5.23 Transmission vs Wavelength 4.0 mA 188 5.24 Transmission vs Wavelength 5.0 mA 188

5.25 Transmission vs Wavelength 6.0 mA 189 5.26 Effective Refractive Index Comparisons 190 5.27 Double State Peak Fitting Example 191 5.28 Double State Peak Fitting Spectra 194 5.29 Travelling Peak Effective Refractive Index vs Current 194 5.30 Travelling Peak Relative Phase vs Current 195 5.31 Travelling Double Peak Signal Contribution 195 5.32 Stationary Peak Effective Refractive Index vs Current 196 5.33 Stationary Peak Relative Phase vs Current 196 5.34 Stationary Double Peak Signal Contribution 197 5.35 Drop Port Modelling 198 5.36 Future Chip Designs 200 6.1 Single Ring Resonator Layout 204 6.2 Micropipette Experimental Process 206 6.3 Initial Sensing Test Spectra 207 6.4 Glucose Evaporation Wavelength vs Time 208 6.5 Surface Functionalisation Approach 210 6.6 Image of Chip During Streptavidin Coating 213 6.7 Transmission Spectra at Each Coating Stage 214 6.8 Functionalisation Spectral Shift Comparisons 214 6.9 Streptavidin Alexa-488 Fluorescence Microscope Image 216 6.10 Silicon Microfluidics Mould 218 6.11 PDMS Bubbles 219 6.12 Set PDMS Cast 220 6.13 Microfluidic Channel on Chip 221 6.14 Microfluidics Glucose Test G10 222 6.15 Microfluidics Glucose Test G12 223 6.16 Laser Tuning Approach 228 6.17 Brightfield Images of Illuminated UCNPs 229 6.18 Brightfield Images of UCNPs Deposited on Surface 230 6.19 Images of UCNPs excited by Ring Resonator 231

6.20 Scattering vs Ring Resonator Illumination 232 6.21 UCNP Results at Different Wavelengths 233

Abstract

This thesis presents a detailed study of complementary metal-oxide-semiconductor (CMOS) compatible silicon waveguide and ring resonator technologies. The project specifically focuses on a range of slotted ring resonator configurations comprised of rib- style waveguides. Single ring resonators and Mach-Zehnder interferometers with double rings and central drop port channels have been successfully characterised. Thermal tuning techniques using on-chip heaters were used to determine their sensitivities. A stringent signal cleaning method was also developed to remove systematic background noise.

Analysing the transmission signals produced by the Mach-Zehnder interferometers with double rings and a central drop port, it was revealed that coupled resonator induced transparency (CRIT) is created along with Fano-type resonances when the resonant peaks of the two ring resonators are tuned to overlap. The tuning of these features revealed a 2.7 and 2-fold improvement in device sensitivity. A 3x3 transfer matrix model has been developed to simulate the behaviour of light travelling through this configuration. Modelling suggests that effective refractive index and relative phase are the key factors in determining this behaviour. When tuned to close proximity, a resonant ‘superstate’ is achieved in which a modified model is required.

Applying the single ring resonators to biosensing applications, basic refractive index testing and a glucose sensing calibration were conducted. A polydimethylsiloxane (PDMS) based microfluidics system was also developed to improve the reliability of sensing and enable automation. Using silicon nitride ring resonators with inkjet-printed upconverting nanoparticles, it was found that the evanescent field of the rings could stimulate the upconversion process revealing visible spectrum emission around the rings.

Declaration

No portion of the work referred to in the thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning.

The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the “Copyright”) and s/he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes.

Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made.

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Further information on the conditions under which disclosure, publication and commercialisation of this thesis, the Copyright and any Intellectual Property and/or Reproductions described in it may take place is available in the University IP Policy (see http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=24420), in any relevant Thesis restriction declarations deposited in the University Library, The University Library’s regulations (see http://www.library.manchester.ac.uk/about/regulations/) and in The University’s policy on Presentation of Theses

Preface

To introduce myself, Tom Catherall as the author of this PhD thesis; I was born and raised in Lancashire in the North West of England. As a college student I realised a talent in the field of science and chose to study a four year MPhys Physics degree at the University of Manchester. During my summer holidays, I gained valuable experience working at the Southampton Optoelectronic Research Centre. Following my degree, I initially opted to take a two year job as a scientific project manager working in the defence industry, taking me to the Salisbury plains in the process. In this role I acquired some great skills and industrial experience, but after two years, I decided to get back into academic research. A friend of mine from university (now Dr Gregory Auton) had been working towards his own PhD in the Northwest Nanotechnology Doctoral Training Centre (NOWNANO DTC), suggesting that I try it out too. I applied for a position and very gratefully accepted the opportunity to start a new PhD Project. In the NOWNANO DTC I was given a six month training period in general nanotechnology then allowed to choose a project to complete my PhD in.

When choosing this PhD project, my aims were to find a new multidisciplinary field with lots of room for further expansion, the chance to discover new science and potentially discover commercial value within my work. I opted to research silicon photonics as the fabrication technology is ever relevant, there is great potential for up-scaling and the prospect for commercialisation is very high. The field is fairly developed, but applications in biosensing and other sensing work is still relatively new, with the potential to be of huge benefit to everyone if effective pathological testing can be realised.

My aim with this thesis is to bring the field to life for the reader, to share my insights gained over the past three years and to clearly present my experimental methods, results and analysis in such a way that future researchers would be easily able to replicate my research and take it further if they desired.

Acknowledgements

My three years of study have been challenging at times. For helping me to overcome these challenges I would like to thank the following people:

 Professor Matthew Halsall for his guidance, support and advice as my main supervisor. I thank you for allowing me freedom to explore the field. I feel a greater sense of independence as a researcher as a result.  Dr Andrew Thomas for his support as my co-supervisor. Through working with you, I have gained more diversity in my knowledge and discovered a lot of enjoyable science. I also enjoyed helping with your STEM outreach activities.  Dr Iain Crowe for sharing his deep knowledge of silicon ring resonator technology and helping me find a relevant direction for my research.  Dr Joseph Lydiate for laying the foundations of this project, enabling it to exist and for designing a microchip platform for my work.  Siham Hussein for teaching me the laboratory basics, providing varied conversation and encouragement.  Eric Whittaker for general laboratory assistance and helping me build my electrical tuning experimental setup.  Dr Steve Edmondson for helping me to develop a robust approach to microfluidic integration.  Dr Matteo Cherchi of VTT for developing a transfer matrix model which worked with my results.  EPSRC for funding the NOWNANO DTC, creating the chance to take on this PhD.  The NOWNANO DTC, including Prof Irina Grigorieva and Prof Tom Thomson, for accepting me into the DTC, My Fellow DTC Students and its great organisation.  Dr Gregory Auton for encouraging me to start my PhD, also for being a great friend and academic peer.  My family for their support and distraction.  My wife Abimbola joining my family and keeping me company through the hard times and the good.

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Chapter 1 – Introduction

Chapter 1 - Introduction

1.1 Research Motivations

Technologies which monitor healthcare and generally improve quality of life are understandably of great interest to everyone. The ability to monitor ones health and spot early warning signs enables users to contain maladies and avoid expensive surgeries, lower risk of death and improve general fitness and health. Developments in chemical and biological sensors in particular can have a huge impact in a range of fields including medicine, pharmaceutics, pathological testing, the defence industry, environmental monitoring and quality control for food and chemical products.

Demand for such technologies has led to significant development over recent years. Results of this development include technologies such as fluorescence microscopy, microfluidics, quantum dot fabrication and labelling, surface plasmon resonances, lab-on- a-chip technologies, silicon photonics and a wide range of biochemical sensors.1 The physical scales of these technologies range from nano to macro. In recent times; it is proving to be especially beneficial to develop these sensors on the microscale. The advantages of this approach are many, including:  The ability to work in self-contained environments.  Avoidance of relative changes in environmental temperature.  Requiring far smaller samples of analyte.  Easier integration of automation and electronics.  The possibility of mass-production and thousands of tests run in parallel.  The ability to self-contain the technology (enabling its use it in hostile environments).  The ability to use in vitro analysis, reducing risk to patients.  Lowered power consumption, quick response times.  The possibility of surface functionalisation and microfluidic compatibility.

Chapter 1 – Introduction

In addition, especially with electronic and optical technologies, increased sensitivities often go hand in hand with improvements to signal modulation, on/off switching and lowered energy consumption rates. Developments in these fields could be of great benefit as compact optical on-chip interconnects are being developed.

1.1.1 Continuation of Group Research

This project is a continuation of the groundwork conducted by Dr Joseph Lydiate during his PhD conducted with Professor Matthew Halsall in the Microelectronics and Nanostructures research group at the University of Manchester.2 During Dr Lydiate’s time in the research group he worked theoretically to simulate, design and ultimately manufacture a novel ring resonator arrayed microchip. Unfortunately the finished product was manufactured as his PhD drew to a close. As such the actual devices remained untested. This created the opportunity to characterise his devices while seeking ways to improve their sensitivities, application and focus on silicon photonic technology, looking at waveguides, ring resonators and their use as a biosensing technology.

1.1.2 Pathological Testing and Biosensing

According to the Department of Health, there are nearly 800 million pathological tests conducted within the NHS each year, or 14 per person.3 This opportunity has formed the foundation for large amounts of biosensing research and development. These tests are typically conducted manually with fluorescent biolabels and fluorescence microscopy techniques; however these tests require highly trained professionals and can be prone to human error.

In day-to-day life, one of the quickest growing biosensing markets is the blood glucose monitoring market.4 According to the World Health Organisation, the number of patients suffering from diabetes has risen from 108 million in 1980 to 422 million in 2014. It is estimated that in 2012 1.5 million deaths were directly caused by diabetes and another 2.2 million deaths were attributed to high blood glucose.5 Devices to self-monitor glucose

Chapter 1 – Introduction are reasonably cheap at approximately £20.6 The cost of testing strips is also reasonably low at £0.28 per strip6 however the accumulative cost can add up over time.

Interstitial fluid from within the extracellular matrix is another biological fluid which until recently has been explored very little compared to blood. The advantage of monitoring interstitial fluid is that novel extraction techniques can be used,7 reducing the risk of infection upon extraction. The levels of creatinine and urea within interstitial fluid can be monitored to determine the health of patient’s kidneys, which in turn can be an alternative approach to determining whether there are other underlying pathological conditions.

It can be seen that technologies which are able to quickly and automatically identify a variety of biomolecules (as fluorescence microscopy does) or technologies which can cheaply monitor glucose levels with low cost re-usability would be of great benefit to the general public. The technology covered in this thesis could easily be developed further to tackle both of these needs at relatively low cost when mass produced.

While the examples given here are of great importance to many people, silicon photonic ring resonator technology is extremely versatile and could easily be adapted to monitor a wide range of biomarkers. Using a functionalised surface, any specific biomolecules or proteins can be targeted as a one-use type testing device. Acting as a non-functionalised bulk sensor, it is also possible to monitor concentration levels of chemicals such as glucose, urea and creatinine in a re-usable way.

1.1.3 Industrialisation

Another key motivator behind this project is the industrial maturity of silicon photonic manufacturing technologies. Silicon photonics is a field which grew in influence on the back of the silicon electronics industry.8 CMOS fabrication techniques and the ability to grow highly uniform crystals of silicon for the electronics and microchip industry led to the ability to manufacture high quality silicon wafers on a massive scale, while increasingly precise etching techniques enable the formation of features on the smallest

Chapter 1 – Introduction scale, as low as 14 nm for commercially produced transistors.9 Control on this level means the ability to fashion waveguides and optical components with incredible precision while maintaining the benefits of mass scale production.

In recent years, silicon photonics has seen heavy investment by major technology corporations, such as Intel and IBM. The motivation for this investment is to eventually replace copper interconnections in computer chips with CMOS compatible optical information highways, capable of transmitting up to 1000x more information than their copper counterparts without the risk of overheating. A result of these developments is the ability to manufacture complicated microstructures and optical circuits on silicon wafers relatively easily, and, when mass-produced, relatively cheaply.10 Devices manufactured in this way have become widely known as ‘lab-on-a-chip’ technology, due to the self-contained nature and size.

Silicon photonics is a rapidly expanding industry with great potential. According to MarketsandMarkets.com the silicon photonics market is expected to grow to $ 1,078.9 Million USD, growing at a compound annual growth rate of 22.1% between 2016 to 2022.11 It can be expected that many developments within this market could be beneficial for silicon on insulator ring resonator technologies, ensuring that the technology improves with the industry.

1.2 Basics of Waveguides

At this stage in the thesis, it is necessary to introduce the basic operating principles of waveguides and ring resonators which ultimately determine the behaviour of silicon photonic devices. A waveguide can be defined as a structure that guides waves (electromagnetic in this thesis) with minimal energy losses by confining expansion in one or two dimensions. One dimensional waveguides are the same as fibre optic cables in principle but in the context of this project they tend to be fixed to the surface of a chip or component.

Chapter 1 – Introduction

1.2.1 Wave Confinement

Step index planar waveguides are considered the simplest optical waveguide structure.12 These structures consist of a high refractive index dielectric layer of thickness h, sandwiched between two layers of material with lower refractive index. The layout is shown in figure 1.1.

Figure 1.1: The dimensionality of a planar waveguide. In this figure a film, with refractive index nf , is sandwiched between a substrate with refractive index ns and an upper cover layer, nc. The film is infinite in the xz-plane and finite in the y-direction. A reference point y = 0 can be taken as the interface between the film and upper cover layer.

Analysis of Maxwell’s equations12 for the system shown in figure 1.1 leads to the following equations:

−γcy Hx(y) = Ae , y ≥ 0

2 γc nf Hx(y) = A [cos( kfy) − 2 sin(kfy)] , 0 > y > -h kf nc

γ n2 c f −γs(y+h) Hx(y) = A [cos( kf ∙ h) − 2 sin(kf ∙ h)] e , y ≤ -h kf nc

Chapter 1 – Introduction

Where H is the magnetic field strength, coefficient A is related to the power carried in the waveguide and coefficients γc, γs and kf are positive real numbers. The magnetic field strength has been used in this derivation (rather than the electric field, which can also be used) as it follows the guide written by Mashanovic et al.12

These equations show that the magnetic field decreases exponentially in the cover and substrate layers, and its dependence is sinusoidal in the film layer. The usual case is that ns > nc, causing the magnetic field to propagate further into the cover layer than the substrate layer. As the mode number m, increases, the penetration into the substrate and cover is deeper, essentially meaning that higher order modes are less confined.

If the thickness of the film or waveguide decreases, there is a certain value for h in which the coefficient γs = 0. When this condition is met, light propagating through the waveguide gets cut-off. When γs becomes imaginary, the evanescent field in the substrate region becomes a radiation field and the waveguide no longer controls the wave, causing leakage into the substrate and cover layers.

1.2.2 Evanescent Field

The behaviour of light interacting at one of these dielectric interfaces can be seen in figure 1.2. When light is propagating through the film layer, it will either refract or reflect. When the angle of incidence is lower than the critical angle, the light undergoes total internal reflection, resulting in the creation of an evanescent wave.

Chapter 1 – Introduction

Figure 1.2: The occurrence of total internal reflection at a refractive index interface leads to the generation of an evanescent wave.13

During total internal reflection, the light partially penetrates into the cover material (n2) before reflecting back into the higher index medium (n1). If the optical ray is considered, it appears as if the reflected ray acquires a parallel shift at the interface before reflecting, as highlighted in figure 1.2. The lateral shifting is known as the Goos-Hänchen shift.14, 15 The “short journey” into the outer media causes the light to experience a phase shift, but the important factor is that there is no net flow of energy across the interface, energetically it acts like a perfect mirror and it is only the evanescent field of the light which penetrates the interface surface. A visualisation of the propagation of the evanescent field into the cover material can be seen in figure 1.3.

Chapter 1 – Introduction

Figure 1.3: During the Goos-Hänchen Shift caused by total internal reflection, the light ray forms an evanescent wave along the interface surface. This decays exponentially with distance from the surface.13

If light is considered as a wave rather than a ray, the light that propagates into the cover material is called the evanescent wave. This wave travels parallel to the interface and has an exponentially decaying amplitude.13 The amplitude of the evanescent wave can be defined by the following equation

푦 (− ) 푑푝 퐴 = 퐴0푒 where y > 0.

In this equation, y is the distance from the interface and dp is the depth of penetration. The depth of penetration can be defined as follows:16

휆 푑푝 = 2 2 2 2휋√푛1푠푖푛 휃 − 푛2

Where λ is the incident wavelength, n1 is the substrate refractive index, n2 is the covering index and θ is the angle of incidence. The label “evanescent” is a reference to the exponential decay of the wave perpendicular to the surface. As such, it is clear that the strongest field generated by the evanescent wave is parallel to the surface and that the

Chapter 1 – Introduction penetration depth of this field can be controlled by choosing the ratio between material indices, the wavelength of light and the angle of incidence.

For the purposes of biosensing, if the covering material of the waveguide is removed and replaced with a liquid (such as blood) containing a mixture molecules, such as proteins, virus samples and bacteria (as shown in figure 1.4), the interaction between these molecules and the evanescent wave can be measured.

Figure 1.4: A demonstration of the evanescent field when applied to biosensing. In order to distinguish between larger molecules such as bacteria, a greater penetration depth is required (b). As such the effect on the field between a virus and bacteria would be harder to decipher for waveguides with lower penetration depths.13

The existence of Goos-Hänchen shifting at a material interface means that light travelling through waveguides experiences a delay in phase compared to light travelling through bulk materials. In order to simplify analysis, it is advantageous to assign an effective refractive index (neff) value to the waveguide. The effective refractive index is the ratio of the propagation constant (β = nk0) in the waveguide to the free space propagation constant. This is visually demonstrated in figure 1.5.

Chapter 1 – Introduction

Figure 1.5: Visualisations of equivalent light behaviour in a vacuum, a high index material n1, a lower index material n2, and a planar waveguide structure.

As the Goos-Hänchen shift elongates the propagation distance within a waveguide, it increases the propagation constant compared to the waveguide core (n1). As a result the effective refractive index typically lies between values of n1 and n2. Waveguides are capable of having several effective refractive indexes if they are capable of containing multiple optical wave modes (higher modes have higher penetration depths). This effect is undesirable as it can lead to noise; hence the majority of waveguides are dimensionally designed in a way which only allows one mode to propagate. In real world experiments, values of neff are difficult to calculate mathematically, but they can be modelled successfully using appropriate simulation approaches.

Chapter 1 – Introduction

1.2.3 Waveguide Designs

The most common basic channel waveguide structures are strip, rib and buried waveguides,12 as shown in figure 1.6. For complex systems such as these there are no direct analytical solutions of the wave equation. As a result numerical solutions for field values must be calculated using techniques such as finite element modelling (FEM), beam propagation method (BPM) and finite difference time domain (FDTD) simulations.

Figure 1.6: The three most common waveguide structures, rib, strip and buried waveguides.

Strip waveguides typically have the largest proportion of external evanescent field, making them ideal for sensing applications due to their design. Rib waveguides can be easier to manufacture, but more of the associated field is contained within the structure. Figure 1.7 gives examples of the field around strip17 and rib18 type waveguides.

Chapter 1 – Introduction

Figure 1.7: (upper) The electric field profile of a strip waveguide17, note how at the interface, the electric field is enhanced. (lower) The electric field profile of a rib waveguide,18 showing how the field strength outside the waveguide is weaker. The transverse electric (TE) mode is shown in each of these images.

Rib and strip waveguides are typically easier to produce due to the nature of the CMOS manufacturing methods.

Due to fabrication restrictions, the waveguide format used for the majority of this project is the rib waveguide. This waveguide type behaves in essentially the same way as a strip waveguide, but the profile of confined field spreads below the surface a bit further, reducing sensitivity.

1.2.4 Waveguide Manufacture

Silicon waveguides were first developed in the mid-1980s, initially with silicon on doped silicon,19, 20 silicon on sapphire,21 silicon on germanium22 and silicon on insulator (SOI).23, 24

Chapter 1 – Introduction

SOI has since become a popular platform in the microelectronics industry and also has the highest promise for optoelectronic integration.12 As a material, silicon is abundant and well characterised. The industrial fabrication methods are well practiced and the science behind many silicon technologies is mature. The technologies used to produce integrated silicon circuits can be easily exploited to produce cost effective silicon waveguide optical devices on an industrial scale. The ability to grow and separate highly controlled, high quality and large scale areas of silicon wafer also means that the manufacturing tolerances are minimised.

As a material to base optical circuits on, SOI has a very high refractive index contrast, consequently allowing for strong confinement of light. Due to this high confinement, the core size for single mode propagation at telecommunications wavelengths (1.3 - 1.5 μm) is a typically a few hundred nanometres. This in turn allows for minimum bend radii of the waveguides to be in the region of a few μm. This unlocks the potential for extremely dense photonic circuits, further reducing the manufacturing cost of producing this technology.12 In addition, silicon waveguides offer such high optical power density (up to 1000 times) when compared to conventional single mode fibres that they enhance nonlinear optical effects, such as four wave mixing, as demonstrated by Fukuda et al.25

In order to suppress the propagation of higher order modes, the cross-sectional dimensions of strip waveguides need to be considered, since even at small dimensions (i.e. less than 1 μm) they can be multimode. Aalto gave an approximate expression for the cross sectional dimensions as W x H < 0.13 μm2 where W is the width and H is the height.26 This expression works well for TE polarisations but for TM, another expression, as deduced by Mashanovich et al is required: W ≤ -1.405H + 0.746.12 Typically the TE mode (parallel to the plane) has a higher E-field component on its side walls and the TM mode (perpendicular to the plane) has a higher E-field component on the top and bottom. For ring resonator purposes, the TE mode is more useful as stronger E-field components at the waveguide sides aids with coupling to the ring resonator. Unfortunately the lithography processes that create the waveguides also tend to produce higher surface roughness for the sidewalls, compared to the top and bottom of the single crystal silicon waveguides. This sidewall roughness leads to higher losses in the TE mode

Chapter 1 – Introduction compared to the TM mode. The roughness is associated with imperfection in the resist pattern during lithography, and can be increased with plasma etching. As a result, careful treatment of the lithography and etching processes is paramount. Sacrificial thermal oxidation of the silicon sidewalls can be used as a technique to smooth the sidewalls.27

Silicon nitride (Si3N4) is another material with great viability for the production of sensing waveguides. Due to the lower refractive index contrast ratio, the penetration depth of the evanescent field is greater in silicon nitride waveguides. This means that Silicon nitride typically has greater sensitivity than SOI. It has been shown that the use of silicon nitride with a buried oxide (BOX) layer fabricated onto silicon wafers produces waveguides with very low losses (0.1dB/cm at 632.8 nm wavelength for TE and TM modes).28 Silicon nitride is also optically transparent at lower wavelengths than Silicon, allowing for a greater range of probe wavelengths and avoiding the 1550 nm wavelength region which suffers from absorption by water, a common sensing medium. A downside to silicon waveguides is that they suffer greater losses from bending compared to SOI waveguides, limiting the minimum radius of waveguide curvature and potential chip feature density as a result.

One of the main fabrication techniques of SOI waveguides is the Smart Cut process29 for transferring high quality ultra-thin single crystal layers of silicon onto a substrate. This process is demonstrated in figure 1.8.

Chapter 1 – Introduction

Figure 1.8: The Smart Cut production method.29 The process results in the formation of a very thin layer of pure silicon single crystal placed on top of an insulating silicon oxide layer, the quintessential silicon on insulator (SOI) setup.

Once a SOI base has been produced, waveguides can be easily etched out of the base substrate using lithography techniques.30

Losses in Waveguides

The main sources of loss in waveguides are scattering, absorption, radiation and curvature related radiation. As mentioned above, the lithography process often leaves remnant sidewall roughness on fabricated waveguides. This factor alone accounts for a large portion of scattering loss experienced by light in a waveguide. Post-etch thermal oxidation can be used to reduce sidewall roughness by up to 38%.31 As a photonic absorber, once the band-gap energy of silicon is exceeded (1.12 eV, Wavelength = 1100 nm),32 photons become highly absorbed by the material, using their energy to excite valence electrons into the conduction band. An easy way to avoid this source of losses is

Chapter 1 – Introduction to use lower energy photons, such as those used in the communications industry at 1550 nm. An advantage of this is that many well developed light sources are commercially available at these wavelengths. As mentioned earlier, if the dimensions of the waveguide become too confined to support the mode travelling through it, energy is radiated into the surrounding cover and substrate media. By ensuring that fabrication dimensions are such that they support a mode travelling through them, but offer enough margin of error away from the cut-off limit, radiation losses caused by this mechanism can be avoided.

An important factor of waveguide losses in optical circuits is the waveguide bend, which is used to redirect the propagation of the optical mode. Bending in waveguides leads to optical loss, this is primarily due to radiation loss from the modal field into the prime cladding as the mode propagates around a bend.33 This is different from the scattering losses experienced in straight waveguides, as already discussed. There is also a modal transition loss caused by modal profile mismatches between straight and curved parts of the waveguide. The size of these losses is dependent on the bend radius and confinement of the waveguide in the bend. As waveguide bends usually take place in the plane parallel to the TE mode, the TE mode has the largest losses as a result. Theory on waveguide bending is extensive, dating back to 1969 with Marcatili.34 Current methods for modelling these bends include the conformal transformation method,35 the method of lines,36 the finite difference method37 and the mode matching method.38

1.2.5 Waveguide Components

There are three main types of optical circuit components which are now described below in detail.

Y-splitting Junctions

One component which will be common in more complex waveguide circuits in this project will be the Y-splitting Junction. This is a junction where one waveguide either splits into two, or two waveguides converge into one. A tapered region is usually used to bridge the area between the one input and two outputs. Y-junctions typically act as splitters or

Chapter 1 – Introduction combiners. When designed symmetrically, the junctions act like 3 dB splitters. In practice, there are other issues, such as fabrication limitations in lithography. Despite this, silica waveguide splitters have been reported with losses as low as 0.2 dB per Y-junction.39 When the Y-splitter is used as a combiner, more subtle behaviour is observed. If the two injected modes are out of phase by an integer value of π, only the antisymmetric phase mode gets excited in the coupling region of the waveguide. As this particular mode is incompatible with the single mode output waveguide, all power gets lost and the light is radiated out from the junction. If the two input modes are in phase, the power is simply combined.33 Y-Splitters can be used to create Mach-Zehnder Interferometers,40 which can then be used to determine the phase difference between light travelling through respective arms of the waveguide cavity. This principle can be exploited for surface and bulk sensing applications, as shown in figure 1.9.

Figure 1.9: A basic schematic of a Mach-Zehnder waveguide interferometer for sensing applications.40 The phase difference experienced by the sensing arm compared to the reference arm can be used to detect changes to the refractive index at the waveguide surface interface.

Slotted Waveguides

In typical silicon waveguides, total internal reflection at the interface between a silicon core and its surrounding cladding confines light within the waveguide. Slot waveguides are an alternative architecture in which a narrow slot of low index material is held between two large strips of high index material.41 This causes significant electric field

Chapter 1 – Introduction discontinuity at the material interfaces, allowing light to be heavily confined and concentrated within the low-index slot in the middle. These slots are typically narrow (of the order of 100 nm in width), the waveguide mode within the slot is almost lossless as demonstrated by Almeida et al in 2004 when they produced a slotted ring resonator with a Q-factor of 20,000.42 A visual demonstration of the field profile of a TE mode travelling through a slot waveguide can be seen in figure 1.10.43 The high confinement and low loss properties lead to an order of magnitude increase in the sensitivity of slot waveguides compared to traditional waveguides. This can be exploited further for biosensing applications where low concentrations of biomaterial may be detectable within the slot region. This is the mechanism that will be used for making biosensors in this project. Sun et al have also shown that the sensitivity of the slot waveguides can be increased even further by using multiple slots.44

Figure 1.10: The electric field profile of a slotted strip waveguide with TE light propagating through it.43 As shown, the electric field profile is substantially higher within the slotted region and externally when compared to a standard strip waveguide (as shown in figure 1.7).

Waveguide Coupling

When there is significant overlap between the fields of two optical modes in two separate waveguides in close proximity, power may be transferred between the two via evanescent coupling. There have been several studies published on the various analytical

Chapter 1 – Introduction methods of optical coupling between two mediums.45 The general conclusions suggest that the coupling strength of an ideal evanescent coupler is reliant on the interaction length between two optical modes and the extent of the overlap/the proximity of the waveguides. For efficient power transfer the two optical modes must be phase matched. There are several ways to achieve phase matching. One of the earliest methods was to use prism coupling, which can be used to couple to microspheres. In these systems, light experiences a Goos-Hanchen shift in the evanescent field, enabling phase matching and more efficient coupling.46, 47 In toroidal cavity couplers, tapered fibres are used to achieve the required phase matching between a fibre and a cavity mode.47-52

The most common approaches used for coupling with waveguides and micro-ring resonators are lateral and vertical coupling.53-55 Both of these techniques have advantages and disadvantages. In lateral coupling, the fabrication process can be completed in one step. The problem with this technique is the limitation on gap separation (caused by fabrication tolerances in the lithography system) and the index contrast range limiting the core/cladding materials. Racetrack geometries can increase the interaction length and keep the separation gap fixed. In vertically coupled systems, the gap separation isn’t adjusted with lithography, but epitaxially. This allows smooth surfaces, reducing loss due to surface roughness. As the adjustment of gap separation is epitaxial, extremely small gap separations can be applied, and control over the separation distances is better too. The disadvantage is that several additional steps of growth are required, raising production costs.55 Diagrams of these geometries can be seen in figure 1.11.56

Chapter 1 – Introduction

Figure 1.11: Evanescent coupling via a microprism, a tapered fibre, lateral and vertical coupling. The waveguides used in this project will be coupled laterally.56

An advantage of waveguides is their miniscule dimensions, typically of the order of 300 nm x 200 nm. Compared to optical fibre cores, which have core diameters of ~ 8 μm in the case of single mode fibres, waveguides are completely dwarfed, making it difficult to couple light to waveguides using direct fibre-waveguide coupling. There is also a high refractive index difference between the two, which would cause further reflection losses on direct coupling. As a result several other coupling methods have been developed.

Tapers have seen a lot of interest as coupling method. In these, the silicon waveguide initially matches the dimensions of the input fibre, and an antireflective coating is used to make sure the losses from reflection are minimal. The silicon waveguide then tapers down until it reaches the dimensions required to support single modes.

While tapers are effective, from a practical point of view they require a lot of careful alignment and offer little flexibility once lined up. Surface grating couplers are another approach to coupling which can be very efficient when several waveguides may need to be accessed in quick succession. In these couplers, an input beam is introduced to a diffraction grating etched into the silicon waveguide at specific heights and spacing. Early research by Ang et al demonstrated coupling efficiencies as high as 70% using this method.57 This principle was taken further by Cary Gunn of Luxtera Inc when they introduced their holographic lens, as seen in figure 1.12.58 The holographic lens is a

Chapter 1 – Introduction structure that is etched, using lithography, onto the surface of the silicon. It is designed to accept light at approximately normal angles of incidence, making it possible to peform analytics by simply illuminating the surface of a waveguide chip. The holographic lenses presented by Luxtera had coupling losses of approximately 1.5 dB in the range of 1530 – 1560 nm, however simulations suggested that coupling losses as low as 0.3 dB could be possible. This rivals the coupling efficiencies of tapers and other methods, making it a perfect approach for the research of this project. A downside to grating technology is that it doesn’t allow all wavelengths to transmit, resulting in Gaussian-shaped cut off in the transmission spectra.59

Figure 1.12: The holographic lens developed by Luxtera Inc is shown in the top right corner. This method of coupling etches directly into the base silicon layer of the waveguide, reducing manufacturing costs and improving photonic circuit integration.58

1.2.6 Ring Resonators

An important part of the ring resonator systems are the rings themselves. When waves such as acoustic or electromagnetic are confined to a resonator cavity with smooth edges

Chapter 1 – Introduction they produce a phenomenon known as a whispering gallery mode. These modes correspond to waves travelling around the cavity under the effect of total internal reflection off the cavity walls. They meet a resonance condition that, after a full roundtrip, they return to the same location with the same phase causing constructive interference and forming standing waves within the cavity. The resonances are heavily dependent on the geometry of the resonator cavities in which they form.60

Whispering Gallery Modes

Whispering Gallery Modes are present in any structures with smooth circular properties, such as spheres, cylindrical fibres, discs and photonic crystals. The work presented in this thesis will be primarily using ring resonators.

Ring resonators have the same functionality as Fabry-Pérot interferometers, creating “comb-like” transmission spectra with Lorentzian shaped peaks or troughs. A ring resonator consists of a waveguide in a closed loop, usually shaped like a ring or racetrack. Unlike Fabry-Pérot interferometers, ring resonators have travelling wave operation. A comparison between ring resonator systems and their standing wave equivalents can be seen in figure 1.13.

Figure 1.13: Ring resonator travelling wave systems and their standing wave equivalents. A single coupling ring resonator follows the same behaviour as a Gires-Tournois interferometer and a double coupling resonator behaves like a Fabry-Pérot interferometer.56

As previously mentioned, light is coupled into the resonator cavity via evanescent field coupling when the input waveguide is fabricated in close proximity to the ring. The ring

Chapter 1 – Introduction behaves like an interferometer and will be resonant when the light which has a total phase change of an integer multiplied by 2π after a full round trip of the cavity. This is the condition for light to be in-phase with the incoming light and for constructive interference to occur. Light that doesn’t meet this resonant condition does not couple with the ring resonator and continues to be transmitted through the linear input waveguide (also known as the input bus). The resonant wavelengths in the rings can be given by the following expression:33

2휋푅푛eff 휆 = 푟 푚

Where R is the radius of the ring, neff is the effective refractive index of the ring and m is an integer.

When ring resonators are coupled to a single waveguide, the transmission response of resonant wavelengths through the bus waveguide strongly depends on the optical losses through the ring resonator. In theory, if the ring waveguide was lossless, the constructive interference pattern inside the ring would destructively interfere with light being transmitted through the bus, completely cancelling out all light transmission at the specific resonant wavelength.

Transmission Spectra

Despite losses in the ring system, reasonably sharp transmission spectra, such as the one shown in figure 1.14 can still be made. As a result, these devices can act as notch filters, giving high extinction in parts of the transmission spectrum. If the light that traverses the ring were to also acquire a phase change, these devices could also be used as phase filters. An output bus (as shown in figure 1.13 in the double coupling system) can be used to separate the resonant wavelengths from the rest of the spectrum transmitted through the bus. The optical power which is actually transmitted is typically significantly lower than that which is output by the light source. This is due to losses when coupling the light to the waveguide (i.e. beam spreading and grating losses).

Chapter 1 – Introduction

50 μm Slotted Ring Resonator Spectrum

1.00E-08

1.00E-09

1.00E-10 AbsolutePower (mW)

1.00E-11 1530 1532 1534 1536 1538 1540 1542 1544 1546 1548 1550 Wavelength (nm)

Figure 1.14: An absolute power vs wavelength spectrum for a 50μm radius slotted ring resonator. Intensity dips are spaced periodically through the spectrum. When using these devices as sensors, shifts in the position of these dips can be monitored. The absolute power values are low due to the indirect grating optical coupling methods employed.

Ring resonators have several key performance parameters, including the free spectral range (FSR), the extinction ratio (ER), the finesse and the Q factor. Finesse is usually defined as the FSR divided by the 3dB bandwidth and the Q factor is defined as the resonant wavelength divided by the 3dB bandwidth, or full width at half height. Historically, the Q factor is quoted more often than the finesse as a measure of the spectral selectivity of the ring resonators.33 The FSR of a ring resonator is similar to that of a Fabry-Pérot interferometer and is given by:

2 휆푟 훥휆 = 2휋푅푛푔

Where ng is the group index of refraction (ng = neff – λ(dneff/dλ)). If it is assumed that the coupling (represented by the coupling co-efficient, κ) between the bus waveguides and

Chapter 1 – Introduction the optical rings (shown in figure 1.13) is weak, the 3dB Bandwidth can be approximated by:

2 2 휅 휆푟 훿휆 ≈ 2 2휋 푅푛푔

When a resonant wavelength is on the ring resonator, light which is coupled to the ring constructively interferes with the input light, as a result, the light in the ring can build up to a significantly higher optical intensity than in the bus waveguide. The field enhancement experienced by the ring resonators at resonant frequency is an important property of ring resonators and can be measured by the finesse or Q factor characteristics. When light passes around the ring, it experiences losses, caused both by transmission loss in the ring and loss caused by coupling to the bus waveguide. If N is the number of roundtrips made before the optical energy falls to 1/e of its original value, then finesse ‘F’ and Q factor ‘Q’ can be given by the following equations:33

퐹 = 2휋푁

푄 = 휔푟푇푁

Where ωr is the resonant angular frequency and T is the time required to make a roundtrip of the ring. These equations indicate that in order to create maximum field enhancement, high finesse and Q factor, the losses must be minimised and the coupling efficiency must be optimised.

In SOI systems, optical confinement is strong due to the large refractive index difference between the Silicon core and the SiO2 cladding. Many SOI systems which are studied are based on compact single mode strip waveguides with core cross-sections of approximately 200 nm x 500 nm. Such small core dimensions mean that very small rings with radii of curvature of the order of a few micrometres can made without significant bend loss. One advantage of producing such small rings is that they can be densely packed onto a single chip, allowing complex analysis functionalities. The small dimensions

Chapter 1 – Introduction also result in extremely high optical power densities within the waveguides which could be used to trigger non-linear optical effects. In addition, as the FSR is inversely proportional to the radius of the rings, smaller rings produce a larger free spectral range, which is important for filtering and sensing purposes.

For sub-micrometre waveguides, one of the most important design parameters is the coupling efficiency between the ring and the input/output waveguides. As the devices operate via evanescent coupling, which exponentially decreases with distance from the source, precision in manufacturing is crucial. As a result, accuracy of a few nanometers is required, and the current technologies which are capable of this are modern deep UV lithography and e-beam lithography, as used in research environments.33

Fano Resonances

Fano resonances will have an impact on the double ring resonators investigated in this project so it is important to introduce them here. In cases where more than one resonator is considered within a system, it becomes possible for Fano resonances to occur. A Fano resonance is an asymmetric resonant scattering phenomenon that appears across physics in many fields.61 They were originally named after Ugo Fano who theoretically explained the scattering line shape of inelastic scattering of electrons from a helium source.62

The line shape is caused by interference between two scattering amplitudes, typically a resonant state and a background state. The energy of the resonant state has to be within the energy range of the background state for the effect to occur. When the background scattering state is close to the resonant state’s energy, the background state’s amplitude varies slowly compared to the resonant state’s amplitude, which changes quickly in both phase and magnitude. This variation leads to an asymmetric profile. Mathematically the transmission profile of these resonances can be explained by the following formula:63 1 (휀 + 푞)2 푇(퐸) = 1 + 푞2 1 + 휀

Chapter 1 – Introduction

Where the reduced energy ε is given by:

퐸 − 퐸푅 휀 = 푤

ER is the resonant energy, w is the peak width and the Fano parameter, q, measures the ratio of resonant state scattering to the direct background scattering amplitude. If the Fano parameter becomes strong (tending towards infinity) the Fano profile reduces to a Lorentzian line shape. Visualisations of the line shapes can be seen in figure 1.15.

q = 0 q = 0.5

1.2 1.2

1 1

0.8 0.8

0.6 0.6

0.4 0.4 Transmission Transmission 0.2 0.2

0 0 -10 -5 0 5 10 -10 -5 0 5 10 Energy Energy

q = 1 q = 4

1.2 1.2

1 1

0.8 0.8

0.6 0.6

0.4 0.4 Transmission Transmission 0.2 0.2

0 0 -10 -5 0 5 10 -10 -5 0 5 10 Energy Energy

Figure 1.15: Fano resonance transmission line shapes for Fano factor q values of 0, 0.5, 1 and 4. The resonant position = 0 and the resonance width = 1. As seen when q = 4, the resonance begins to take on a Lorentzian peak shape.

Chapter 1 – Introduction

Ring Resonator Examples

There have been several research groups working to optimise the manufacturing process and design layouts to get high Q factor ring resonators. In 2003 Vorckel et al reported silicon on insulator micro-ring resonators with a Q factor of 2500 and a free spectral range of 26.5 nm. The structures themselves had a footprint of 60 μm2. The rings had a radius of 3 μm and a separation from the bus of 150 nm, with a cross section of 400 nm x 400 nm. e-beam lithography and reactive ion etching were used to manufacture the devices.64 The biggest cause of loss in this device was side wall scattering. In 2004 Dumon et al demonstrated the use of deep ultraviolet lithography to make single mode optical waveguides, racetrack resonators and ring resonator systems. The waveguides showed a propagation loss of 2.4 dB/cm and the racetrack resonators had Q-factors higher than 3000.65 The waveguides were 500 nm wide and 220 nm tall. The racetrack design allowed more precise control of the coupling efficiency between the ring and bus waveguide. At resonant wavelengths, the attenuation through the bus port was nearly 25 dB. In another study by Tsuchizawa et al, a new technique using a spot size converter and improved microfabrication techniques were used to create optical waveguides with losses as low as 2.8 dB/cm and a coupling loss of 0.5 dB/connection. Using 200 nm x 400 nm waveguides and a 5 μm ring with a 300 nm separation from the bus waveguide, they were able to create channel dropping filters with Q factors of 13,000 and a free spectral range of 17.9 nm.66 On a slightly larger scale, rib waveguides have also been investigated for reducing losses. Kiyat et al were able to report a Q factor of 119,000 for a 350 μm radius racetrack resonator with 1 μm x 1 μm waveguides and a ring to bus separation of 800 nm.67 However, despite the high Q factor, the free spectral range was only ~290 pm, which is difficult to apply within the scope of this project.

Another challenge is creating a polarisation independent ring resonator coupling system; however, Headley et al were able to achieve this using a 1 μm x 1.35 μm rib waveguide- racetrack system. In this case, the coupling length was carefully selected to yield similar efficiencies for both TE and TM modes of light. The coupling length needed to transfer TE is typically different for the two modes; however, the racetrack was designed to couple

Chapter 1 – Introduction with several TE transistions while the TM made one transition. The resonator was 400 μm in radius and had a single bus waveguide. The device had a Q factor of 90,000, but the free spectral range was only 190 pm.68

Silicon ring resonators have also been used to make active devices. An example of this is in 2005 when Xu et al created an electro-optic modulator by creating a change in the free carrier density, which leads to a change in the refractive index of the material. The modulator itself was a p-i-n diode with a 6 μm radius Si ring as the intrinsic region. The area inside the ring was p-doped and the region outside was n-doped. By applying a bias voltage the effective refractive index of the ring was changed, this in turn changed the optical power in the through port. Data transmission was demonstrated with speeds of up to 1.5 Gbps.69

The earliest experimental examples of using slot waveguides for biosensing were reported in 2007 by Barrios et al70 in which they recorded the shift in wavelength of the ring resonator systems when submerged in water, isopropanol and cyclohexane. Figure 1.16 shows the setup used. Further work has also been conducted by Claes et al,71 in which they proved that the surface chemistry for label-free sensing of proteins can be applied within a 100 nm slot and they also demonstrated that a slot can increase the sensitivity of the ring resonator by a factor of 3.5 compared to a traditional strip waveguide.

Chapter 1 – Introduction

Figure 1.16: The slot waveguide setup used by Barrios et al for the initial investigations into biochemical sensing with slot ring resonators. In this setup Si3N4 was used as the waveguide medium as it allows larger radius resonators and a larger slot width.72

Chapter 1 – Introduction

1.3 References

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32. M. A. Green and M. J. Keevers, Progress in Photovoltaics: Research and Applications, 1995, 3, 189-192. 33. A. Liu, N. Izhaky and L. Liao, Silicon Photonics: The State of the Art, 2008, 229-267. 34. E. Marcatili, Bell System Technical Journal, 1969, 48, 2103-2132. 35. M. Heiblum and J. H. Harris, IEEE Journal of Quantum Electronics, 1975, 11, 75-83. 36. J.-S. Gu, P.-A. Besse and H. Melchior, Quantum Electronics, IEEE Journal of, 1991, 27, 531- 537. 37. T. Yamamoto and M. Koshiba, Lightwave Technology, Journal of, 1993, 11, 1579-1583. 38. L. Prkna, M. Hubálek and J. Ctyroky, Photonics Technology Letters, IEEE, 2004, 16, 2057- 2059. 39. Y. P. Li and C. Henry, IEE Proceedings-Optoelectronics, 1996, 143, 263-280. 40. D. Yuan, Y. Dong, Y. Liu and T. Li, Sensors, 2015, 15, 21500-21517. 41. S. Weiss, G. Rong and J. Lawrie, Physica E: Low-dimensional Systems and Nanostructures, 2009, 41, 1071-1075. 42. V. R. Almeida, Q. Xu, C. A. Barrios and M. Lipson, Opt. Lett., 2004, 29, 1209-1211. 43. K. Debnath, A. Z. Khokhar, S. A. Boden, H. Arimoto, S. Z. Oo, H. M. H. Chong, G. T. Reed and S. Saito, Frontiers in Materials, 2016, 3. 44. R. Sun, P. Dong, N.-n. Feng, C.-y. Hong, J. Michel, M. Lipson and L. Kimerling, Optics express, 2007, 15, 17967-17972. 45. K. R. Hiremath, Coupled mode theory based modeling and analysis of circular optical microresonators, Kirankumar R. Hiremath, 2005. 46. M. Gorodetsky and V. Ilchenko, Optics Communications, 1994, 113, 133-143. 47. M. L. Gorodetsky and V. S. Ilchenko, JOSA B, 1999, 16, 147-154. 48. J. Knight, G. Cheung, F. Jacques and T. Birks, Opt. Lett., 1997, 22, 1129-1131. 49. B. E. Little, J.-P. Laine and H. A. Haus, Journal of Lightwave Technology, 1999, 17, 704. 50. M. Cai, O. Painter and K. J. Vahala, Physical review letters, 2000, 85, 74. 51. M. Cai and K. Vahala, Opt. Lett., 2000, 25, 260-262. 52. S. Spillane, T. Kippenberg, O. Painter and K. Vahala, Physical Review Letters, 2003, 91, 043902. 53. A. Melloni, Opt. Lett., 2001, 26, 917-919. 54. M. Chin and S. Ho, Journal of Lightwave Technology, 1998, 16, 1433. 55. R. Grover, T. Ibrahim, T. Ding, Y. Leng, L. Kuo, S. Kanakaraju, K. Amarnath, L. Calhoun and P.-T. Ho, Photonics Technology Letters, IEEE, 2003, 15, 1082-1084. 56. L. Y. Tobing and P. Dumon, in Photonic Microresonator Research and Applications, Springer, 2010, pp. 1-27. 57. T. Ang, G. Reed, A. Vonsovici, A. Evans, P. Routley and M. Josey, IEEE Photonics Technology Letters, 2000, 12, 59-61. 58. C. Gunn, Micro, IEEE, 2006, 26, 58-66. 59. Y. Wang, Yun, H., Lu, Z., Bojko, R., Shi, W., Wang, X., Flueckiger, J., Zhang, F., Caverley, M., Jaeger N.A. and Chrostowski, L., IEEE Photonics Journal, 2015, 7, 1-10. 60. P. Féron, in Annales de la Fondation Louis de Broglie, Fondation Louis de Broglie, 2004, pp. 317-329. 61. Y. S. Joe, A. M. Satanin and C. S. Kim, Physica Scripta, 2006, 74, 259. 62. U. Fano, Physical Review, 1961, 124, 1866. 63. A. Rau, Physica Scripta, 2004, 69, C10. 64. A. Vorckel, M. Monster, P. Haring Bolivar, H. Kurz and W. Henschel, in Lasers and Electro- Optics, 2003. CLEO'03. Conference on, IEEE, 2003, pp. 866-867. 65. P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman and D. Van Thourhout, IEEE Photonics Technology Letters, 2004, 16, 1328-1330.

Chapter 1 – Introduction

66. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J.-i. Takahashi, J.-i. Takahashi, T. Shoji, E. Tamechika, S.-i. Itabashi and H. Morita, Selected Topics in Quantum Electronics, IEEE Journal of, 2005, 11, 232-240. 67. I. Kiyat, A. Aydinli and N. Dagli, Optics express, 2005, 13, 1900-1905. 68. W. R. Headley, G. T. Reed, S. Howe, A. Liu and M. Paniccia, Applied physics letters, 2004, 85, 5523-5525. 69. Q. Xu, B. Schmidt, S. Pradhan and M. Lipson, Nature, 2005, 435, 325-327. 70. C. A. Barrios, K. B. Gylfason, B. Sánchez, A. Griol, H. Sohlström, M. Holgado and R. Casquel, Opt. Lett., 2007, 32, 3080-3082. 71. T. Claes, J. G. Molera, K. De Vos, E. Schachtb, R. Baets and P. Bienstman, Photonics Journal, IEEE, 2009, 1, 197-204. 72. C. A. Barrios, Sensors, 2009, 9, 4751-4765.

Chapter 2 – Literature Review

2.1 Introduction

2.1.1 Context

The research in the project is focussed primarily on silicon or silicon nitride waveguides, fabricated with CMOS techniques. The reason for this specificity is that CMOS manufacturing offers one of the fastest routes towards mass production and ultimately, industrial applications. A lot of interesting work has also been conducted using non-CMOS techniques, and where appropriate, this shall be explored too, giving greater context to the field of novel waveguides.

Another area of specific interest for this project is the application of biosensing and signal modulation using silicon waveguide technologies. There have been significant developments in this field in recent years and there is a lot of material to cover in order to distinguish the difference between my research and that conducted by other groups, as well as giving insights into good research approaches which could be used to further develop the technology covered in this thesis.

2.1.2 Trends in the Field

Within the context of these fields, there are several recurring themes which should be described in more detail, these include:  Techniques used for modelling waveguides.  Novel approaches to waveguide design.  Ring enhanced Mach-Zehnder interferometer (REMZI) type devices.  Doped ring resonators.  Novel Fabrication Techniques.  Silicon photonic biosensing.

Chapter 2 – Literature Review

Modelling is highly influential in the design process for a lot of novel waveguide designs; as such it is introduced first.

2.2 Main Body

2.2.1 Techniques used for Modelling Waveguides

As many research articles rely on the following techniques for modelling waveguides and ring resonators it is important to initially introduce the main techniques used within the field. Introduced in the early 1990s, CAD is now the standard for all industrial manufacturing. Without the development of robust modelling techniques to accurately predict the expected behaviours of these designs, the tools to design complex optical components would not exist. A well-considered review of the recurring techniques was published in 2000 by Scarmozzino et al.1 Here the key techniques which are commonly used are described.

Optical wave-guided propagation modelling can fall under two categorisations, time- harmonic (monochromatic CW operation) and time dependent (pulsed operation). There are strengths and weaknesses to each of these approaches.

The first question to ask when modelling waveguides is which optical modes can propagate through a uniform cross-section of waveguide. As mentioned in chapter 1, the confinement of optical modes is of great importance to waveguide behaviour.

The Finite Difference Method

The finite difference method (FDM) is a numerical method of solving differential equations by approximating them with difference equations. In these, finite differences are used to approximate the derivatives. This is the dominant approach for solving a range of partial differential equations.2, 3 In the case of optics, derived from Maxwell’s equations, the wave equation can be expressed as follows:

Chapter 2 – Literature Review

2 2 ∇ 푬 + 푘0 휀푟푬 = 0

2 2 2 Where the angular frequency ω is included within 푘0 and 푘0 = 휔 휀0휇0. 휀푟(푥, 푦) is the function describing the dielectric constant over the cross section of the waveguide. For non-magnetic media, 휇푟 = 1 meaning it can be disregarded for calculations involving non-magnetic materials. Different waveguide shapes have different dielectric constants over different regions. 휀푟(푥, 푦) is piecewise in form, and the solutions to the equation in each region must also satisfy regional boundary conditions around the waveguide.

The Finite Element Method

The finite element method yields approximate solutions by subdividing a large problem into smaller, simpler parts called finite elements. The equations that model the finite elements are then merged to form a larger, complicated system that can model the entire problem. This method uses variational formulation for the solution of waveguide problems. In dielectric waveguides, the standard approach is to use all three components of the H or E vector. The advantage of this approach on the H field is that no boundary conditions are required except at the exterior boundary.1 Maxwell’s equations give the following formula.

−1 2 ∇ × 휀푟 (∇ × 푯) = 푘0푯

Taking the inner product of this relation 푯∗ leads to a functional equation.

∗ −1 2 ∗ 퐹 = ∫ [(∇ × 푯) ∙ 휀푟 (∇ × 푯) − 푘0푯 ∙ 푯 ]푑푥푑푦 푆

휕퐹 If trial function coefficients are denoted 푎푖 then setting the requirement = 0 provides 휕푎푖 equations for the matrix eigenvalue problem. Trial functions are required to span the whole domain and satisfy exterior boundary conditions. For arbitrary shapes this becomes difficult. To overcome this, the finite element method breaks the domain down

Chapter 2 – Literature Review into a set of contiguous triangles, with trial functions defined within each triangle with unknown coefficients. The integrations of the functional are conducted on each triangle before the matrix equation is produced.

For photonic devices which involve propagation through non-uniform structures, numerical techniques such as the beam propagation method (BPM) and the finite difference time domain method (FDTD) can be used. FDTD is especially useful as it is applicable to problems involving both CW and pulsed light sources.

The Beam Propagation Method

The Beam Propagation Method is widely used to approximate the exact wave equation for monochromatic waves and solving these equations numerically.4, 5 The beam propagation is confined to a narrow range of angles for the propagation of light. The field is assumed to be scalar, which enables the wave equation to be written in the form of the Helmholtz equation. Finite differences are used to replace the continuous partial differential Maxwell equations. The main concept in this method is that all optical waves are subject to diffraction. The inhomogeneity of the propagating medium causes phase shift to accumulate as the wave propagates through its medium. The phase shift experienced is related to the refractive index of the waveguide material.6

The spatial mode is modelled using plane waves all travelling in slightly different directions. After the plane waves have propagated through the waveguide medium, the plane waves are superimposed to produce the spatial mode. This method of modelling operates entirely in the frequency domain, and assumes the modelled waveguide has an optical axis with most of the light travelling along it. The beam propagating method enables the use of large step sizes which can be several times the optical wavelength. This leads to fast simulation times. The limiting factor is the fixed directionality of the model.

Chapter 2 – Literature Review

The Finite Difference Time Domain Method

The Finite Difference Time Domain (FDTD) method is widely used in modelling integrated optics, especially in systems where the beam propagation solutions can’t cope with complicated geometry. The main downside to this technique is that the three dimensional version demands large storage and computation times. There are several books and papers that cover this model in detail,3, 7, 8 but here, a quick overview shall be given.

In this method, the Maxwell equations are converted into finite difference equations and a Taylor series expansion using central differences is used to solve the derivatives. The Yee algorithm is used to derive solutions in time and space. Once an initial E or B field approximation is obtained, the information is processed to produce a solution to the H field. The H field solution is then be used to form another solution for the E-field. This approach allows non-paraxial propagation in all directions.

Transfer Matrix Modelling

Another popular modelling method is the transfer matrix method, which can be used to model the behaviour of light passing through a series of optical components such as waveguides and ring resonators. This technique is mainly used for modelling in this thesis and is covered in more detail in chapter 5.

2.2.2 Novel Approaches to Waveguide Design

Having now covered the typical techniques used for modelling waveguide designs, their application and novel waveguide designs will be discussed. Basic waveguide designs such as rib, strip, buried and slotted waveguides have already been covered in chapter 1, along with an introduction to the basic components which can be made with them, including ring resonators, Y-splitters and Mach-Zehnder interferometers.

Chapter 2 – Literature Review

In this section, an assessment will be made of novel techniques which have been recently reported as alternative ways to improve signal propagation, increase sensitivity and improve potential for signal modulation.

Sub Wavelength Grating (SWG) Waveguides

An exciting new area of dielectric optical waveguides is that of Sub Wavelength Grating (SWG) waveguides. It is well known that diffraction effects are suppressed for waves travelling through materials designed at the sub-wavelength scale.9 This quality has been exploited for many years in free space optics,10 but the use of subwavelength periodic structures in dielectric optical waveguides is relatively unexplored.11, 12

In recent years, various research groups have been developing these SWG waveguides, through FDTD modelling and manufacture.13-15 Using SWG waveguides, Cheben et al13 have been able to directly control the mode confinement by changing the refractive index of a waveguide core between 1.6 – 3.5 using lithographic patterning. Using this technique, they were also able to make a microphotonic fiber-chip coupler with losses down to -0.9 dB with minimal wavelength dependence. An image of the waveguide can be seen in figure 2.1.

SWG waveguides have also been used to produce ring resonators for sensing applications as demonstrated by Flueckiger et al.16 This is shown in figure 2.2. They were able to engineer the effective refractive index and mode profile of a SOI waveguide and report its performance as a biosensor. The ring had a Q-factor of 7000 and bulk sensitivity of 490 nm/RIU with a limit of detection of 2 x 10-6 RIU.

Chapter 2 – Literature Review

Figure 2.1: The SWG waveguide developed by Cheben et al.13 The graph shows dispersion diagrams for the SWG and an equivalent strip waveguide with an engineered core refractive index of 2.65. The waveguide is silicon on insulator material.

Figure 2.2: An SEM image of the SWG ring resonator developed by Flueckiger et al. The ring resonator was fabricated by e-beam lithography and the waveguide dimensions are a width of 500 nm, a grating period of 250 nm, a waveguide thickness of 220 nm and a duty cycle of 0.7.

The additional free space surrounding SWG waveguides means that for biosensing, it should be possible to interact with much more of the E-field than with standard waveguides, making this an exciting area for development in ring resonator design.

Chapter 2 – Literature Review

Photonic Crystals

Another area of academic interest has been the use of 2D photonic crystal waveguides.17- 20 Photonic crystals are made of periodic dielectric microstructures that affect the flow of electromagnetic wave propagation. These crystals contain regularly repeating regions of high and low contrasting dielectric constant. These can be etched into the surface of a SOI (or alternative material) chip using e-beam and photolithography. They can also be deposited through photomasks. Using patterning of the photonic crystals, it is possible to permit the transmission of specific optical modes, while prohibiting others. This makes photonic crystals a great medium for constructing low loss optical waveguides. As a rule of thumb, the periodicity of the crystal structure should be around half the wavelength of the EM waves being diffracted. Figure 2.3 shows an example of a 2D crystal resonator fabricated by Mehta et al in 2014.19

Figure 2.3: (a) An optical micrograph of a single cavity device with grating couplers and tapers. (b) An SEM image of the photonic crystal device with FDTD calculated mode profile overlaid. (c) Transmission spectra through cavities with resonant wavelength at 1512 nm and (d) The equivalent with resonant wavelength of 1549 nm. (c) and (d) have black red and blue curves to match data with 8, 12 and 18 mirrored holes. (e) Peak transmission versus measured Q-factor. The maximum Q-factor for the 1512 nm peak is shown in black and measured at 58,000 and the 1549 peak is shown in red with Q-factor of 51,000.19

Chapter 2 – Literature Review

In this device, the photonic crystals are mirrored along a waveguide and are designed in such a way that they only allow a certain wavelength to pass through, with more holes leading to more selectivity and higher Q-factors. Allowing material to pass over these waves would shift the position of the resonances, enabling biosensing also and optical switching.

Multiple Ring Resonator Filters

The use of multiple ring resonators in series is closely related to the work studied in this thesis. They are often used as optical filters and add/drop multiplexers.21-30 In 2006, Popovic et al demonstrated a multi-stage design for microphotonic add-drop filters that provided reduced drop port losses and relaxed tolerances for achieving high in-band extinction.23 This system is shown in figure 2.4. This demonstrated the first micro-ring resonator filter with a rectangular notch stopband in the throughput (compared to the usual Lorentzian shape of a single ring). Extinction ratios of 50 dB were also achieved. Extinction ratios this low have applications in microphotonic notch circuits for spectroscopy, wavelength conversion and quantum cryptography. It should be noted that high precision manufacturing of the order of less than 8 nm precision is required for these configurations to be reliable.31, 32

Chapter 2 – Literature Review

Figure 2.4: a) An SEM image of the fabricated 3 stage filter. b) Spectral response of one stage filter. c) Spectral response of two stage filter. d) Spectral response of three stage filter.23

Theoretical analysis of coupled ring resonators has also revealed that coherent effects in coupled ring resonators are also similar to those displayed in atoms, especially in the case

Chapter 2 – Literature Review of electromagnetically induced transparencies. In a different multi-ring analysis experiment conducted by Xu et al in 2006,31 using the SOI ring resonator geometry shown in figure 2.5, it was revealed that coupled ring resonators are able to form coupled resonator induced transparency (CRIT) features, as shown in figure 2.6.

Figure 2.5: A microscope image of the ring resonator system used by Xu et al.31 As can be seen, two ring resonators lie in series along the input waveguide. The transmission (T) and drop port reflected signal (R) can be analysed accordingly. Putting two ring resonators together enables the superimposition of two ‘reflected’ outputs in the upper drop port. The separation distance S was controlled in order to vary the relative phase of light interacting in each ring resonator.

Chapter 2 – Literature Review

Figure 2.6: Experimental transmission spectra acquired by Xu et al31 for separation distances of a) 15.69 μm, b) 15.71 μm, c) 15.73 μm, d) 15.75 μm and e) 15.77 μm. Dashed red lines represent theoretical fits.

This work demonstrates experimentally the existence of a ‘dark’ transparency state, similar to those found in electromagnetic induced transparencies. Being able to produce these transparencies is of great use for bandwidth filtering, switching and non-linear optics applications. If tuned, systems like this could be used for on-chip optical interconnects and optical processing.

2.2.3 Ring Enhanced Mach-Zehnder Interferometer (REMZI) Type Devices

Typically, ring resonators produce symmetric Lorentzian peak resonance shapes, but the ability to produce sharper asymmetric Fano-resonance peak shapes would mean that the phase change required for optical switching could be dramatically reduced.33 Several studies have now shown that ring enhanced Mach-Zehnder interferometer (REMZI) devices are capable of producing Fano resonance lines in their transmission spectra.28, 34-

Chapter 2 – Literature Review

36 In a 2009 paper by Wang et al,28 a Mach-Zehnder Interferometer with a dual-bus- coupled cross-ring resonator is proposed as a two beam interferometer, capable of generating Fano-resonances in the transmission spectra. The setup and some results are shown in figure 2.7. In this setup, the ring resonator couples to both arms of the Mach- Zehnder Interferometer. When phase shift is introduced to the ring waveguide, it becomes possible to use the setup as an ON/OFF switch. Models suggest that complete extinction is possible if the phase difference in the MZI arms is adjusted.

Figure 2.7: Transmission spectra when a) the refractive index change equals zero and b) when the RI change equals 0.052. (1) and (2) show the corresponding field distributions at a wavelength 1591 nm. The transfer matrix method and FDTD modelling were used to produce these figures. The area highlighted PS represents a phase shifter, used to modify the phase of light travelling through the ring.28

In a separate 2011 report by Darmawan et al,27 an experimental demonstration of the formation of the CRIT phenomenon was reported using a combined ring-bus-ring (RBR) geometry (a central bus waveguide with ring resonators on either side) mixed with a Mach-Zehnder Interferometer (RBRMZI) as depicted in figure 2.8. In this setup, the transparency was achieved by increasing the light intercavity interaction by tuning the RBR phase response, ensuring balanced MZI operation throughout. They were able to report a CRIT response with a Q-factor of ~18,000.

Chapter 2 – Literature Review

Figure 2.8: a) The RBRMZI system proposed by Darmawan et al and b) the fabricated device constructed on a SOI platform.27

Interestingly, similar CRIT-type results have been also been reported in plasmonic systems with equivalent designs.37

2.2.4 Doped Ring Resonators

Doped Modulators

An important aspect of ring resonator development is the use of doping to enable p-n junction signal modulation. Several research groups have reported developments in this area in recent years.38-43 The usual approach is to use a p-doped region inside the ring resonator cavity and an n-doped region outside. Using a changing voltage across the regions, signal can be modulated within the ring resonators. A typical doped ring resonator modulator can be seen in figure 2.9, as reported in 2009 by Preston et al.40 This particular modulator was able to reach 2.5 Gbps and 10 dB signal modulation using polysilicon as the waveguide material (rather than the single crystalline wafers typically used).

Chapter 2 – Literature Review

Figure 2.9: a) The doping regions of the modulator, b) a tilted view SEM image of the contacts required for modulation and c) a cross section of the doped area.40

An important issue with optical ring resonators is that thermal changes in the external environment can make them unstable. In 2013, Padmaraju et al reported a novel technique to overcome this difficulty.44 In this study, a defect enhanced silicon photodiode and heater are used to thermally stabilise the ring resonator modulator. They were able to achieve error free modulation of speeds up to 5 Gbps while subjected to 3 K background temperature fluctuations (these would normally render modulators inoperable). A diagram of the setup used can be seen in figure 2.10.

Chapter 2 – Literature Review

Figure 2.10: The thermally stable ring resonator modulator developed by Padmaraju et al.44 (a) shows a schematic of the integrated device along with an SEM image, (b) shows the silicon photodiode layout and (c) shows the depletion mode style microring modulator.

Silicon ring resonator modulators are capable of modulating signal in the gigahertz spectrum, offering possibilities for on-chip integration with other gigahertz technologies, such as graphene gigahertz field effect transistors45 and electro-optic ring oscillators.46

On-Chip Laser Cavities

Tuneable lasers that can be constructed on the microchip scale are important for both communication and sensing applications.21 They are light weight, small in size and low cost to manufacture compared to mechanically tuned lasers. As such, their integration into microchip technologies is integral to bringing the lab-on-a-chip concept into realisation in an affordable manner. Many of these laser types have already been realised, utilising ring resonators inside the laser cavity.47-52 The use of ring resonators allows wide-tuneability by exploiting the Vernier effect and also improves laser linewidth as the cavity length is effectively increased at ring resonance. In 2017, Komlkenovic et al published a thorough review of the current state of on-chip semiconductor laser cavities21 which provides a great overview of the current state of the art.

Chapter 2 – Literature Review

2.2.5 Novel Fabrication Techniques

While traditional CMOS fabrication techniques (as mentioned in chapter 1) offer high quality single crystal layers of silicon, it is worth mentioning the alternative waveguide manufacturing methods which have been explored by other research groups as they provide an insight into ways in which the ring resonator technologies mentioned so far could be adapted in the future.

In 2011 Luo et al53 reported a novel technique for producing high quality etchless silicon photonic ring resonators. In this process (shown in figure 2.11) a 500 nm layer of silicon is thermally oxidised, leaving a 140 nm thick layer of silicon and 785 nm layer of thermally grown oxide. A resist is then used for patterning, and the thermally grown oxide is etched away, leaving a 50 nm gap. Selective wet thermal oxidisation of the silicon is then conducted, leaving behind a smooth structural profile of the oxidised silicon waveguides. A further layer of 300 nm HTO is used to coat the waveguides and 1.8 μm PECVD silicon dioxide. In this process, no actual etching of the silicon (used as a waveguide) is conducted. As a result, one of the main sources of loss (surface roughness) is severely reduced. Using this method, a 50 μm radius ring resonator was produced with a Q-factor of 510,000 and ring loss of 0.8 dB/cm. This approach was then adapted further, producing an equivalent ring resonator with a Q-factor of 760,000.54

Chapter 2 – Literature Review

Figure 2.11: The etchless silicon waveguide fabrication process. (a) Thermal oxidation, (b) Patterning of ma-N 2405 resist, (c) etching of thermally grown oxide, (d) wet thermal oxidation of the silicon, (e) The structural waveguide profile and (f) HTO and PECVD silicon dioxide deposition.53

The idea of etchless waveguides has also been explored by other groups, with ring resonator Q-factors into the millions.55, 56 In the method adopted by Nezhad et al56, a layer of hydrogen silsequioxane (HSQ) was used to mask the silicon base layer. The silicon around the mask was then completely thermally oxidised leaving behind a silicon waveguide core. In the process, the HSQ becomes glass-like in consistency. SEM images of the waveguide profiles can be seen in figure 2.12. Using this technique, a ring resonator with a radius of 150 μm was able to produce Q-factors of 1,570,000.

Chapter 2 – Literature Review

Figure 2.12: SEM images of the HSQ masked etchless waveguides in the form of (a) a rib waveguide and (b) a buried channel waveguide.56

Cheng et al have taken a different approach to waveguide production, building theirs on a pedestal.57 In this approach, a basic strip waveguide is carefully etched using hydrofluoric acid, slowly changing the strip waveguide into a pedestal waveguide. The process was proven to be highly reproducible. A diagram and image of the final waveguide can be seen in figure 2.13. The pedestal waveguide demonstrated an extinction ratio of more than 20 dB at 1550 nm, demonstrating its potential was an on-chip polariser. From a biosensing point of view, waveguides on pedestals will also have a greater surface area exposure, potentially making them of greater use in ring resonator surface functionalised biosensing.

Figure 2.13: (a) a Schematic of pedestal supported waveguides and (b) an SEM image of a typical pedestal waveguide sample.

Chapter 2 – Literature Review

2.2.6 Silicon Photonic Biosensing

With regards to lab-on-a-chip biosensors, Ciminelli et al have published a very comprehensive review of the optical resonant sensor field.58 In addition to optical biosensors, electrical and mechanical biosensors are also prevalent in the industry. The advantage of optical systems is that they don’t typically modify or deconstruct the molecules measured, they are highly sensitive, highly accurate (having typically high signal to noise ratios) and have immunity to electromagnetic interference. In closed waveguide systems, free-space optics is avoided, reducing the chance of signal corruption due to phase aberration and light scattering. Optical devices also have very fast response times, offering real-time measurement capabilities.

Surface Functionalisation

Biosensors should have high selectivity. In order to ensure this, the sensor should recognise specific biomolecules in a way that produces a signal which is distinguishable from background signal. In evanescent field sensing, it is necessary to ensure that the target molecules are properly immobilised on the surface of the sensing area. When functionalising a surface, the required biomolecule coupling agent interaction is dependent on the application. For diabetes, the targeting of glucose would be important as an example. The most common bioreceptors are antibody/antigen pairs, enzymes, nucleic acids and cellular structures.

One method of surface functionalisation can be realised through the physical surface adsorption by direct deposition of a target molecule.59 In this approach, the hydrophobic and electrostatic interactions between the target molecule and surface are exploited. This technique is simple and rapid to implement, but can have problems with receptors desorbing under the presence of turbulent flow, low pH solutions and solvents. This technique also orients layers randomly leading to lower repeatability, making it less reliable for sensing applications.

Chapter 2 – Literature Review

An alternative approach is to covalently bond molecular chemical groups to the sensing interface.60 In this technique, a range of linkers can be used to attach a receptor to the surface. This adds flexibility to the approach, but it is necessary to make sure that the process of attaching the molecules doesn’t affect the sensor’s functionality as a receptor. When binding proteins with this technique thiol, amino and carboxylic groups are typically used. When binding nucleic acids, DNA is typically preferred.

Non-covalent interactions are also commonly used with deposited active layers. The biotin - avidin/streptavidin combination is one of the most popular affinity pairs in the field. This is mainly due to its bonding strength and specific interaction.60 This process is characterised by a binding between a protein (biotin) with a vitamin (avidin) or the bacterial protein equivalent (streptavidin). Streptavidin is more commonly used as it is typically easier to obtain commercially in many engineered forms. One of the main strengths of this binding process is that the bonding forms quickly and is highly stable over a wide range of temperatures and pH values.

Many non-ring resonator surface functionalised studies also deal with the bioconjugation of gold surfaces and nanostructures, based on the specific properties of gold-sulphur interactions.61-64 In addition to these surfaces, polymers65 and dendrimers66 have been addressed as functionalised surfaces too.

Before a surface can be functionalised, it is necessary to chemically activate it. In the case of silicon, silicon oxide and silicon nitride, which are the three most commonly used materials in optical waveguide biosensors, silane chemistry is often used. Silane coupling agents are able to form durable bonds between organic and inorganic materials. These coupling agents are typically suited to activating inorganic surfaces with hydroxyl –OH groups which convert into stable oxane bonds when reacting with silane. Many silanes are thermally stable up to 350 °C and are very effective on inorganic materials,67 making them the natural choice for waveguide functionalisation. Despite the versatility of silane, surfaces functionalised with this technique can have limited homogeneity.68

Chapter 2 – Literature Review

Binding Mechanisms

Each specific target biomolecule needs to be considered in terms of the binding mechanism used for adsorbing it.

The antibody-antigen biosensing system is one of the most established, and typically works exceptionally well. Antibodies are proteins that may consist of hundreds of amino acid subunits. The typical antigen targets typically exceed 5000 Da (Atomic Mass Unit) in order to prompt an immunogenic response. In antibody-antigen systems, the antibodies act as receptor sites towards larger protein target molecules. The binding mechanism means that only a specific sequence of amino acid subunits can connect with the antibody, making this a lock and key fit. If it’s the wrong sequence, it won’t connect.69

Enzymes are typically a specific type of protein, comprised of amino acids. They can either be made up of pure amino acids, or in some cases they can include co-factors (such as transition metal ions) or co-enzymes made up of complex organo-metallic molecules. Enzymes are usually used in biosensing because of their specific binding capabilities and catalytic activity.69

Nucleic acids are a popular choice for biorecognition and have been a point of interest for biochip technologies that use nucleic acids as bioreceptors for detecting molecules other than complementary DNA strands. These have flexibility in defining a specific nucleic acid sequence and their lengths can allow for the generation of large libraries of DNA sequences, this in turn increases the chance of finding a suitable bioreceptor for specific targets of interest.69

Ring Resonator Biosensors

Conventionally, ring resonator systems have been used as optical switches and modulators as mentioned above, but in 2001, two theoretical papers proposed that they could also have applications as labelled70 and label-free biosensors.71 The Strong electric field enhancement within the ring (resulting from the high Q-factors and low mode

Chapter 2 – Literature Review volume within the resonator) make these systems a great candidate for the detection of biomolecules in low analyte concentrations.

In ring resonator systems, a shift in the position of resonance peaks, changes in peak intensity and Q-factor can all be used to quantify the biorecognition of target biomolecules. One consideration, and potential disadvantage of ring resonator biosensors is their susceptibility to changes in the ambient temperature of the system. In high Q- factor systems, even miniscule changes in temperature could lead to a shift in the position of resonance peaks due to the silicon waveguides refractive index changing with temperature.72

There have been a few prominent early cases where silicon ring and disk resonators have been applied as sensors. In a study by Armani and Vahala,73 distinguished detection of

D2O and H2O on a parts-per-million scale was reported. In this case, monitoring the change in Q-factor led to the discovery. In this case H2O was found to preferentially adsorb onto the detector, leading to a noticeable difference in Q-factor when compared to a D2O sample. The same group were also able to demonstrate single molecule detection of interleukin-2 using an optical microcavity with a Q-factor greater than 108 with a functionalised silica surface.74 Wang et al have also demonstrated the use of SOI and silica based ring resonators for monitoring cell growth and the detection of toxic chemicals in water.75 The detection of DNA, bacteria and proteins have all been demonstrated too.76-78 Washburn et al have also detected shifts in the resonance wavelength caused by cancer biomarker in undiluted serum.79

The use of slot waveguides as biosensors is a more recent science, but as the evanescent electric field contained within the slot is typically higher than the field outside a standard silicon waveguide, there is great potential for their use as biosensors. In one report by

Barrios et al, Bovine serum albumin (BSA) and anti BSA binding events on a Si3N4 slot waveguide ring resonator systems were monitored.80 These biosensors were found to exhibit sensitivities of 1.8 and 3.2 nm/(ng/mm2) respectively. It is expected that with slotted waveguide systems with slot widths below 100 nm, there will be many size-

Chapter 2 – Literature Review dependent infiltration and immobilization challenges that will need to be addressed and overcome.81

To date, many biosensors have been reported which incorporate the use of streptavidin to sense biotinylated molecules. In a seminal paper by Gunn et al82, a variation on this functionalisation technique was reported, using aminopropyl-trimethoxysilane (APTMS), PEG3-biotin and streptavidin. The sensors they used had a bulk refractive index sensitivity of 7.6 x10-7 and were able to observe binding at concentrations as low as 60 fM using biotin to capture immobilized streptavidin. They were also able to demonstrate multiplexing in complex media using two DNA oligonucleotide probes, the time to acquire results and repeatability were concluded to be adequate for clinical applications.

The same research group had also previously reported ‘Quantitative, Label-Free Detection of Five Protein Biomarkers Using Multiplexed Arrays of Silicon Photonic Microring Resonators’.83 In this report they were able to detect the concentrations of prostate specific antigen (PSA), r-fetoprotein (AFP), carcinoembryonic antigen (CEA), tumor necrosis factor-r (TNF-r), and interleukin-8 (IL-8) simultaneously in three unknown protein cocktail solutions. In the process they demonstrated that multiple immunoassays can be performed concurrently on a single microresonator platform without any accompanying loss of sensitivity or measurement precision.

In a paper published in 2014 by O’Sullivan et al84 a silicon-on-insulator (SOI) chip was reported which featured an array of 64 optical ring resonators used as refractive index sensors for real time and label-free DNA detection. They used a slightly modified design to the type of ring resonator shown in figure 2.14. In this experiment, the chip surface was azido-silanised, which allowed hexynyl-terminated DNA capture probes to link to its surface. Using this method, short 25-mer single strands of DNA fragments were detected along with 144-bp double stranded DNA. This experiment achieved a detection limit of 7.8x10−13 M (6x105 copies in 50 µL). An automatic liquid handler injection instrument connected to an integrated resealable chip interface was used and enabled the use of multiple microfluidic injection protocols. Air plugs between different solutions were used

Chapter 2 – Literature Review to prevent intermixing and a proportional-integral-derivative temperature controller reduced temperature based drifts.

Figure 2.14: A schematic representation of the waveguide used in O’Sullivan et al’s study.84 The waveguides are designed in such a way that the output grating couplers are on the opposite side to the input grating coupler. This design is advantageous as it reduces the effect of optical noise from the input signal.

A recent paper by Arce et al85 has proposed a novel approach to ring resonator biosensing through the use of reaction tubes, as shown in figure 2.15. The drive behind this research is based on the fact the ring resonator sensors require a fluidic component that allows the continuous delivery of a sample to the sensing surface. These types of microfluidic systems are typically far removed from the daily practices of hospital laboratories, which still use devices such as 96-well microtiter plates or reaction tubes. To improve the compatibility of ring resonator sensors, a combination of a simple lab-compatible reaction tube is used in conjunction with a special microfluidic perforation system embedded into the chip, where flow passes through the chip, rather than over the surface, as traditional designs use. Their results demonstrate that label-free nanophotonic ring resonators can also be user friendly while conserving the high performance of traditional surface flow microfluidic designs at a much lower cost.

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Figure 2.15: The reaction tube design as reported by Arce et al.85 In this design, a reaction tube with its end removed is placed over a photonic chip, using vacuum and pump technology beneath the chip, fluid can be passed through the chip rather than over it. The design and layout of perforations on the surface ensures that vortices within the fluid allow sufficient liquid flow over the ring resonator sensors for biosensing applications.

In a paper by Campanella et al86 an optical biosensor based on two vertically stacked silicon on insulator microring resonators is proposed. In this system, the ring resonators interact with a microfluidic ring channel as shown in figure 2.16. The device acts as a resonant coupler and is incredibly sensitive to variation in the coupling coefficient between the two vertically stacked ring resonators. In this design a microfluidic channel is built into the coupling region between two vertically stacked ring resonators, the inner walls of the microfluidic channel are functionalised using streptavidin-biotin system. This would add a biological thickness of about 3 nm. Through the use of finite-difference time- domain and 3D full-vectorial finite element method modelling, they are able to predict a sensitivity of the spectral response to the streptavidin adlayer variation of about 20% nm−1 for TE polarization and 34% nm−1 for TM polarization. This represents an important achievement in obtaining selective SOI bio-sensors with ultra-high resolution.

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Figure 2.16: From the report by Campenella et al,86 (a) 3D view of the stacked sensor architecture including an optical cavity made by two vertically-stacked micro-ring resonators (excited by the underlying bus waveguide) interacting with a microfluidic ring channel (excited by the micropump).

Alternative Optical Biosensing

In alternative techniques, such as the capillary-based optofluidic ring resonator reported by Li and Fan87, a similar process is used for biotin detection. The optofluidic ring resonator has its inner surface silanized using aminopropyltriethoxysilane in water and activated using bis(sulfosuccinimidyl) suberate. Following this, streptavidin is flowed across the surface for a substantial time then cleaned. The optofluidic ring resonator is

Chapter 2 – Literature Review then purged filled with phosphate buffer saline (PBS) and becomes ready for biotin detection. In this small molecule detection test, 10 nM of biotin solution was detected with surface mass density of 1.6 pg/mm2. The measurements also showed a distinct difference in detection patterns for higher concentrations of biotin, suggesting that quantitative analysis is also possible using this technique.

In a more recent 2014 paper, He et al reported a ‘High-sensitivity optical biosensor based on cascaded Mach–Zehnder interferometer and ring resonator using Vernier effect’.88 An APTES/glutaraldehyde procedure was used because it offers an effective covalent attachment of streptavidin to the SiO2 surface. The application of streptavidin was followed by a bovine serum albumin (BSA) to block unoccupied sites, and PBS was used to remove redundant BSA molecules. Finally the functionalized sensor was immersed in 0.1 mg/ml of biotinylated goat IgG for the deposition of receptor molecules, followed by a PBS rinse. Different concentrations of antigoat IgG solutions were then analysed, separated by PBS buffers. The design of the waveguide circuit used can be seen in figure 2.17. The measured results show that 1 ng/ml IgG resulted in 0.035 nm and 0.5 nm wavelength shifts for their MZI sensor and their MZI-ring sensor, respectively. This high performance sensor design is promising for medical diagnostic applications.

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Figure 2.17: Optical microscope image of the cascaded Mach Zehnder Interferometer (MZI) and ring resonator sensor used by He et al88 (a), the SEM images of the sensing waveguide (b), the directional coupler for ring-waveguide coupling (c), the directional coupler-based unequal-power splitter of the MZI (d), and the Y-junction power combiner of the MZI (e).

Competing Biochemical Sensor Technologies

In electrical biochemical sensors, the electrical properties of the sensor are changed by the proximity or presence of analyte. One of the main advantages of this type of sensor is that the electric signal generated can be directly interpreted and processed (unlike with optical sensors). The main type of sensor within this category is the field effect transistor

Chapter 2 – Literature Review

(FET) biosensor.89 In these sensors, analyte absorbed by the semiconductor between the source and gate electrodes causes the electric field at the gate to change and as a result, the carrier density in the channel also changes. The current flowing through the transistor is used to directly output the sensing signal. Electro biochemical sensors are typically capable of sensing on the nM scale for most biomolecules, with performance typically limited by the penetration depth of the electric field within the channel. Improvements have been made with the use of nanostructures such as nanowires90, 91 and carbon nanotubes92-94 placed between the drain and source electrode. The use of nanostructure increases the surface area to volume ratio, allowing the electric field to analyse a greater portion on the sensing channel. Using this technique single molecule detection has been demonstrated.95

Mechanical biosensors include devices such as microcantilevers.96, 97 For cantilever devices, a binding event on the cantilever surface can cause a static deflection which can be measured to determine the analyte concentration.98 The oscillatory frequency depends on the levers size weight and structural properties. The addition of material to the cantilever changes its oscillatory deflection; this can be measured by shining a laser onto the back of the lever, as is done with atomic force microscopy (AFM) techniques, any deflections cause a change to the reflected signal. Changes in stress (caused by additional weight) can also lead to piezoelectric current signal differences, offering an alternative sensing mechanism. Cantilever sensors are already commercially available and typically demonstrate a limit of detection of approximately 1 pM.98, 99

The magnetoresistive effect can also be manipulated for biosensing applications.100, 101 In these magnetic biosensors, a layer of magnetoresistive material is covered with a functionalised layer, enabling the binding of ferromagnetic particles. When the ferromagnetic particles bind, current is induced across the device. Only a few materials have natural magnetic properties, so often the target analytes require ferromagnetic nanoparticle labelling for the technique to be effective. The mutual interaction of magnetic particles can also lead to deceptive results.

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Surface plasmon resonance biosensors are also becoming increasingly popular.102, 103 A surface plasmon wave is an oscillation of charge (usually electrons) along the interface between two media with opposite dielectric constant signs (i.e. a metal and dielectric). Surface plasmons can be excited using prism coupling, waveguide coupling, optical fibre coupling and grating coupling. Using prism coupling as an example, light travelling through the prism is totally reflected at the prism metal interface, generating an evanescent field (as discussed in chapter 1), this field penetrates into the metal layer. By adjusting the angle of incidence, the propagation constant of the evanescent field can be made to match that of the surface plasmon wave, at this angle, power is transferred to the surface plasmon wave. The required angle depends on the refractive index of the medium surrounding the metal surface; hence refractive index changes can be measured. Surface plasmon sensors are highly sensitive, capable of sensing changes down to 10-7 refractive index units,104 but they are also slightly bulky and difficult to integrate onto lab- on-a-chip platforms.

2.3 Summary

Having reviewed the current modelling techniques FDTD offers the best versatility, functioning with both continuous wave and pulsed light propagation. It has also has fewer restrictions and can model more complex non-uniform structures. A weakness of this technique is that for larger 3D models, the computing speed can be slow. The beam propagation method is substantially faster and can also model non-uniform structures; it is however limited by the directionality of the light. For uniform structures such as standard waveguides, the finite difference method and finite element method can both be used as viable alternatives.

Reviewing the latest novel waveguide designs, sub wavelength grating (SWG) waveguides show a lot of promise, performing comparably to standard waveguides, the field is still relatively new and the fabrication process is more complex than with standard waveguides. The increased waveguide surface area has good potential for surface functionalised biosensing provided the target analytes are small enough to fit between the spacing. Manufactured photonic crystal waveguides also offer great potential for

Chapter 2 – Literature Review biosensing applications, having comparable Q-factors to ring resonators and requiring a smaller footprint. They are more complex to manufacture however, which may be a limiting factor. The use of multiple ring resonators in series provides an interesting way to produce a rectangular notch optical filter.

Ring enhanced Mach-Zehnder interferometers and double ring configurations in series demonstrated the capability to produce coupled resonance induced transparencies, which if tuned, could provide improved device sensitivity compared to standard ring resonator tuning. A single ring with light pumped through both an input and a drop port also demonstrated the ability to produce Fano resonances. As mentioned before these interference shapes are sharper than typical Lorentzian resonances and are capable of improving device sensitivity.

Doped ring resonators have proven to be very capable of high frequency signal modulation and optical switching, with one system capable of modulating a signal up to 5 Gbps. Developments with thermal feedback controls also resulted in a much improved thermal operating range. Ring resonators have also been used to build on-chip lasers, increasing the viability of silicon waveguide technologies and complete lab-on-a-chip systems.

The latest waveguide fabrication techniques included maskless etching. This technique has been used to produce ring resonators with incredibly high Q-factors, up to 1,570,000 in a 150 μm radius ring resonator. If trying to design a system with ultimate signal modulation performance or high sensitivity, this technique may be of great importance.

Reviewing the use of ring resonators as biosensors, it was found that there are many approaches to surface functionalisation which could be employed, enabling a wide range of biosensing targets and applications. The lowest limit of sensitivity found in this search was 60 fM, detecting streptavidin binding to biotin, demonstrating the incredible sensitivity of ring resonator technology. The detection of a single molecule of interleukin- 2 has also been demonstrated, along with the ability to decipher between mixtures of biomolecules. Non-photonic biosensing mechanisms were also reviewed, but these were

Chapter 2 – Literature Review typically either more damaging to testing samples, less space efficient or less industrially mature than CMOS produced ring resonator sensors.

Potential for Development

The design of waveguides and ring resonators leaves space for further development. Basic configurations of single or multiple ring resonators have been explored already, but novel configurations with additional input and drop port waveguides for further analysis are still open for investigation. The combination of dual ring resonator interference to create CRIT and Fano resonances can also be further explored and compared to equivalent single ring resonator systems. The merging of novel fabrication techniques and waveguide designs could also be explored in future research, finding systems with the greatest sensitivity or functionality for biosensing or signal modulation. The adaptation of ring resonators into a complete biosensing technology for the healthcare industry can also be explored in much greater depth. Several companies (such as Genalyte) are already developing blood sensors commercially, however the field of pathological testing is diverse and there are many avenues which could still be explored.

The Big Picture

In general terms, the field of CMOS chip production is heavily dominated by electronic applications such as transistors for computing, but lab-on-a-chip technologies are quickly growing in feasibility and have the potential to become commonplace and in the healthcare consumer market. The ability to quickly105 (within minutes) assess a sample with minimal assessment material required (a drop of blood) and little to no formal training (if systems are automated) could be ground-breaking. Commercial companies are already developing systems that incorporate ring resonator sensors on a clinical scale. The use of photonic sensing enables non-invasive probing where electronics could damage a target sample. On-chip optical modulators and transistors also have great potential, as the physical limit of electronic interconnects is being reached, these alternative methods of transferring large amounts of data across a microchip without the adverse overheating effects of electrical nanowires could be of great value.

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2.4 References

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62. G. Doria, J. Conde, B. Veigas, L. Giestas, C. Almeida, M. Assunção, J. Rosa and P. V. Baptista, Sensors, 2012, 12, 1657-1687. 63. K. Saha, S. S. Agasti, C. Kim, X. Li and V. M. Rotello, Chemical reviews, 2012, 112, 2739- 2779. 64. N. M. Adams, S. R. Jackson, F. R. Haselton and D. W. Wright, Langmuir, 2011, 28, 1068- 1082. 65. J. M. Goddard and J. Hotchkiss, Progress in polymer science, 2007, 32, 698-725. 66. A. Trinchi and T. H. Muster, Supramolecular chemistry, 2007, 19, 431-445. 67. J.-N. Chazalviel, P. Allongue, A. Gouget-Laemmel, C. H. de Villeneuve, A. Moraillon and F. Ozanam, Science of Advanced Materials, 2011, 3, 332-353. 68. J. H. Moon, J. W. Shin, S. Y. Kim and J. W. Park, Langmuir, 1996, 12, 4621-4624. 69. J. L. Lawrie and S. M. Weiss., Silicon photonics for telecommunications and biomedicine, 2011. 70. S. Blair and Y. Chen, Applied Optics, 2001, 40, 570-582. 71. R. W. Boyd and J. E. Heebner, Applied Optics, 2001, 40, 5742-5747. 72. S. Weiss, M. Molinari and P. Fauchet, Applied physics letters, 2003, 83, 1980-1982. 73. A. M. Armani and K. J. Vahala, Opt. Lett., 2006, 31, 1896-1898. 74. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan and K. J. Vahala, Science, 2007, 317, 783-787. 75. S. Wang, A. Ramachandran and S.-J. Ja, Biosensors and Bioelectronics, 2009, 24, 3061- 3066. 76. A. Yalcin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van and S. Chu, Selected Topics in Quantum Electronics, IEEE Journal of, 2006, 12, 148-155. 77. K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman and R. Baets, Optics express, 2007, 15, 7610-7615. 78. K. De Vos, J. Girones, S. Popelka, E. Schacht, R. Baets and P. Bienstman, Biosensors and Bioelectronics, 2009, 24, 2528-2533. 79. A. L. Washburn, L. C. Gunn and R. C. Bailey, Analytical chemistry, 2009, 81, 9499-9506. 80. C. A. Barrios, M. J. Banuls, V. Gonzalez-Pedro, K. B. Gylfason, B. Sanchez, A. Griol, A. Maquieira, H. Sohlström, M. Holgado and R. Casquel, Opt. Lett., 2008, 33, 708-710. 81. S. Weiss, G. Rong and J. Lawrie, Physica E: Low-dimensional Systems and Nanostructures, 2009, 41, 1071-1075. 82. M. Iqbal, M. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey and L. C. Gunn, Selected Topics in Quantum Electronics, IEEE Journal of, 2010, 16, 654-661. 83. A. L. Washburn, M. S. Luchansky, A. L. Bowman and R. C. Bailey, Analytical chemistry, 2009, 82, 69-72. 84. J. S. del Río, T. Steylaerts, O. Y. Henry, P. Bienstman, T. Stakenborg, W. Van Roy and C. K. O’Sullivan, Biosensors and Bioelectronics, 2015, 73, 130-137. 85. C. L. Arce, S. Van Put, A. Goes, E. Hallynck, P. Dubruel, K. Komorowska and P. Bienstman, Journal of Applied Physics, 2014, 115, 044702. 86. C. Campanella, C. Campanella, F. De Leonardis and V. Passaro, The European Physical Journal Special Topics, 2014, 223, 2009-2021. 87. H. Li and X. Fan, Applied Physics Letters, 2010, 97, 011105. 88. X. Jiang, Y. Chen, F. Yu, L. Tang, M. Li and J.-J. He, Opt. Lett., 2014, 39, 6363-6366. 89. D. Grieshaber, R. MacKenzie, J. Voeroes and E. Reimhult, Sensors, 2008, 8, 1400-1458. 90. J.-i. Hahm and C. M. Lieber, Nano letters, 2004, 4, 51-54. 91. E. Stern, J. F. Klemic, D. A. Routenberg, P. N. Wyrembak, D. B. Turner-Evans, A. D. Hamilton, D. A. LaVan, T. M. Fahmy and M. A. Reed, Nature, 2007, 445, 519.

Chapter 2 – Literature Review

92. D. Pantarotto, J.-P. Briand, M. Prato and A. Bianco, Chemical communications, 2004, 16- 17. 93. J. O. Lee and H. M. So, Nanotechnologies for the Life Sciences, 2011. 94. A. Star, J.-C. P. Gabriel, K. Bradley and G. Grüner, Nano letters, 2003, 3, 459-463. 95. F. Patolsky, G. Zheng, O. Hayden, M. Lakadamyali, X. Zhuang and C. M. Lieber, Proceedings of the National Academy of Sciences of the United States of America, 2004, 101, 14017- 14022. 96. C. Ziegler, Analytical and bioanalytical chemistry, 2004, 379, 946-959. 97. M. Alvarez and L. M. Lechuga, Analyst, 2010, 135, 827-836. 98. N. V. Lavrik, M. J. Sepaniak and P. G. Datskos, Review of scientific instruments, 2004, 75, 2229-2253. 99. L. G. Carrascosa, M. Moreno, M. Alvarez and L. M. Lechuga, TrAC Trends in Analytical Chemistry, 2006, 25, 196-206. 100. D. R. Baselt, G. U. Lee, M. Natesan, S. W. Metzger, P. E. Sheehan and R. J. Colton, Biosensors and Bioelectronics, 1998, 13, 731-739. 101. D. L. Graham, H. A. Ferreira and P. P. Freitas, TRENDS in Biotechnology, 2004, 22, 455-462. 102. V. Nanduri, A. K. Bhunia, S.-I. Tu, G. C. Paoli and J. D. Brewster, Biosensors and Bioelectronics, 2007, 23, 248-252. 103. J. Homola, Analytical and bioanalytical chemistry, 2003, 377, 528-539. 104. R. Karlsson and R. Stahlberg, Analytical biochemistry, 1995, 228, 274-280. 105. Genalyte, Results Matter: Now., http://www.genalyte.com/, Accessed 09/09/2017, 2017.

Chapter 3 – Experimental Setup

Chapter 3 - Experimental Setup

3.1 Introduction

A large portion of work in this thesis has been conducted on a single type of microchip layout which was built with several varied ring resonator configurations. The majority of optical measurements were also taken on one of two optical analytical setups. Each setup is compatible with any mid-IR (~1550 nm) fibre optically coupled light source and any complimentary spectrometer. This chapter will introduce the equipment specifications used for this thesis, the design of the main project microchip, the experimental methodologies and discuss the main sources of experimental noise analysed during this thesis.

To recap from chapter 1, the principle of ring resonator sensing is reasonably simple. Light transmitted through waveguides can be analysed. While light is travelling through the waveguide, different features (such as ring resonators, Mach-Zehdner interferometers and Y-splitting junctions) can be used to modify the transmitted output signal. When ring resonators are used in close proximity to the waveguide, light is able to evanescently couple between the waveguide and ring resonator at wavelengths which enable the formation of a travelling wave within the ring resonator.

With the use of specially designed diffraction grating optical inputs and outputs, light can be injected into waveguides. By focusing a bright light source, such as a laser, onto the grating we can generate a strong transmission spectrum and measure the intensity of light at an output grating with a focussed spectrometer. Alternative coupling methods are available, such as directly fusing optical cables to the waveguides, but these methods lack the experimental flexibility and ease of alignment that diffraction grating couplers offer. Figure 3.1 shows the graphic representation of the basic operating principles of the ring resonator sensors presented in this thesis.

Chapter 3 – Experimental Setup

Figure 3.1: The operating principles of a ring resonator sensor, such as those presented in this thesis. Light, typically IR at ~1550 nm in wavelength is inserted into the waveguide using an input grating. At certain resonant wavelengths the light evanescently couples with the ring resonator cavity. This causes the generation of a traveling wave within the cavity, where each photon travels around the ring multiple times, building up a greater intensity of light and associated field within the ring. The larger field in the cavity causes destructive interference with light in the waveguide, causing a substantial drop in transmitted intensity at the resonant wavelengths. The size of the waveguide features can vary depending on requirements, but waveguides are usually of the order of 300-500 nm wide and ~200 nm tall. Ring resonators are typically built between 10 μm and 200 μm in radius.

When analysing ring resonator systems experimentally, the controllable elements for assessing their behaviours are the ring resonator configurations, the illuminating light sources and the corresponding spectrometers. In this section we will give an overview of each of these elements.

Chapter 3 – Experimental Setup

3.2 Laser and Spectrometer Specifications

Two main light sources have been used throughout this project, the Thorlabs TLK-L1550M Littman configuration laser kit (as a narrow bandwidth tuneable laser) and the Thorlabs Fibre Coupled Superluminescent Diode SM model S5FC1005S (as a broadband light source).

3.2.1 Thorlabs TLK-L1550M Littman Configuration Laser Kit

The TLK-L1550M tuneable laser kit1 features a single-angled-facet (SAF) gain chip which provides a gain medium for light centred at 1550 nm. These chips feature anti-reflective coatings, an angled waveguide and a proven semiconductor optical amplifier structure. This gain chip is used in an external cavity laser setup, allowing high power and a wide tuning range. The temperature of the gain chip is controlled and tuned using incorporated thermoelectric cooler and thermistor technology. Light in this laser is controlled using a Littman diffraction grating configuration. This configuration has a fixed grating angle and a motor controlled rotating mirror. Light diffracted from the grating is then reflected off the mirror and diffracted off the mirror a second time before coupling back into the gain medium. Figure 3.2 shows the arrangement of this optical layout.

Chapter 3 – Experimental Setup

Figure 3.2: The optical layout of the tuneable laser kit. Light from the gain chip is incident on the fixed grating, reflecting into the pivot arm mirror, reflected back onto the grating and back into the gain chip. The dual grating reflection enables narrower line widths and a fibre optic cable can be coupled onto the end of the gain medium.1

This type of configuration offers narrower line widths at the expense of power and tuning range. Figure 3.3 shows the Power vs Wavelength profiles of the various Tunable Laser Kit packages.

Chapter 3 – Experimental Setup

Figure 3.3: The Power (dB) vs Wavelength graph of the various tuneable laser kits available from Thorlabs. The kit used in this setup is the TLK-L1550M, represented by the dark blue curve (fourth from the right). As can be seen, the tuning range drops off at higher wavelengths due to the Littman tuning configuration.

In terms of the laser performance characteristics, the centre wavelength is typically 1550 nm, The 10 dB tuning range is 120 nm, the peak power is typically 35 mW, the wavelength tuning resolution is 3 pm, the linewidth is typically 100 kHz, power stability over 30 seconds is 1%, power stability over 24 hrs is 10%, the wavelength stability over 30 seconds is 4 pm and over 24 hours is 50 pm.

3.2.2 Single Mode Thorlabs Fibre Coupled Superluminescent Diode

A model S5FC1005S Single Mode Thorlabs Fibre Coupled Superluminescent Diode (SLD)2 is the broadband light source which was used for many of the characterisation measurements in this project. It features a SLD1005S model superluminescent diode centred on 1550 nm. SLDs are excellent high power light sources. This diode in particular is indium phosphide based with its output coupled to a single mode fibre and has an integrated thermoelectric cooling system to keep the transmitted spectra stable. The optical output from these devices is close to Gaussian, making analysis of the resulting spectra easy to analyse and correct. Figure 3.4 shows the specified device transmission spectrum.

Chapter 3 – Experimental Setup

Figure 3.4: The transmission spectrum of the model S5FC1005S Single Mode Thorlabs Fibre Coupled Superluminescent Diode with an operating current of 600 mA. The curve is asymmetric but towards its peak intensity follows an approximately Gaussian shape.2

The optical properties of this device are as follows: The wavelength is centred by weight around 1550 nm, the output power is 22 mW, the optical bandwidth at -3 dB is 50 nm, the RMS gain ripple at maximum drive current is typically 0.2 – 0.35 dB.

3.2.3 BaySpec Super Gamut NIR-SWIR Spectrometer

A BaySpec Super Gamut NIR Spectrometer3 which operates in the range of 900 – 1700 nm is used in experiments in conjunction with the Thorlabs TLK-L1550M laser.1 This spectrometer has a spatial resolution of 5 – 20 nm depending on slit length, but in conjunction with the optical setup and fibre optic coupling, this is likely to be significantly lower. It also features a signal integration time of 20 μs to 30 seconds, this allows the amplification of weaker signals if required. It features a detector array of 256 pixels over which it collects data. With this system, a custom LabVIEW program was used which communicates between the laser and the spectrometer. As the laser is tuned across a

Chapter 3 – Experimental Setup

range of wavelengths, the intensity of light measured at each tuning step is made. The detector typically saturates after approximately 70,000 counts, however the intensity of light being exposed can be controlled using a built-in iris and setting the exposure time of the detector. The detector has a systematic dark room noise of 10 counts RMS, but in the laboratory under lit conditions, the noise reading reaches approximately 50 counts.

3.2.4 Thorlabs Optical Spectrum Analyser OSA 203B 1.0 – 2.6 μm

A Thorlabs Optical Spectrum Analyser OSA 203B4 functioning in the optical range of 1.0 – 2.6 μm was used in conjunction with the Thorlabs SLD light source. This product has a variable spectral resolution but lies in the region of 50 pm as demonstrated by the graph in figure 3.5,5 with spectral readings measured every 29 pm around the 1500 nm wavelength region. The maximum sensitivity of the spectrometer is -70 dB/nm; the maximum optical input power is 10 mW. The optical noise floor profile is shown in figure 3.6.4 The spectrometer is fibre coupled and provides a visible red laser through its optical input port to assist with aligning the detector.

Figure 3.5: The spectral resolution of the Thorlabs Optical Spectrum Analyser OSA 203B. There are two modes, high resolution and low resolution, as can be seen, the best spectral resolution at 1.5 μm is approximately 50 pm.5

Chapter 3 – Experimental Setup

Figure 3.6: OSA Noise floor in absolute Power Mode. As can be seen, this value is between -90 dBm and -100 dBm for the OSA203B system between 1 and 2 μm. Optical signals need to overcome this floor in order to be detected.4

The main advantage of the OSA system for biosensing applications is the speed at which it can measure an entire spectrum between 1 – 2.6 μm wavelengths. On high resolution and high sensitivity settings, the OSA203B is able to refresh its output every 9.5 seconds. This is substantially faster than the BaySpec tuning configuration and enables close to ‘real- time’ measurements to be made. This response time can be especially useful for time related sensing applications such as biosensing where flow rates and concentrations may need to be monitored over time.

The Thorlabs Fibre Coupled Superluminescent Diode (SLD) source2 centred around 1550 nm is used as a broadband infrared light source when measuring spectra with this spectrometer. Light is directed via a single mode infrared fibre-optic cable into the aligned optical setup.

Chapter 3 – Experimental Setup

3.3 Standard Photonic Chip Design and Specifications

The majority of tests presented in this thesis were made on a chip designed by Joseph Lydiate.6 An image of the chip design can be seen in figure 3.7. The chips were manufactured in A-Star IME silicon foundry in Singapore. During manufacture, a starting material thickness of 220 nm of SOI was deposited on top of a 2000 nm buried oxide (BOX) layer. The coupling waveguides have a width of 320 nm and a slab thickness of 90 nm. There is a variable gap between the waveguides and the ring resonators, with 200 nm, 250 nm and 300 nm separation gaps available for all ring resonator configurations. The ring resonators themselves are designed with a double slit configuration (to reduce losses and improve sensitivity) with an outer width of 250 nm, a gap of 200 nm and an inner width of 290 nm. The double slits come in two sizes; the rings have a total outer edge-to-edge diameter of either 50.7 μm or 100.7 μm. Diffraction gratings are used for optical coupling. For heating, a zig-zagging TiN element with a thickness of 150 nm is placed 1200 nm over the coupled ring resonator-waveguide region and further coated by a 400 nm silicon oxide layer, which also provides environmental isolation. In total, the waveguides typically have a 1600 nm silicon oxide layer protecting them from the surrounding environment. Each ring resonator comes in two varieties, with a window etched through the 1600 nm protective layer and without a window etched over part of the ring resonator.

Chapter 3 – Experimental Setup

Figure 3.7: (A) The ring resonator chip architecture with (from bottom to top) single ring resonators, single ring resonators with drop ports, y-splitting double ring resonators with central drop ports, and recombining Mach-Zehnder double ring resonators with central drop ports. The upper eight designs were spare designs. (B) Closer image of the heating element (blue markings) and sensing window (red rectangle) design. (C) The double ring resonator configurations and (D); Single ring (lower) and single ring with drop port (upper) configurations for 50.7 μm and 100.7 μm rings.

Alternative chip designs have been used in some cases, however details will be noted when this is the case. After manufacture, the chips were protected by a PMMA layer which can easily be dissolved and removed with a cleaning bath sequence of acetone, IPA/Ethanol/Methanol and Deionised water.

Chapter 3 – Experimental Setup

3.4 Optical Setups and Experimental Procedure

The main optical setup for this research project is shown in Figure 3.8. In this setup, one of the combinations of light sources (either broadband and OSA, or tuneable laser and BaySpec) is used and the surface of the microchip is scanned.

Figure 3.8: The main optical setup for non-probing measurements. Laser light is focussed through a lens, the intensity can be varied using an iris, an optional dispersion lens can be used if the user wants to highlight a larger portion of the chip using the laser, the light reflects off a 50/50 beam splitter onto the surface of the chip. When the light is focussed onto a chip-surface input diffraction grating, a secondary output grating at the opposite end of the waveguide emits light. Using the adjustable mirror, the spectrometer and camera can be focussed onto the output signal. The output transmission is then measured using a computer. The adjustable platform is used to control the position of the chip relative to the laser light.

The main steps in running an experiment involve the following: 1. The chip is placed onto the adjustable platform. 2. The laser, camera and spectrometer are switched on. The camera is infrared specific, enabling views of the chip surface and laser spot.

Chapter 3 – Experimental Setup

3. The height of the platform is adjusted to ensure that the spot from the laser is at its smallest focus. 4. A reference marker is placed on the screen to determine where the laser’s focal point is, and then a dispersion lens is added to the circuit. This spreads the beam out, illuminating the surface of the chip, thereby enabling users to locate the position of input diffraction gratings. 5. Using the original marker reference, a target input grating on the chip is lined up and the dispersion lens is removed from the setup, allowing the focussed laser to illuminate the input grating. 6. The adjustable mirror is then moved to focus the camera and detector onto the output grating. If the laser is correctly lined up with the input grating and the light is correctly polarised, a signal will emit from the output grating. 7. Using a separate positional marker to denote the most sensitive part of the camera image with respect to the spectrometer, the adjustable mirror can be moved until an optimal signal is received through the spectrometer. In some cases this may be oversaturate the spectrometer, if this happens, the iris can be used to reduce the intensity of light incident upon the chip. 8. Once the optics are correctly lined up, the x and y-controllers of the adjustable platform can be used to quickly switch between different ring resonator targets. As figure 3.7 (A) shows, the chip grating positions to be conveniently designed. 9. The spectrometer signals can either be recorded in a moment, or the position of spectral peaks can be monitored over time. The time dependent measurements have greater utility in biosensing applications, but high definition spectral outputs can be more useful for theoretical modelling and understanding.

For electrical probing experiments, a slightly modified system is used. In this case, the same combinations of light source and spectrometer are used, but the optical injection and extraction method is different. In this case a fibre optic cable is brought into close proximity to the diffraction gratings on the surface of the chip. Conducting needles are used to apply current through the electrical contact pads, heating the devices. In order to navigate around, the needles and fibre optical cable ends are repositioned around the

Chapter 3 – Experimental Setup

chip, rather than moving the chip relative to the laser and spectrometer as shown in figure 3.8.

3.5 Sources of Drift and Uncertainty

The main sources of signal drift and uncertainty in these experimental setups are thermal drift, i.e. temperature instability in the system, manufacturing intolerances (i.e. the built- in inaccuracies from the fabrication process), the light source (i.e. temperature instabilities in the gain media), dust and material on the ring resonators themselves, the spectrometer and environmental optical signal.

In the tuneable laser setup, there is an additional source of uncertainty generated from the motor position, specifically when resetting the motor position, directly relating to the measured tuned wavelength.

Thermal instability is caused by environmental changes to the temperature of the silicon material, which subsequently change its effective refractive index. The act of illuminating a chip with an IR light source can also have a heating effect on the chip. These effects make the ring resonators essentially seem larger in radius (if the ring is hotter), changing the spectral position of peaks in the transmission spectrum. In order to observe the effects of thermal fluctuations, a measurement was taken in order to assess the magnitude of variation over a 24 hour period and gain an indication of how significant this could be. The results of this test are shown in figure 3.9.

Chapter 3 – Experimental Setup

Peak Position Change vs Time Over 24 Hours 0.01 0 -0.01 -0.02 -0.03 -0.04 -0.05 1547.7 -0.06 1552.1

Wavelength Change (nm) Change Wavelength -0.07 1556.6 -0.08 0 200 400 600 800 1000 1200 1400 Time (minutes)

Figure 3.9: A plot of the wavelength change of three consecutive peaks in a transmission spectrum over time for the 50.7 μm diameter single ring system with a gap between the waveguide and ring resonator of 300 nm and an oxide layer (i.e. no window) protecting the ring resonator. The maximum change can be seen in the 1556.6 nm peak, measuring approximately 0.07 nm.

The broadband fibre coupled superluminescent diode was used in conjunction with the OSA 203 B spectrometer as the scanning time enables measurements to be taken more frequently. In this particular experiment, a peak position reading was taken every minute. Intensity spectra were also recorded at the beginning and end of the experiment. These can be seen in figure 3.10.

Chapter 3 – Experimental Setup

Intensity Spectra Before and After 24 Hours

1.20E-07

1.00E-07 Beginning Spectrum End Spectrum 8.00E-08

6.00E-08

4.00E-08

Absolute Power (mW) Power Absolute 2.00E-08

0.00E+00 1510 1520 1530 1540 1550 1560 1570 1580 1590 Wavelength (nm)

Figure 3.10: The absolute power transmission spectra taken before and after the 24 hour signal stability test. As seen, there is approximately 20% difference in relative signal strength between the two readings.

As shown in figure 3.10, the relative magnitude of signal changed by approximately 20 % between the start and finish of the 24 hour experiment. The reasoning for this difference could be due to a slight change in the position of the controllable pad over time, or variations in the thermal operating temperature of the SLD light source. Figure 3.9 suggests that there is a general downward shift in the peak positions between 200 and 400 seconds which then stabilised. Due to the gradual nature of the change (rather than a sudden jump which would be expected with a knock) it is sensible to conclude that this source of signal drift is either produced by a change in the laboratory temperature overnight, or a gradual decrease in the light source intensity (due to thermoelectric cooling controls), reducing the localised heating effect of light building up within the ring resonator. These would make the ring resonator appear to shrink in size, leading to a negative shift in spectral peak position.

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Chapter 3 – Experimental Setup

3.6 References

1. THORLABS, Tunable Lasers: Prealigned Littrow and Littman Kits, https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=4757&pn=TLK-L1550M, Accessed 04/09/2017, 2017. 2. THORLABS, Benchtop SLD Light Sources, https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=4285, Accessed 04/09/2017, 2017. 3. BaySpec, SuperGamut™ NIR-SWIR, http://www.bayspec.com/spectroscopy/nir-swir/, Accessed 04/09/2017, 2017. 4. THORLABS, OSA203B - Fourier Transform Optical Spectrum Analyzer, 1.0 - 2.6 µm, https://www.thorlabs.com/thorproduct.cfm?partnumber=OSA203B, Accessed 04/09/2017, 2017. 5. THORLABS, Resolution In Spectrometer Mode, https://www.thorlabs.com/images/TabImages/OSA_Resolution_1015_780.gif, Accessed 04/09/2017, 2017. 6. J. Lydiate, University of Manchester, 2016.

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Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems

Chapter 4 - Characterisation and Thermal Tuning of Ring Resonator Systems

4.1 Introduction

This chapter will cover the characterisation of the resonator chips described in section 3.3. The microchip mainly studied in this thesis is silicon on insulator (SOI) based with TiN heating elements fabricated over the coupling regions between the waveguides and ring resonators.

When trying to modify the effective refractive index of a ring resonator, surface based heating elements offer greater environmental control than the application of biomaterials and other surface analytes over an exposed window (illustrated in figure 4.1). As mentioned in section 2.2.6 of the literature review chapter, functionalised surfaces can be laden with systematic uncertainty and error due to the random nature of particles suspended in a flowing liquid. For this reason, the process of thermal tuning with a buried heating element is optimal for device characterisation.

The aims of this chapter are to:  Characterise the ring resonators, their Q-factors and typical spectra.  Explore the experimental process of thermally tuning ring resonators.  Calibrate thermal shifting using a single ring resonator as a reference.  Investigate the dynamics of more complex double ring systems.

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Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems

Figure 4.1: An illustration of the different approaches which can be used for spectral tuning. An exposed window could be used if fluids with known refractive indices for passed over the ring’s surface. Controlled layers of material could also be added to the surface of the ring resonators. In order to apply these fluids or layers, a complex application system would be required and the random nature of deposition would lead to systematic error. By thermally tuning the ring resonators with embedded titanium nitride heating elements, improved control over spectral tuning can be achieved with greater ease and improved reliability.

4.2 Un-tuned Ring Resonator Spectra

Initially, it is useful to characterise the devices under ambient laboratory conditions. When characterising ring resonators, measurements such as the free spectral range, full width at half maximum, finesse, quality factor and extinction ratios are often used in literature.1

The free spectral range (FSR) Δλ can be defined as the spectral distance between two adjacent resonant states as shown in figure 4.2. Mathematically, this can be approximately equated to the following equation:

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Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems

휆2 훥휆 ≅ 푛푔퐿

Where ng is the refractive index of the waveguide and L is the path length or circumference of the ring resonator (2πr). The full width at half maximum (FWHM) δλ is another useful parameter, defined as the width of a spectral peak half at half of its maximum height, or at -3 dB from the top if measuring on a logarithmic scale.

1.2 Δλ 1

0.8

0.6 δλ

0.4

Normalised Power Normalised 0.2

0 1514 1515 1516 1517 1518 1519 1520 1521 λ (nm)

Figure 4.2 A transmission spectrum demonstrating the measurements of free spectral range Δλ and full width at half maximum (FWHM) δλ parameters as measured on a spectrum.

Finesse is defined as the ratio between the free spectral range (FSR) and the full width half maximum.

퐹푆푅 훥휆 퐹 = = 퐹푊퐻푀 훿휆

Physically this value can be related to 2π times the number of round trips made by light in the ring.

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Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems

Quality factor or Q-factor of a resonator is the ratio of operating wavelength divided by the resonant FWHM.

휆 푛푔퐿 푄 = = 퐹 훿휆 휆

For high Q-factor resonators, this value represents the number of oscillation periods required for the stored energy to decay to 1/e (~37%) of its original value. As a result, higher Q-factor resonators have lower losses and narrower FWHM values.

The extinction ratio of a ring resonator is the ratio of the maximum and minimum transmitted powers.

푃푡푚푎푥 퐸푅 = 푃푡푚푖푛

4.2.1 Single Ring Single Input

A detailed understanding of the ring resonators in their most basic, single input waveguide versions is critical before moving onto more complex systems. Once these are understood, it becomes much easier to analyse systems with additional complexity such as those with an additional drop port waveguide or the more complicated double ring Y- splitting and Mach-Zehnder type setups.

The ring resonator systems either come with 50.7 μm or 100.7 μm diameter configurations as a base. As a further distinction, the input waveguides and ring resonators have three different separation distances, 200 nm, 250 nm and 300 nm. By increasing the distance between the waveguides and the ring resonators, it is possible to physically alter the evanescent coupling coefficients, offering a novel parameter to analyse. The titanium nitride (TiN) heating elements embedded in SiO2 are fabricated to be 150 nm in thickness, in zig-zag geometry and positioned 1200 nm above the waveguide-ring resonator coupling region. There are also duplicate copies of all the ring

105

Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems resonator designs with windows fabricated over the ring resonators themselves. These come in 64 μm x 35 μm varieties as seen in figure 4.3 or 128 μm x 70 μm version for the larger ring resonators.

Figure 4.3: The single ring resonator layout with a 64 μm x 35 μm window exposing the ring resonator. This figure also shows the placement of the TiN Heating element used for thermal tuning calculations, coloured in blue.

In total, there are twelve versions of each configuration, categorised in the table below.

Diameter 200 nm gap 250 nm gap 300 nm gap 100.7 μm No Window Window No Window Window No Window Window 50.7 μm No Window Window No Window Window No Window Window

For thermal tuning experiments, the systems with no window possibly offer greater thermal stability (due to the rings being covered), but the systems with a window are required for biosensing applications as the surfaces of the ring resonators need to be accessed.

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Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems

In order to measure transmission spectra, the broadband SLD light source and OSA 203B (described in chapter 3) were used as they provide higher spectral stability and they don’t have the associated motor tuning travelling noise. This however comes at the expense of spectral resolution and signal strength. For throughput waveguide signals (i.e. light travelling from the optical input grating through to the corresponding output grating), the intensity of light is typically high enough to be detected on the highest sensitivity of the OSA 203B spectrometer.

Figures 4.4 - 4.8 show typical unmodified transmission spectra for a plain waveguide and single ring resonator systems with a 200 nm gap.

Plain Waveguide (No Ring Resonator) 7.00E-09

6.00E-09 5.00E-09 4.00E-09 3.00E-09 2.00E-09

AbsolutePower (mW) 1.00E-09 0.00E+00 1500 1505 1510 1515 1520 1525 1530 1535 1540 Wavelength (nm)

Figure 4.4: Transmission spectrum for a plain waveguide with no ring resonator. It should be noted that there is an approximately Gaussian background shape and sinusoidal oscillations are also observed in this transmission spectrum. The oscillations may be attributed to a physical cavity in the experimental set-up.

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25 μm Radius, 200 nm Gap, No Window 1.00E-08

9.00E-09

8.00E-09 7.00E-09 6.00E-09 5.00E-09 4.00E-09 3.00E-09

2.00E-09 AbsolutePower (mW) 1.00E-09 0.00E+00 1500 1505 1510 1515 1520 1525 1530 1535 1540 Wavelength (nm)

Figure 4.5: Transmission spectrum for a 25 μm radius ring resonator with a 200 nm gap and no window. The ring resonator induced ‘peaks’ are visible, with free spectral ranges between 4 and 5 nm as wavelength increases.

25 μm Radius, 200 nm Gap, Window 7.00E-09

6.00E-09 5.00E-09 4.00E-09 3.00E-09 2.00E-09

AbsolutePower (mW) 1.00E-09 0.00E+00 1500 1505 1510 1515 1520 1525 1530 1535 1540 Wavelength (nm)

Figure 4.6: Transmission spectrum for a 25 μm radius ring resonator with a 200 nm gap and a window. The free spectral ranges are equivalent to the non-windowed system, but the apparent width of the peaks has increased.

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50 μm Radius, 200 nm Gap, No Window 8.00E-09

7.00E-09 6.00E-09 5.00E-09 4.00E-09 3.00E-09 2.00E-09 AbsolutePower (mW) 1.00E-09 0.00E+00 1500 1505 1510 1515 1520 1525 1530 1535 1540 Wavelength (nm)

Figure 4.7: Transmission spectrum for a 50 μm radius ring resonator with a 200 nm gap in a non-windowed configuration. As can be seen, the free spectral range has effectively halved compared to the 25 μm radius ring.

50 μm Radius, 200 nm Gap, Window 8.00E-09

7.00E-09 6.00E-09 5.00E-09 4.00E-09 3.00E-09 2.00E-09 AbsolutePower (mW) 1.00E-09 0.00E+00 1500 1505 1510 1515 1520 1525 1530 1535 1540 Wavelength (nm)

Figure 4.8: Transmission spectrum for a 50 μm radius ring resonator with a 200 nm gap in a windowed configuration.

Figures 4.4-4.8 show a significant amount of systematic interference mixed with the resonant peak shapes. In order to make accurate and reliable measurements of peak positions and Q-factors, it is necessary to reduce this interference level to within workable limits. The process of cleaning the signal will also be useful at later stages in

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Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems technological development as it will help automate the transmission spectrum scanning process for potential biosensing applications.

Figure 4.4 shows a spectrum from a plain waveguide with no ring resonators. This spectrum appears to contain both a Gaussian contribution and a sinusoidal contribution. The Gaussian contribution can be attributed to both the SLD broadband light source and gratings, as highlighted in figure 3.4. The source of the sinusoidal noise is more difficult to distinguish, but it might be caused a physical cavity within the experimental setup causing a standing wave through optical reflections within the cavity. Unfortunately in this experimental setup the ring resonator signal can’t simply be divided by the plain waveguide signal to remove the background effects and normalise the signal. This is because the amplitude of input light (due to slight misalignments) and phase of sinusoidal contributions vary from reading to reading. In order to extract the useful ring resonator signal, it is necessary to carefully fit and remove these effects in each case.

A Gaussian curve is defined by the following equation:

(푥−푏)2 − 퐹(푥) = 퐴푒 2푐2

Where A is the amplitude of the Gaussian curve, b is the central position of the curve and c is half width at half maximum (HWHM) value. In order to fit the curve to experimental data, a calculation of the sum of the difference between data points squared (Σdiff2) can be used in conjunction with software that can solve for a minimum value. This research utilised the Microsoft Excel 2010 Solver function on the GRG non-linear solving setting. Once reliable estimates are input for the A, b and c coefficients, the Σdiff2 can be solved to find a minimal value by making small changes to the values of the A, b and c coefficients. In most cases this approach yields significantly reduced Σdiff2 values and improved data fitting. Figure 4.9 shows an example of this Gaussian fitting approach.

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Gaussian Fit, 25 μm, 200 nm, No Window

1.2

0.8

0.6 Data 0.4 Gaussian Fit

0.2 Intensity(Arbitrary Units) 0 1500 1510 1520 1530 1540 Wavelength (nm)

Figure 4.9: A Gaussian fit applied to the data for the 25 μm ring resonator with a 200 nm gap and no window. The A coefficient is ~0.818, the b coefficient is ~1521.94 nm and the c coefficient is ~11.58 nm. The Σdiff2 is 11.15 over 1415 data points.

Once a good fit of the Gaussian curve is achieved, the data can then be divided through by the Gaussian curve data, leading to a flattened dataset where all peaks are represented proportionally. At this stage, there is still a sinusoidal noise contribution which needs removing, but this becomes easier to process once the Gaussian contribution has been removed. It should be noted that once the data has been flattened, the effects of noise are increased in regions where the signal was weak to begin (i.e. edges of the signal). As such, it is useful to cut the lower intensity edge data out, leaving the cleanest signal for sinusoidal fitting.

When fitting a sinusoidal shape to the data, the following equation was used:

퐹(푥) = 퐴푠푖푛푏(푥 + 푐) + 푑

Where A is the amplitude of oscillation, b is the frequency of oscillation, c is the phase and d represents the sinusoidal intensity offset. For small oscillations such as the sinusoidal ones observed here, it is necessary to remove the data close to the ring resonator peaks to ensure that their presence doesn’t interfere with the sinusoidal fitting.

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Once ring resonator peak data has been removed from Σdiff2 calculations, the solver function can be used in the same way that it was with the Gaussian fit. This ensures optimal signal smoothing. Figure 4.10 shows the fitting of a sinusoidal wave which is likely due to a physical cavity within the system.

Sine Fit, 25 μm, 200 nm, No Window 1.4

1.2 1 0.8 0.6 Data 0.4 Sine Fit

NormalisedIntensity 0.2 0 1510 1515 1520 1525 1530 Wavelength (nm)

Figure 4.10: A demonstration of sine fitting using the data from a 25 μm radius ring resonator with a 200 nm gap and no window. As demonstrated, in this case there is quite a clear indication of a sinusoidal background pattern.

Once a good sinusoidal curve fit has been achieved, the data points can be divided through by the sine values, removing the sinusoidal signal, leaving the plain Lorentzian peak shapes normally associated with ring resonators. Figures 4.11 – 4.15 display the background-removed spectra, offset and on a logarithmic intensity scale for viewing ease. The initial units before offsetting were normalised intensity.

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Plain Waveguide Background Removed Signals

100

Plain 1

1 Plain 2 Intensity(Arbitrary Units)

0.1 1510 1515 1520 1525 1530 Wavelength (nm)

Figure 4.11: A comparison between two background removed plain waveguide signals (i.e. no ring resonators)

25 μm Ring With Window, Background Removed 1000

100

10 200 nm

1 250 nm

300 nm Intensity(Arbitrary Units) 0.1

0.01 1510 1515 1520 1525 1530 Wavelength (nm)

Figure 4.12: Background removed data for the 25 μm radius ring resonator setup with a window at 200, 250 and 300 nm waveguide separation distances.

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25 μm Ring, No Window, Background Removed 1000

100

10 200 nm 1 250 nm 300 nm

Intensity(Arbitrary Units) 0.1

0.01 1510 1515 1520 1525 1530 Wavelength (nm)

Figure 4.13: Background removed data for the 25 μm radius ring resonator setup without a window at 200, 250 and 300 nm waveguide separation distances.

50 μm Ring With Window, Background Removed 1000

100

10 200 nm 1 250 nm 300 nm

Intensity(Arbitrary Units) 0.1

0.01 1510 1515 1520 1525 1530 Wavelength (nm)

Figure 4.14: Background removed data for the 50 μm radius ring resonator setup with a window at 200, 250 and 300 nm waveguide separation distances.

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50 μm Ring, No Window, Background Removed 1000

100

10 200 nm

1 250 nm

300 nm Intensity(Arbitrary Units) 0.1

0.01 1510 1515 1520 1525 1530 Wavelength (nm)

Figure 4.15: Background Removed data for the 50 μm radius ring resonator setup without a window at 200, 250 and 300 nm waveguide separation distances.

Figures 4.12 to 4.15 reveal that the spectral positioning of each resonant peak is not equal. This suggests that manufacturing intolerances in the separation gaps and radius of the ring resonators are important when predicting the spectral positioning of resonant peaks.

In most cases, it appears that the ring resonator interaction with the transmission signal decreases as the separation between waveguide and ring resonator increases. This results in lower magnitude interference peaks in the systems with greater coupling distance increases. The clean-up of the data results in an appropriate format for measuring the quality factors of each setup.

The quality factor of each peak could be read from the graphs with an accurate ruler; but more reliable readings can be achieved by fitting Lorentzian peak shapes to each peak. The Lorentzian function can be defined by the following equation:

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푎2 퐹(푥) = 퐼 2 2 + 퐶 (푥 − 푥0) + 푎

Where I is the height (-ve for depth) of the Lorentzian peak, a is the half width at half of maximum (HWHM) value, x0 is the central peak position and C represents the baseline Y- intercept (1 in the case of the background removed data). The advantage of using this format of the Lorentzian is that only three parameters need to be changed to get a good fit, this makes computational fitting using a solver function easier. Figure 4.16 shows an example of the Lorentzian fitting process.

Lorentz Fit, 25 μm, 200 nm, No Window 1.2

0.8

0.6 Data 0.4 Lorentz

NormalisedIntensity 0.2

0 1515 1515.5 1516 Wavelength (nm)

Figure 4.16: A typical Lorentzian fit applied to a peak in the 25 μm ring resonator with a 200 nm waveguide separation and no window. In this case, the peak depth, I, is 0.782, the HWHM is 0.0539 nm and the peak wavelength is 1515.779. The Q-factor calculated with these numbers is 14,073 and the Lorentz fitting R2 value is 0.955, showing strong correlation.

Rather than taking a solitary measurement of the Q-factor for each setup, it is preferable to measure the Q-factor on several peaks and find an average with an associated standard deviation. On each 25 μm radius ring resonator dataset, four peak Q-factor measurements were made. On each 50 μm radius ring resonator dataset, eight peak Q- factor measurements were made (due to the lower free spectral range). Graphic

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Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems representations of the measured Q-factors can be seen in figure 4.17. The numerical measurements are noted in the table below.

Figure 4.17: Q-factor measurements made at 200 nm, 250 nm and 300 nm input waveguide to ring resonator separation gaps.

Separation Q-Factors

(nm) 25μmWindow 25μmNoWindow 50μmWindow 50μmNoWindow 200 7900 ± 900 14000 ± 800 13300 ± 1100 19000 ± 1700 250 8300 ± 1000 16500 ± 1700 14000 ± 1300 24300 ± 3500 300 11700 ± 2500 17300 ± 4000 16000 ± 1800 28100 ± 4300

These results clearly show that windowed systems have lower Q-factors than their non- windowed counterparts. This makes sense when considering Q-factor as a measure of how many oscillations light makes around the rings before decaying in value to 1/e intensity. Systems with greater losses, such as those with windows would have lower Q- factors.

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We can also see that the larger 50 μm radius ring resonators also have higher Q-factors in general. This may be explained by the greater radius of curvature decreasing the effect of bending losses. The uninterrupted path length of photons travelling through the larger ring resonators increases compared to smaller radius ring resonators. As such the angle of incidence is lower, leading to less significant losses from the total internal reflection angle required for whispering gallery mode production.

A final observation is that the measured Q-factors increase with increasing separation, however the observed extinction ratios (visible in figures 4.11-4.15) for these systems also decrease with increasing separation. This is because the optical coupling is weaker as the waveguide to ring resonator gap increases in distance. As such, the light that does manage to evanescently couple has a lower interaction with light in the input waveguide, and a lower chance of coupling back into the waveguide.

These measurements of Q-factor are useful as a reference, and by explaining the signal cleaning process, a greater understanding is gained of the main contributors to noise and ways to remove them from the transmission signal to produce cleaner spectra.

An important distinction which should be made is that single ring systems with a second drop port will have lower Q-factors than systems with a single input waveguide. This is due to losses of light through the secondary drop port waveguide, lowering the number of passes the photons can make before “decaying” out of the system. For the more complicated double ring systems, a second drop port is often used. For this reason it is important to include an analysis of the single ring Q-factors with secondary drop ports included.

4.2.2 Single Ring Drop Port

A second key configuration, with a greater relevance to upcoming double ring resonator tuning is the single ring resonator configuration with an additional drop port. A drop port is a secondary waveguide acting as an alternative output or “drop port” for light confined within the ring resonator. Figure 4.18 shows the optical flow of this configuration.

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Figure 4.18: A GDS based schematic of a single ring resonator with an additional drop port waveguide. The bold red lines indicate the directionality of light flow within this system.

The addition of a drop port leads to additional losses within the ring resonator. It is expected that systems with additional drop port will have a lower Q-factor compared to their single input wave guided equivalents.

Unfortunately the microchips studied in this research had their drop port diffraction gratings fabricated too close in proximity to the input diffraction grating. This made it impossible to take a direct measurement of the drop port signal on these devices. As a result, only direct comparisons can be made to the throughput results gained from the single input devices in section 4.2.1. The ring resonators are dimensionally identical to those in 4.2.1, but have the additional drop port feature as explained.

Figures 4.19-4.22 show background removed transmission spectra for the ring resonators under their titled conditions. When measuring this data, the previously observed sinusoidal effect was reduced (compared to the plain single ring data), so the step to remove it was omitted. The Gaussian flattening process was still applied. Data has been multiplied by incremental values of 10 to provide logarithmic offsets.

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25 μm Ring With Window, Background Removed 1000

100

10 200 nm 1 250 nm 300 nm

Intensity(Arbitrary Units) 0.1

0.01 1545 1550 1555 1560 1565 Wavelength (nm)

Figure 4.19: Transmission spectra for the 25 μm radius ring resonator with a window at 200 nm, 250 nm and 300 nm separation gaps.

25 μm Ring, No Window, Background Removed 1000

100

10 200 nm 1 250 nm 300 nm

Intensity(Arbitrary Units) 0.1

0.01 1545 1550 1555 1560 1565 Wavelength (nm)

Figure 4.20: Transmission spectra for the 25 μm radius ring resonator without a window at 200 nm, 250 nm and 300 nm separation gaps.

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50 μm Ring With Window, Background Removed 1000

100

10 200 nm 1 250 nm 300 nm

Intensity(Arbitrary Units) 0.1

0.01 1545 1550 1555 1560 1565 Wavelength (nm)

Figure 4.21: Transmission spectra for the 50 μm radius ring resonator with a window at 200 nm, 250 nm and 300 nm separation gaps.

50 μm Ring, No Window, Background Removed 1000

100

1 200 nm 250 nm

0.1 300 nm Intensity(Arbitrary Units) 0.01

0.001 1545 1550 1555 1560 1565 Wavelength (nm)

Figure 4.22: Transmission spectra for the 50 μm radius ring resonator without a window at 200 nm, 250 nm and 300 nm separation gaps.

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Figures 4.19-4.22 show a visible increase in peak width (indicating lower Q-factors) and depth (higher extinction ratio) compared to their single input equivalents from section 4.2.1. These changes can be attributed to the additional drop port, significantly increasing the systematic loss of light confined within the ring resonator. When fitting Lorentzian curves to the peaks to measure values of Q-factor, greater peak widths are observed, as shown in figure 4.23.

Lorentz Fit, 25 μm, 200 nm, No Window 1.2

0.8

0.6 Data 0.4 Lorentz

NormalisedIntensity 0.2

0 1561 1561.5 1562 1562.5 Wavelength (nm)

Figure 4.23: A Lorentzian peak fitted to data from the spectra for a 25 μm radius ring resonator with a 200 nm waveguide separation gap and without a window. This data can be compared directly with figure 4.15.

By measuring a four value average of Q-factor for the 25 μm radius rings and an eight value average for the 50 μm rings, average system Q-factors and their associated uncertainty can be seen in figure 4.24 and its accompanying table.

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Figure 4.24: Averaged Q-factors and their associated uncertainties at the stated gaps for the associated 25 μm radius, 50 μm radius, windowed and non-windowed systems. Numerical values are listed in the table below.

Separation Q-Factors

(nm) 25μmWindow 25μmNoWindow 50μmWindow 50μmNoWindow 200 3200 ± 400 3000 ± 400 4600 ± 400 5100 ± 600 250 4200 ± 700 4500 ± 100 5800 ± 900 6000 ± 800 300 5700 ± 700 5600 ± 1200 7200 ± 900 7800 ± 900

Assessing this data, the Q-factor values are much lower than their single ringed equivalents. As mentioned, this is expected as the drop port is a major source of loss in the ring resonators. Coupled with the high extinction ratios, this leads to noticeable difference in the transmitted signal compared to the plain ring resonators. One benefit of these larger spectral ‘footprints’ is that they have a broader signal, making peak fitting and tracking (for biosensing applications as an example) easier to achieve and more

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Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems accurate. For pure single point sensitivity and signal modulation applications however, higher Q-factors are more desirable.

Having now characterised the ring resonators in their single input and additional drop port formats the effects of thermally tuning these peaks can be investigated.

4.3 Single Ring Tuning

A significant amount of effort in this project has been spent characterising the ring resonators when applying different current values through the ‘on-chip’ heating elements.

As the temperature of silicon increases, so does its refractive index, which should result in a measureable change in the transmission spectrum of a ring resonator system. A depiction of the heating elements can be seen in figures 4.1, 4.3 and 4.25. By thermally tuning the ring resonators, it becomes possible to characterise device sensitivity. By keeping the microchip’s positioning stationary it is possible to apply two microneedles to the conductive pads to the chip’s surface. This enables the controlled flow of current through the selected TiN microheaters.

Using the experimental layout described in figure 4.25 (fibre optic input and electrical contacts to heating elements), the aim of this section is to investigate how power applied through the nanoscale heating element affects the peak positions in single ring transmission spectra.

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Figure 4.25: The general experimental setup for taking heating measurements. Rather than moving the platform with the chip, polished fibre optic cables are moved relative to the chip’s surface using 3D adjustable platforms.

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4.3.1 Method

In order to apply current through the heating element, careful manipulation of the electrical contact probes is required. The contact pads have an area of 50 μm x 50 μm and are slightly raised from the surface. The chip surface can be viewed using a high resolution, high zoom Thorlabs visible spectrum camera. A lamp can be used to illuminate the chips surface during the initial alignment process.

The ring resonator silicon chip could slip around on its fixed position surface. In order to prevent this, a thin layer of silica gel can be used to remove the air gap between the chip and its surface, increasing friction and reducing the sliding problem.

Once the area of interest on the chip has been aligned with the focal plane of the camera, the electrical contact can be brought into close proximity with the electrical contact pads. If the probes are initially aimed slightly behind the contact pads, and if the target is missed, the probes can be slid over the raised contact pad surface and with luck, may establish a connected circuit. This may cause slight scratching of the SiO2 surface, but should avoid actually damaging the waveguides as they are embedded underneath a 1600 nm protective SiO2 layer. When contacting the probes to the contact pads, it can be useful to use a resistance meter to indicate a connection. The heaters used in this experiment registered a resistance of ~1-2 kΩ depending on the connection quality.

The contact probes often slipped when exposed to slight optical bench vibrations, typically caused by an arm placed on the lab bench or a door closing. To avoid this, the contact probes were pressed firmly against the contact pads once a connection was made. Precautions were also taken to ensure laboratory traffic and disruption was minimised. Failure to do this could invalidate the results of an entire tuning run. It is critical to establish a firm electrical connection before aligning the light source and spectrometer arms; otherwise the chip may slide, invalidating the original optical alignment.

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In order to align the optics, visible red laser light can be transmitted through the fibre inputs, giving an indication of where the input and output arms are pointing. Using the camera and 3D adjustable platforms, the input and output arms can be brought into close proximity to the input and output diffraction gratings as shown in figure 4.24. Once an approximate alignment has been achieved, the IR light source and spectrometer can be connected to the fibre arms, and aligned further until maximum signal has been achieved. Signal strengths can be quite low, in which case, a brighter IR light source, such as the Thorlabs TLK-L1550M Littman configuration laser kit, can be used during the initial alignment stage.

Once the electronics and optics are aligned, spectral readings can be taken and current can be passed through the heating elements to tune the peaks. In this project a Tektronix PWS4602 programmable DC power supply unit was used as the heater power source.

In order to track the peak positions of the ring resonator transmission spectra as they are being tuned, the fastest scanning time possible is preferred, while maintaining a reasonable resolution. The broadband SLD source and OSA offer the quickest scanning times (approximately 20 seconds at highest resolution settings), making them the most suitable light source and spectral analyser combination for thermal tuning peak tracking experiments.

In the initial experiment the plain single ring resonator systems on the chip had been damaged before the experiment was setup, as a result, a single ring resonator with an additional drop port was used for testing instead. The only difference in spectral behaviour would be evident in the Q-Factors and extinction ratio values. In this instance the peak’s translational behaviour is of greater interest, which is equivalent for equal radius ring resonators. The ring resonator used in this case had a radius of 25 μm with no etched window above the ring. It had a separation of 250 nm from the input bus waveguide.

In order to gain a good spread of data for this initial testing, set heater currents were increased by 1 mA steps up to 8 mA and back down to 0 mA, checking for hysteresis

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Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems effects. Every 20 minutes, the heater current was changed over a five hour period. This was to ensure that a state of thermal stability could be achieved and so that average peak shifting values could be measured.

4.3.2 Results

As with all spectra, there were several peaks which could be analysed, and depending on their base wavelength, their behaviour would slightly change, shifting more for higher wavelength peaks and less for lower wavelength peaks. Analysing the data for the first peak in the measured spectrum, the following results were obtained.

Wavelength Shift vs Time: 25 μm, Peak 1 1528.5 85.79 mW

1528

65.21 mW 65.28 mW

1527.5 46.81 mW 46.81 mW

31.58 mW 1527 30.54 mW

Wavelength Wavelength (nm) 20.47 mW 11.56 mW 11.26 mW 1526.5 5.14 mW 5.33 mW 1.17 mW 1.42 mW 0 mW 1526 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 Time (s)

Figure 4.26: The wavelength of a resonant peak (peak 1) versus time with different applied powers.

Taking measurements of the average position at each heater power setting provided greater accuracy when plotting the following graph of wavelength shift vs applied power.

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Wavelength Shift Versus Applied Power: 25 μm, Peak 1 1528.5 y = 0.0236x + 1526.3 R² = 0.9999

1528

1527.5

1527 Wavelength Wavelength (nm)

1526.5

1526 0 10 20 30 40 50 60 70 80 90 100 Applied Power (mW)

Figure 4.27: Average wavelength shift versus applied heater power for Peak 1. A fitted line indicates the linear relationship between the two with an R2 value of 0.9999 and wavelength shift of 0.0236 nm/mW.

The power was ramped up and ramped down at approximately equal rates in order to determine whether any hysteresis effects would be observed. The power readings fluctuated slightly over time, but readings were taken every 20 seconds for a total duration of 1200 seconds (20 minutes) before each change of the power. This was to ensure that heater was stable and that reliable average readings for wavelength shift could be calculated. As shown in figure 4.27, there appears to be a clear relationship between the applied power and the measured wavelength shift of resonant peaks, with a gradient of 0.0236 nm/mW. This is to be expected as the refractive index of silicon increases approximately linearly with temperature for smaller increments above room temperature.2 This data also suggests that hysteresis effects are negligible when the devices are heated under a controlled regime such as this.

Equivalent testing was conducted on a 50 μm radius ring resonator with a 250 nm separation gap however the power was taken to a much higher value at 207 mW. At

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Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems higher power values, the peak position became unstable, showing an exponential decay over time, which affected the accuracy of average values, as a result higher power readings were discarded when calculating the gradient. In the 50 μm case, the gradient was found to be 0.0132 nm/mW. Figures 4.28 and 4.29 show these results.

Figure 4.28: The wavelength of a resonant peak (peak 1) versus time with different applied powers. Note how the peak positions appear to exponentially decay at higher applied power values.

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Wavelength Shift Versus Applied Power: 50 μm, Peak 1 1533.5 y = 0.0132x + 1531.4 R² = 0.9989

1533

1532.5

1532 Wavelength Wavelength (nm)

1531.5

1531 0 20 40 60 80 100 120 140 160 Applied Power (mW)

Figure 4.29: Average wavelength shift versus applied heater power for Peak 1. A fitted line indicates the linear relationship between the two with an R2 value of 0.9989 and wavelength shifting gradient of 0.0132 nm/mW

It should be noted that the response time of the OSA was longer than the time it takes for the heating element to stabilise. As a result, it is impossible to measure the behaviour of the ring resonators during the active heating stage in more detail using the described experimental setup.

4.3.3 Discussion

The results of this comparative investigation clearly show linear relationships between the power applied to the TiN heating elements and the position of resonant peaks/valleys. It is expected that the wavelength shift of both the 50 μm and 25 μm radius ring resonators would be dependent on the ‘perceived’ optical path length difference of light within the ring resonators. The 50 μm radius ring resonator demonstrated a power vs peak shift gradient equal to 0.56 of the 25 μm ring resonators gradient. Reasons for this could be due to the 50 μm having a greater proportion of its

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Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems ring resonator exposed to the heating element. In order to further investigate this effect, it would be worthwhile to repeat this experiment using a racetrack resonator, rather than a ring where it will be easier to ensure that equal lengths are heated.

These results also demonstrate that it is relatively easy to electrically tune the position of resonance peaks. While this effect may be arbitrary in single ring systems, in double ring systems the user would be able to tune the relative positions of individual peaks in a two peak system; this feature is useful for creating an overlap of peaks, which will be discussed later in this chapter. In a system where a window has been etched over one ring resonator but not over another, this tuning could be used to make a stable reference point for improved sensitivity biosensing.

4.4 Thermal Calibration

To take this investigation further, it is necessary to calibrate the setup to learn how applied power relates to temperature experienced by the ring resonator. An easy way to do this is to place the microchip on a varying temperature hot plate, heating the entire chip to see how the spectral results compare to those of the heating element tuning. Once the temperature measurements are known, it will be possible to directly correlate the temperature change to a difference in the refractive index of the ring resonator’s silicon.

While the measurements above are interesting to compare, from an experimental point of view, due to spatial constraints on the microchip surface, the systems with 25 μm radii and a 300 nm separation gap were found to be the most successful in calibration testing. Figure 4.30 shows the linear relationship of the single ring resonator with a 25 μm radius and a 300 nm separation.

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Wavelength Shift vs Power: 25 μm radius, 300 nm separation 1503

y = 0.0241x + 1500.6 R² = 0.9997

1502.5

1502

1501.5 Peakposition (nm)

1501

1500.5 0 10 20 30 40 50 60 70 80 90 Power Applied (mW)

Figure 4.30: The relationship between peak position (in nm) and applied heater power for a 25 μm radius ring resonator with a 300 nm separation from its input waveguide. As can be seen, there is effectively a linear relationship for power increases up to at least 85 mW. The graph has a gradient of 0.0241 nm/mW.

To extend this experiment, it would be useful to determine the effective temperature change experienced by the ring resonator, rather than just the applied power. This experiment aims to provide such data.

4.3.1 Method

A single ring resonator with a radius of 25 μm and an input waveguide separation of 300 nm was used for this experiment. The chip was placed on top of a heated pad next. A reference silicon chip was also placed next to the chip on the heating pad. A thermocouple was attached to the top of the reference silicon chip using thermal tape to give an approximate estimate of the surface temperature of the microchip. The assumption is made that this will give an equivalent to the temperature of the ring

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Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems resonator (as they are also fabricated close to the surface of the chip). An image of the setup can be seen in figure 4.31.

Figure 4.31: The microchip placed onto the thermal heating pad. When taking measurements, a sample of silicon was placed under the thermocouple (central wire) to give equivalent surface temperature readings.

Real time results for this experimental were taken using the broadband Thorlabs fibre coupled superluminescent diode (SLD) source centred on 1550 nm in conjunction with the 1.0 – 2.6 μm Thorlabs optical spectrum analyser, OSA 203B. While real-time results were being gathered, the microchip was heated from 19.4 °C up to 42.2 °C with stepped intervals and back down again to check for hysteresis effects.

As the entire chip was heated in this experiment, compared to the use of the TiN heating elements (which only heated a specific area), a conversion factor is required to make like- for-like comparisons. This further explained in figure 4.32.

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Figure 4.32: The chord of the ring resonator exposed to the heating element is measured at 26.22 μm. Taking the ring radius to be 25 μm and using simple trigonometry, the corresponding arc-length exposed to the localised heater is calculated to be 27.6 μm in length. When heating the entire ring resonator, the ring resonator circumference of 157.08 will be exposed to thermal shifting. This means that for equivalent resonant shifting caused by the heating element, approximately 5.69 times the temperature difference (of the full ring resonator) would be needed.

4.4.2 Results

Peak Position vs Temperature: 25 μm radius, 300 nm seperation 1504 y = 0.0886x + 1499.5 R² = 0.9976 1503.5

1503

1502.5

PeakPosition (nm) 1502

1501.5

1501 19 24 29 34 39 44 Temperature (Celcius)

Figure 4.33: A plot of peak position versus temperature in degrees Celsius. As can be seen, the main source of error is in the temperature readings, but a linear relationship is still observed. The graph has a gradient of 0.0886 nm/°C.

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Equating the two line equations and factoring for the different lengths of the ring which are heated, it can be deduced that the heating elements built onto the chip have a localised heating effect of approximately 1.548 °C/mW.

4.4.3 Discussion

The analysis above suggests that for the 25 μm radius ring resonator, a power of 80 mW applied through the heating element would lead to a localised temperature change of 124 °C in the ring resonator waveguide directly below the heating element. Comparatively, if the whole ring was being heated, a temperature change of 22 °C would be required to produce the same shift.

The value of the heating effect is an approximation based on several assumptions; one is that only the area directly above the TiN heating element will be responsible for heating the ring resonator. The reality is that the TiN heating element could possibly heat a larger region due to thermal dispersion around the heating element. There is also an assumption that the comparative silicon wafer will have the same temperature as the ring resonator chip, and that the temperature read from the surface is an accurate value.

The measured tuning gradient of 0.0886 nm/°C is in fairly close agreement with the measured shift of 0.1 nm/°C measured by Padgaonkar et al3 on slightly smaller diameter devices. The slight discrepancy may be related to the quality of thermocouple contact and the use of additional thermal tape to attach the thermocouple. The result stated above is the approximate heating effect of the TiN heater on the ring resonator. In reality, the temperature of the TiN heating element, which is slightly distanced from the ring resonator, would be even higher still.

In reality, this problem is more complicated than the quick comparison conducted here reflects, but the testing conducted here gives an indication of the temperatures involved when using the thermal heating elements.

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An important consideration when using these devices is that there is a substantial difference in thermal expansion coefficients between TiN (4.1 – 9.35 e-6/K) and SiO2 (0.55 – 0.75 e-6/K) which surrounds the heating elements. This is approximately a factor of 10 different; which, at higher temperatures may cause the heating elements to shatter, rendering them useless for further testing. The aluminium contact pads used to connect to the heating element are also at risk of melting at higher current values.

4.5 Double Ring System Thermal Tuning

Taking the thermal shifting experiment further, it would be beneficial to discover what happens when a double ring resonator system is analysed. The effect of tuning one resonant peak relative to a stationary one is of scientific interest and the built-in heaters will enable this experiment.

This section will look at the effects of thermally tuning one ring relative to the other in a Mach-Zehnder waveguide interferometer4 with two additional central ring resonators and a central drop port between them.

4.5.1 Method

The experimental setup from section 4.3 and figure 4.25 is used again for this investigation. The main optical system of interest for this experiment is shown in figure 4.34.

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Figure 4.34: The system of interest for double ring thermal tuning. By heating the lower TiN heating element, it is possible to heat one ring resonator separately from its mirrored ring. This leads to the tuning of one ring resonator interference peak relative to the stationary ‘reference’ peak of the upper ring resonator. Light is inserted through diffraction grating A, signal that interacts with the ring resonators can be detected in diffraction grating B and throughput signal can be detected in diffraction grating D. The ring resonators used in this experiment have a radius of 25 μm and a waveguide separation of 300 nm.

Results for this experimental setup were initially taken using the broadband Thorlabs fibre coupled superluminescent diode (SLD) source centred on 1550 nm in conjunction with the 1.0 – 2.6 μm Thorlabs optical spectrum analyser OSA 203B. Subsequently, higher resolution scans were taken using the external cavity diode laser (Thorlabs TLK-L1550M), tuneable from 1480 – 1610 nm with a maximum power of 35 mW in conjunction with the BaySpec super gamut NIR spectrometer which functions in the range of 900 – 1700 nm.

Initially results were gathered for the drop port signal using the faster (but lower resolution) broadband setup which enabled the tuning of a peak through its entire free spectral range. It was noted that the higher currents required to achieve this were damaging the heating elements, making repeat measurements unreliable.

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Following the initial lower resolution results, it was noted that in some cases, one peak seemed to have a lower relative starting wavelength (possibly due to manufacturing discrepancies). This made it possible to tune the travelling peak across the stationary peak at much lower currents (instead of having to tune across a full free spectral range), thus raising the step resolution and preventing irreversible damage to the heating elements. The higher resolution tuneable laser setup was then used to acquire data for the drop port and throughput at equivalent working currents, enabling ‘equivalent’ but not perfect comparisons between datasets.

4.5.2 Results

Figure 4.35: The tuning of one peak relative to a stationary peak for the setup described in figure 4.34. Starting from the bottom, each plot represents and heater current increase of 1 mA from 0 up to 13 mA. After this point, the heating element becomes unstable. As shown, the travelling peak is able to sweep across a whole free spectral range by a total distance of more than 4 nm. These plots were taken with the Thorlabs fibre coupled superluminescent diode (SLD) source centred on 1550 nm in conjunction with the 1.0 – 2.6 μm Thorlabs optical spectrum analyser OSA 203B. This resulted in lower signal and lower resolution results, but quicker scanning times.

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Figure 4.36: A closer look at the tuning of one peak relative to a stationary peak for the setup described in figure 4.34. This diagram shows 0.1 mA step intervals between 12 mA and 13.3 mA from bottom to top. The point of interest in these graphs is when the peaks overlap and it becomes apparent that the intensity of both peaks significantly reduces. These plots were taken with the Thorlabs fibre coupled superluminescent diode (SLD) source centred on 1550 nm in conjunction with the 1.0 – 2.6 μm Thorlabs optical spectrum analyser OSA 203B.

These initial observations revealed that at the points where peaks are expected to overlap, rather than combining intensities, they seem to cancel each other out. In literature, this is sometimes referred to as a coupled resonator induced transparency (CRIT)5-8 as discussed in the literature review. At the high temperatures required to cause a peak overlap over a free spectral range shift, the heating elements were prone to breaking, making repeat measurements difficult. As a result, higher resolution plots were taken on a chip with a slight manufacturing error induced offset of the peak positions at room temperature. This allowed much finer tuning of the applied currents and control of the tuned peak position. Results were also acquired for both throughput and drop port signals at equivalent heating powers. These results can be seen in figures 4.37 and 4.38.

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Figure 4.37: Drop port signal for the experimental setup shown in figure 4.34. Starting from the bottom the plots show the drop port spectrum from 0 – 6 mA in 0.3 mA current steps. The dotted line shows the expected shifted position for each current value. As shown, there is a clear interference effect occurring as the two peaks overlap. Analysing the two stationary peaks individually, it appears that the stationary resonance on the left starts lower and becomes greater in magnitude than the travelling peak. The stationary peak that starts on the right starts higher in magnitude and becomes lower than the travelling peak as it passes across.

Figure 4.38: Throughput signal for the experimental setup shown in figure 4.34. Starting from the bottom the plots show the drop port spectrum from 0 – 4.5 mA in 0.3 mA current

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Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems steps. Looking carefully, the formation of sharp Fano-shape features can be seen around 2.7 mA tuning current. The intensity is offset by multiplicative factors of 1000 for viewing ease on a logarithmic scale.

4.5.3 Discussion

While the drop port signal from this system reveals some interesting information about the nature of the two peaks interacting (i.e. that they form coupled resonator induced transparencies), the throughput signal appears to be very noisy. This will be due to the Mach-Zehnder effect of the double Y-splitting interferometer. When one arm is heated relative to the other, a shift in relative phase between the two arms will be expected. This is depicted in the wave-like background signal surplus to the interaction between the two peaks. A result of this secondary source of interference is that further analysis of the throughput data will be difficult in this system. Fortunately the studied chip also had an equivalent setup with a Y-Splitting junction and two ring resonators.

4.6 Y-Splitting Double Rings

Using a Y-splitting junction rather than a complete Mach Zehnder optical interferometer, it should be possible to separate the combined throughput signal from figure 4.38 into separated, non-interfering waveguide arm signals. From this point of view, it should be easier to analyse how light is interacting in the rings, and also how the rings interact with each other.

4.6.1 Method

Figure 4.39 shows a graphic representation of the Y-splitting device and labels the input and output gratings accordingly. As this setup creates two output waveguides, they are referred to as the travelling output and stationary output. The travelling output refers to signal travelling through the waveguide with the ring being heated. The stationary output refers to the opposite arm, which isn’t being thermally tuned, hence should show a stationary resonant spectrum.

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Figure 4.39: A) a graphic representation of the system studied in this experiment. Infrared light is injected through the laser input diffraction grating. This light is then split using the Y-splitter into two separate arms. Each arm has its own reference ring resonator with a built in heater unit for electrical heater tuning. The output for the heating arm is labelled the ‘travelling’ output, as the signal from this ring moves and the opposite output is called the stationary output, as the signal shouldn’t move in this arm. The centralised waveguide has a drop port diffraction grating for intermediate analysis of light interacting with each ring resonator. B) A photograph of the experimental injection and detector setup. Diffraction gratings 1 – 5 have their individual roles (1 being the laser input, 2 – the central drop port, 3 – drop port on opposite side, 4 – travelling peak throughput, 5 – stationary peak throughput).

As the experimental setup only allows for one input and output at one time, it is necessary to take repeat measurements for the travelling output and stationary output in separate experimental runs. To do this reliably, experimental conditions such as heater current have to be copied as closely as possible for both data sets. It is expected that the

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Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems drop port signal will be equivalent to the Mach-Zehnder configuration hence this wasn’t measured in this experiment.

When testing the device, the broadband infrared light source was used in conjunction with the OSA 203B spectrometer. To tune the device and acquire the highest tuning resolution possible, the heating element was tuned in 0.1 mA steps from 0 to 6 mA. Complete spectra were gained for both the travelling and stationary outputs under these conditions. A resistance of 1.19 kΩ was measured for the heating element used for these measurements. To ensure equivalent testing conditions, the results were taken under one continuous run over a 16 hour period run in a controlled temperature environment with no other users, sources of noise or unnecessary vibrations. The signal from the throughputs (both travelling and stationary) required the removal of both sinusoidal and Gaussian background effects from the signal. These effects were caused by the Y-spliter splitting the waves phase, reflections down the waveguide from the diffraction gratings at the end and general background shape from the light source.

4.6.2 Results

Scanning the travelling output (grating path 1-4), the raw data seen in figure 4.40 was acquired. All 60 plots have been overlaid to demonstrate the uniformity of background signal contribution

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Travelling Peak Raw Data

2.5E-08

2.0E-08

1.5E-08

1.0E-08

5.0E-09 AbsolutePower (mW)

0.0E+00 1536 1537 1538 1539 1540 1541 1542 Wavelength (nm)

Figure 4.40: The raw data acquired for the travelling peak tuned from 0 – 6 mA. The travelling peaks can be seen around 1538.5 – 1539.5 nm. As can be seen, there are several background effects, but these don’t change dramatically with tuning unlike the data in figure 4.38 for the double Y-splitting Mach-Zehnder interferometer setup.

Assessing the data in figure 4.40, it becomes apparent that the background signal effects need to be removed before the peaks can be accurately analysed.

From previous measurements, it is known that there is a Gaussian contribution from the light source, removing this effect results in the data shown in figure 4.41

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Travelling Peak Gaussian Removed 0.9 0.8 0.7 0.6 0.5 0.4 0.3

NormalisedPower 0.2 0.1 0 1536 1537 1538 1539 1540 1541 1542 Wavelength (nm)

Figure 4.41: The data with Gaussian background effects removed. The red dots represent the mean data point position and the red line shows a sinusoidal fit to this data, excluding regions of peak movement. Removing this sinusoidal effect results in the data represented in figure 4.42.

Travelling Peak First Sinusoidal Removed 0.7

0.6

0.5 0.4 0.3

0.2 NormalisedPower 0.1 0 1536 1537 1538 1539 1540 1541 1542 Wavelength (nm)

Figure 4.42: The data after the initial sinusoidal effect has been removed. As can be seen in the average data point plot and fitted sine curve, there still appears to be a second sinusoidal effect of lower intensity and higher frequency.

Removing this secondary sinusoidal noise and focussing on the peaks between 1538 and 1540 nm results in the data shown in figure 4.43. Spectral samples are presented every 0.5 mA of thermal tuning and are offset for viewing ease.

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Figure 4.43: Travelling peak data after background signal has been removed. Ascending from the bottom, the spectra represent data from 0 to 6 mA heating current values increasing in 0.5 mA steps. Data has been offset for viewing ease. As highlighted, it can be seen that the stationary peak contributes to the signal, and as the travelling peak approaches it, the overarching peak shape becomes a Fano-type resonance. After the peaks have overlapped (top plot), they appear to mirror their original interaction (bottom plot).

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If the same signal removing process is used for the stationary peak data, the results shown in figures 4.44 – 4.47 are gained.

Stationary Peak Raw Data 4.0E-08

3.5E-08 3.0E-08 2.5E-08 2.0E-08 1.5E-08 1.0E-08 AbsolutePower (mW) 5.0E-09 0.0E+00 1536 1537 1538 1539 1540 1541 1542 Wavelength (nm)

Figure 4.44: Stationary peak raw data.

Stationary Peak Gaussian Removed 1.2

0.8

0.6

0.4 NormalisedPower 0.2

0 1536 1537 1538 1539 1540 1541 1542 Wavelength (nm)

Figure 4.45: Stationary peak data with Gaussian background removed. Note how the sinusoidal background appears to be almost entirely out of phase with the data in figure 4.41.

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Stationary Peak First Sinusoidal Removed 0.8

0.7

0.6 0.5 0.4 0.3

0.2 NormalisedPower 0.1 0 1536 1537 1538 1539 1540 1541 1542 Wavelength (nm)

Figure 4.46: The Stationary Data after the first sinusoidal signal has been removed. Using the data average plotted in red dots.

Figure 4.46 shows that there isn’t a clearly correlated secondary sinusoidal background signature. As a result the data in figure 4.47 hasn’t had any further modification before being offset for viewing ease. As the magnitude of the secondary sinusoidal oscillations is small, it shouldn’t drastically affect the shape of peaks.

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Figure 4.47: Stationary peak data after background signal has been removed. Ascending from the bottom, the spectra represent data from 0 to 6 mA heating current values increasing in 0.5 mA steps. Data has been offset for viewing ease. As the travelling peak approaches the stationary, the overarching peak shape becomes a Fano-type resonance with the opposite orientation to figure 4.43.

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4.6.3 Discussion

The results displayed here show several interesting effects. The initial aim of removing Mach-Zehnder interferometer contributions to the throughput signal has been achieved, resulting in a steady background signal which can be removed to enable further analysis of the peak interactions. Interestingly, the use of a Y-splitting junction appears to add a secondary source of background noise which is in perfect antiphase between the stationary and travelling transmission signals.

Looking closely at the cleaned signals, it can be clearly seen that the signals interact with each other as they begin to overlap. As the travelling peak approaches the stationary peak, it appears to ‘push’ against the stationary peak and form a Fano-shape resonance.9- 11 At the same time, the stationary peak forms an opposite and equivalent Fano resonance to balance this.

As spectral sensing or switching probes, Fano resonances are typically much sharper along one edge than symmetric Lorentzian resonance shapes; this dramatically boosts their potential sensitivity.

4.7 Analysis of Double Rings

As the results above show, using the double ring configuration with a central drop port channel, coupled resonance induced transparency (CRIT) features have been produced. In addition to this, assessing the signals from the throughputs of the Y-splitting junction Fano-shape resonances have been produced, which can also be tuned. This section aims to determine the implications of these phenomena on the general device sensitivity and responsiveness.

4.7.1 Method

The responsiveness in this section represents the greatest change in normalised optical power against the corresponding power applied to the heating elements. As the base

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Chapter 4 – Characterisation and Thermal Tuning of Ring Resonator Systems units of optical normalised power are arbitrary due to the multiplicative factors involved in removing background contributions, a reliable method for achieving this comparison is to view transmission spectra in the logarithmic scale. In a logarithmic scale exponential curves can be easily fitted to the data, extrapolating the log of normalised optical power changed per unit of applied heater power.

Figure 4.48 demonstrates how the normalised optical power can quickly change as a small amount of power is applied to the heating element. Comparing the optical power difference to the current applied at various wavelengths, the regions with the greatest change in optical for the smallest change in applied heater power can be identified (representing the highest responsivity).

Travelling Peak Intensity vs Wavelength

~13 dB

0.1 NormalisedPower

0.01 1538.6 1538.8 1539 1539.2 1539.4 Wavelength (nm)

Figure 4.48: Travelling peak normalised power versus wavelength displayed on a logarithmic scale. In this graph, the blue line represents the travelling peak with a 4.7 mA driving current and the red line represents the travelling peak with a 5.0 mA driving current. The green line represents the expected Lorentzian peak shape generated by a single ring resonator with a 25 μm radius and a 300 nm waveguide separation gap, as a peak shape comparison. As highlighted, a 0.3 mA current can be enough to cause a 13 dB normalised power change in the travelling peak.

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If 2D normalised power maps are plotted of heater current versus wavelength, it becomes easy to identify the wavelengths which register the highest normalised optical power change for applied heater power over a specific tuning region. To make further comparisons, simulations can be made of the lateral tuning of the Fano shapes and the plain single ring resonator to see which setup provides the highest signal responsivity.

4.7.2 Results

Figures 4.49 and 4.50 show the central drop port intensity changes with heater current.

Figure 4.49: A 2D normalised power map of heater current versus wavelength for the central drop port data. As highlighted, there is a region where the two peaks overlap creating a coupled resonator induced transparency (CRIT). The normalised power change with applied power can also be analysed, resulting in high responsivity measurements.

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Figure 4.50: A closer look at the drop port spectra at different current values. Data is displayed on a logarithmic axis and has been offset by a multiplicative factor for viewing ease. As can be seen, the CRIT feature exhibits a large change in intensity for low changes in applied current. The Intensity base scale was originally in counts, but has been logarithmically offset so becomes arbitrary.

Figures 4.51 and 4.52 show the travelling peak intensity changes with heater current.

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Figure 4.51: a 2D intensity map of heater current versus wavelength for the travelling peak data. The circled region is where the Fano formation occurs. Measuring along the black line; the highest heating signal responsivity changes for this setup can be calculated.

Figure 4.52: A closer look at the travelling peak spectra at different current values. As shown, the formation of Fano resonances leads to great differences in intensity at the highlighted wavelength.

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Figures 4.53 and 4.54 show the stationary peak intensity changes with heater current.

Figure 4.53: A 2D intensity map of heater current versus wavelength for the stationary data. The circled region is where the Fano resonance occurs. Measuring along the black line; the highest heating signal responsivity changes for this setup can be calculated.

Figure 4.54: A closer look at the stationary peak spectra at different current values. As shown, the formation of Fano resonances leads to great differences in intensity at the highlighted wavelength.

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When the change in intensity is analysed against the applied power (converting from current for linearity), along the highlighted lines of interest and at the most responsive power settings, the responsivities highlighted in figure 4.55 and its corresponding table can be achieved. For further comparison, simulated responsivities for single ring resonator tuning and Fano translation tuning (i.e. keeping the Fano shape fixed and tuning separately, using the central heating channels for example) have been added to the plot. This allows the determination the most responsive approach for general sensing and switching applications.

Figure 4.55: Intensity versus applied heater power for the range of assessed setups. Intensity is represented on a logarithmic scale and data fits have been applied using the f(x) = A*ekx equation. As shown, CRIT tuning produces the greatest responsivity, followed closely by Fano translational tuning. Travelling peak, stationary peak and single ring peak tuning produce roughly equal responsivities when compared. As intensities have been normalised and offset by multiplicative factors on a logarithmic scale, the units of intensity are arbitrary.

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Tuning Type Exponential Fitting Gradient, Relative responsivity k, (mW-1) (vs single ring) f(x) = A*e(kx) CRIT 1.626 2.697 Fano Translation 1.218 2.020 Travelling 0.701 1.163 Single Ring 0.603 1 Stationary Fit 0.479 0.794

4.7.3 Discussion

As shown with further analysis, CRIT type tuning has the greatest responsivity, being 2.7 times higher than an equivalent single ring resonator. Using this information a biosensing system with two ring resonators could be imagined, where one ring is exposed to an analyte, while the other is tuned to perfectly match the spectral positioning of the windowed ring. They would start in a CRIT type state, and as analyte passes and attaches to the sensing ring, 2.7 times less material would be required to bind to the ring in order to sense its presence. Using this approach, the need for a spectral analyser could be completely removed, using instead, optical band pass filters and photodiodes to detect signal. This could remove one of the key obstacles to commercialising ring resonator biosensing technology. If used for optical switching this factor also translates to 2.7 times less energy required to switch a signal between on/off states. If the TiN heating element was instead replaced by a PN junction constructed within one of the ring resonators, it would be much easier to achieve efficient optical switching.

The ability to switch peak shapes from individual Lorentzian shapes into merged Fano shapes also has several advantages. Fano shapes have directionally asymmetric orientations and are typically much sharper down one slope than Lorentzian peaks are. This is highlighted by their responsivity being double that of a single ring.

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While these results are only comparing devices under equivalent fabrication conditions, it is not completely unreasonable to suggest that similar effects may also be achievable in systems with higher Q-factors manufactured using more advanced techniques such as sub wavelength grating wave guiding for sensing and etchless wave guiding for switching.

4.8 Conclusion

To summarise, in this chapter single ring resonator systems with 25 μm and 50 μm ring resonator radii have been characterised, along with systems both with and without windows for sensing. The throughput responses of ring resonators with a secondary drop port waveguide have also been measured.

Following this, the thermal tuning of a single ring resonator system was achieved using the on-chip heater and a separate external heating plate. Comparing these experiments the thermal sensitivity of the ring resonators was calibrated.

Progressing to double ring resonator systems, an investigation was conducted on the effects of thermally tuning double ring resonators in both a Mach-Zehnder interferometer and Y-splitting configuration with a central drop port channel. Looking at the responsivities, it was discovered that CRIT tuning through the central drop port provided a 2.7 times increase in sensitivity compared to an equivalent single ring resonator, providing a viable alternative to the single ring configuration. The creation of Fano Resonances in the double ring system introduced a 2 fold sensitivity increase compared to a single ring and a peak directionality which may also be exploitable in different applications.

The in-depth experimental characterisation here gives an indication of the typical experimental phenomena encountered when working with ring resonators and general techniques for analysis with different experimental systems. In the next chapter an investigation will look into modelling the behaviours encountered here, developing a theoretical understanding of why the observed CRIT and Fano behaviours are seen.

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4.9 References

1. C. Ciminelli, C. M. Campanella, F. Dell’Olio, C. E. Campanella and M. N. Armenise, Progress in Quantum Electronics, 2013, 37, 51-107. 2. H. Li, Journal of Physical and Chemical Reference Data, 1980, 9, 561-658. 3. V. Padgaonkar, A. Arbor, M. Lipson and S. Pradhan, NNIN REU Research Accomplishments, 2004, 98-99. 4. B. Luff, J. S. Wilkinson, J. Piehler, U. Hollenbach, J. Ingenhoff and N. Fabricius, Journal of lightwave technology, 1998, 16, 583. 5. D. D. Smith, H. Chang, K. A. Fuller, A. Rosenberger and R. W. Boyd, Physical Review A, 2004, 69, 063804. 6. Y. Zhang, S. Darmawan, L. Y. M. Tobing, T. Mei and D. H. Zhang, J. Opt. Soc. Am. B, 2011, 28, 28-36. 7. S. Darmawan, L. Y. M. Tobing and D. H. Zhang, Optics Express, 2011, 19, 17813-17819. 8. X. Zhou, L. Zhang, W. Pang, H. Zhang, Q. Yang and D. Zhang, New Journal of Physics, 2013, 15, 103033. 9. B. Luk'yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen and C. T. Chong, Nature materials, 2010, 9, 707-715. 10. F. Wang, X. Wang, H. Zhou, Q. Zhou, Y. Hao, X. Jiang, M. Wang and J. Yang, Optics express, 2009, 17, 7708-7716. 11. S. Fan, W. Suh and J. Joannopoulos, JOSA A, 2003, 20, 569-572.

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Chapter 5 - Modelling of Double Ring System

5.1 Introduction

Having assessed the experimental results gained in chapter 4, a logical next step is to investigate the theory behind the double ring tuning phenomena previously discovered. The occurrence of Fano resonance peak shapes and coupled resonator induced transparencies (CRITs) suggests that there are discreet effects happening within the ring resonators which modelling may help to resolve. Taking the approach of transfer matrix modelling, it will be important to see how this technique performs when modelling ring resonators.

The aims of this chapter are to:  Review the factors which influence ring resonator behaviour.  Look into Transfer Matrix modelling techniques.  Determine a model which fits the experimental data the best along with reasoning for its choice.

5.2 Influencing Factors of Light Confined Within Ring Resonators

When light is confined within a ring resonator, there are essentially five factors which can cause significant differences in its transmission spectra. These are changes to the effective refractive index, losses due to scattering and absorption, the coupling efficiency of input and output waveguides, the phase of light confined within the ring resonator and the path length of light travelling around the resonator.

On a basic level, the individual peaks and dips caused by a single ring resonator can be mathematically modelled by the Lorentzian function, as described in chapter 4:

푎2 퐹(푥) = 퐼 2 2 + 퐶 (푥 − 푥0) + 푎

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Where I is the height (-ve for depth) of the peak, a is the half width at half of maximum

(HWHM) value, x0 is the central peak position and C represents the baseline intensity Y- intercept (1 for normalised data).

In order to describe the behaviour of single ring resonators coupled to an input waveguide, reference can be made to the early transfer matrix models proposed by Yariv et al in the early 2000s.1-3 Using figure 5.12 as a reference, a basic transfer matrix model for single ring resonators can be derived.

Figure 5.1: The basic geometry for ring resonator waveguide coupling.2

In this process, the coupling region can be thought of as a box, with two input field signals

(a1 and a2) and two output field signals (b1 and b2). As light with field a1 enters the ‘box’, it can either be transmitted, t, or coupled to the ring resonator, κ, transmitted light contributes to the throughput signal, b1, and coupled light becomes confined to the ring resonator, b2. As light loops around the ring resonator (with a perimeter L), it experiences losses α, becoming signal a2, which re-enters the initial coupling ‘box’ and undergoes the process again.

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The interaction within the box can be described by the following matrix equation:

푏1 푡 휅 푎1 | | = | ∗ ∗| | | 푏2 −휅 푡 푎2

The complex mode amplitudes bi and ai are normalised so that their squared magnitude corresponds to the modal power. The coupling matrix is unitary, meaning that

|휅2| + |푡2| = 1

The coupling coefficient κ can take on different forms depending on the experimental setup. Equating the input a1 to 1, all fields can be normalised to a1. As such, the transmission around the ring can be described by the following:

푖휃 푎2 = 훼푒 푏2

Where α is the internal circulation factor, a real number with zero internal losses being equal to 1. With these equations in mind, the transmitted signal and light around the ring resonators can be equated to the following:

−훼 + 푡푒−푖휃 −훼휅∗ 푏 = 푎 = 1 −훼푡∗ + 푒−푖휃 2 −훼푡∗ + 푒−푖휃

The transmission after the ring resonator can be written as:

2 | |2 | | ( ) 2 훼 + 푡 − 2훼 푡 cos 휃 + 휑푡 |푏1| = 2 2 1 + 훼 |푡| − 2훼|푡| cos(휃 + 휑푡)

Where

푡 = |푡|푒푖휑푡

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The total power circulating the ring resonator can be given by:

2( | |2) 2 훼 1 − 푡 |푎2| = 2 2 1 − 2훼|푡| cos(휃 + 휑푡) + 훼 |푡|

At resonance, (θ + φt) = m2π, with m as an integer where θ = βmL, β is the phase constant and L is the total ring circumference, 2πr. As such, the equations break down to:

(훼 − |푡|)2 훼2(1 − |푡|)2 |푏 |2 = |푎 |2 = 1 (1 − 훼|푡|)2 2 (1 − 훼|푡|)2

When the internal losses α equal the coupling losses, the total transmission equals zero, hence the comb toothed transmission spectra is produced. This is referred to as the critical coupling condition.

The addition of a drop secondary waveguide to the ring resonator (drop port) changes the situation slightly. From the perspective of the original waveguide, the drop port modifies the internal loss parameter from α to α|t2|, where ‘1’ and ‘2’ subscripts denote the original and new waveguides. Changing t to t1, κ to κ1 and α to α|t2|, all of the above equations still apply. The output power from the second waveguide can be described by the following equation at resonance:

| |2 | |2 2 (1 − 푡1 )(1 − 푡2 )훼 |푎푟| = 2 (1 − 훼|푡1푡2|)

2 The power can be fully transferred from the input waveguide to the drop port when |ar|

= 1, in systems where there are negligible internal losses, α = 1, and |t1| = |t2|. As such, 2 the transfer of power between waveguides can be controlled by changes in t1 or t2.

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5.3 3x3 Transfer Matrix Modelling

The double ring system with a central drop port is a bit more complicated than the single ring analysis which has just been covered. Similar double ring resonator problems have been theoretically investigated by a few research groups,4-6 but these theories can be complicated and require lengthy calculations that depend on chosen boundary conditions and the particular geometry chosen. As a result, being personally experimentally inclined, I have been working with Matteo Cherchi from the VTT Technical Research Centre of Finland, who has developed a novel working 3x3 transfer matrix model7 for the double ring experimental system analysed in chapter 4.

The aim of Matteo’s model is to generalise the standard 2x2 matrix approach covered in section 5.2 to cover any system with 3x3 couplers, calculating the transfer matrix of any complicated system just as a product of simple 3x3 matrices. Figure 5.2 shows a visual guide to resolving this problem.7

Figure 5.2: a) A visual representation of the light pathways. b) The focussed section for modelling. c) A topologically equivalent circuit divided into 5 sections to build a suitable transfer matrix model.7

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The system in figure 5.2b can be divided into a topologically equivalent cascade of 3-arm sections. These include two sections with 2x2 couplers, one uncoupled waveguide, two sections with three uncoupled arms and one where all three waveguides are coupled together. All of these are shown in figure 5.2c. All systems have a characterising forward propagating fields Ef and two backward propagating fields Eb and Ed. Ultimately the model aims to determine the transfer matrix T linking the field on the right hand side to the field on the left hand side of the system, resulting in:

휓푅 = 푇푡표푡휓퐿

Where vectors ψx (x = R, L) are defined as:

푋 퐸푓 푋 휓푋 = (퐸푏 ) 푋 퐸푑

Figure 5.2c shows that the transfer matrix T is a product of five matrices:

푇푡표푡 = 푉2푈2푊푈1푉1

Where Vp matrices accounts for the 2x2 coupling, Up propagates the uncoupled waveguides and the matrix W models the central 3x3 coupling. The Up matrices can be based on the 2x2 model and can be written as follows:

푒푖휑푝 0 0 −푖휑 푈푝 = ( 0 푒 푝 0) 0 0 1

The phase change of Ed can be set to zero as no light is input this way, φp ≡ kpLp/2 are the phases accumulated by the Ef and Eb fields propagating with a propagation constant kp (this can also have an imaginary part to account for propagation losses) in half the ring length Lp.

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The matrices for Vp can be written as follows:

−1 푟∗ 0 1 푝 푉푝 = (−푟푝 1 0 ) 푖푡푝 0 0 푖푡푝

The element (Vp)33 = 1 imposes zero phase change to Ed, without any loss of generality. The top left 2x2 submatrix is the standard transfer matrix of a coupler,8 with a field transmission tp and field reflection rp.

Matrix W requires more effort to derive. The transfer matrix of a 2x2 coupler is derived from the scattering matrix. By adapting the scattering matrix, it is possible to derive a 3x3 coupling transfer matrix. Figure 5.3 shows a comparative breakdown.

Figure 5.3: a) Scattering matrix model of a 2x2 coupler, b) transfer matrix model for the same coupler, c) scattering matrix model of a 3x3 coupler and d) transfer matrix model for the same coupler.7

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The 2x2 scattering matrix in figure 5.3a links input and output values as follows:

휙푂 = 푆휙퐼

With input and output vectors ϕX (X = I, O) defined as follows:

푋 퐸1 휙푋 = ( 푋) 퐸2

The 2x2 transfer matrix T (Fig 5.3b) linking the left and right hand sides of the coupler can be defined as follows:

휓푅 = 푇휓퐿

Where the vectors ψX (X = R, L) are defined as:

푋 퐸푓 휓푋 = ( 푥 ) 퐸푏

From the linked input and output values and using the identities:

퐿 퐼 퐿 푂 푅 푂 푅 퐼 퐸푓 = 퐸1, 퐸푏 = 퐸1 , 퐸푓 = 퐸2 푎푛푑 퐸푏 = 퐸2

T can be calculated as:

1 |푆| 푠 푇 = ( 22) 푠12 −푠11 1

Where |S| is the determinant of matrix S. Using the standard scattering matrix for S:

푟 푖푡 푆 = ( ) 푖푡 푟∗

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Assuming |S| = 1 due to it being a lossless coupler, results in:

1 −1 푟∗ 푇 = ( ) 푖푡 −푟 1

As |T| = 1 too, for synchronous couplers:

푟 = cos(휅퐿 ) { 퐶 푡 = sin(휅퐿퐶)

With κ being the coupling coefficient and with LC being the coupling length. In order to extend these relations to asynchronous couplers with a propagation constant differing by δ, the reflection and transmission coefficients can be used as:

푟 = cos(휇퐿 ) + 푖 sin(휇퐿 ) cos(훾) { 퐶 퐶 푡 = sin(휇퐿퐶) sin(훾)

In which case:

훿 2 −훿 휅 휇 ≡ √휅2 + ( ) 푎푛푑 cos 훾 ≡ , 푖푚푝푙푦푖푛푔 sin 훾 ≡ 2 (2휇) 휇

In order to derive the 3x3 transfer matrix T in figure 5.3d from the scattering matrix S (in figure 5.3c), the following identities can be used:

퐿 퐼 퐿 푂 퐿 푂 푅 푂 푅 퐼 푅 퐼 퐸푓 = 퐸1, 퐸푏 = 퐸1 , 퐸푑 = 퐸2 , 퐸푓 = 퐸3 , 퐸푏 = 퐸3 푎푛푑 퐸푑 = 퐸2

Which lead to T:

1 |푆| −푀12 푀21 푇 = ( 푀33 −푠22 푠12 ) 푀31 −푀32 푠23 −푠13

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Where 푀 ≡ |(푠 ) | are the (i, j) minors of the matrix S, the determinants of the 푖푗 푝푞 푝≠푖. 푞≠푗 submatrices are obtained by eliminating the i-th row and the j-th column.

To calculate the scattering matrix of the coupler in figure 5.3c, the geometric approach adopted by Matteo Cherchi in 2003 can be used.9 In this approach, the differential equations of the coupled mode theory in space are used.10, 11 These are found in literature on tri-couplers.12, 13 Looking specifically at asynchronous couplers with two identical external waveguides, but a different middle waveguide, δ being the difference of propagation constants, and assuming nearest neighbour coupling only and no losses, the system of differential equation is:

푑퐸1 훿 = 푖휅퐸2 + 푖 퐸1 푑푧 2 푑퐸 훿 2 = 푖휅(퐸 + 퐸 ) − 푖 퐸 푑푧 1 3 2 2 푑퐸 훿 3 = 푖휅퐸 + 푖 퐸 { 푑푧 2 2 3

1 The symmetric and anti-symmetric combinations can be defined as 퐸 ≡ (퐸 + 퐸 ) and 푆 √2 1 3 1 퐸 ≡ (퐸 − 퐸 ). These reduce to the 2x2 case, with EA already being an eigenmode of 퐴 √2 1 3 the system:

푑퐸2 훿 = 푖√2휅퐸푆 − 푖 퐸2 푑푧 2 푑퐸 훿 푆 = 푖√2휅퐸 + 푖 퐸 푑푧 2 2 푆 푑퐸 퐴 = 0 { 푑푧

Where κ is the coupling coefficient between two adjacent waveguides. If the input and output vectors ϕX (X = I, O) are introduced:

푋 퐸2 푋 휙푋 = (퐸푆 ) 푋 퐸퐴

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The solution can be written as 휙푂 = 푆̅휙퐼 where 푆̅ is the scattering matrix in the rotated basis {E2, ES, EA}

휚 푖휏 0 푆̅ = (푖휏 휚∗ 0) 0 0 1

Defining the reflection and transmission coefficients:

휚 = cos(휇퐿 ) + 푖 sin(휇퐿 ) cos(훾) { 퐶 퐶 휏 = sin(휇퐿퐶) sin(훾)

Where Lc is the effective coupler length and:

훿 2 −훿 √2휅 휇 ≡ √2휅2 + ( ) 푎푛푑 cos 훾 ≡ , 푖푚푝푙푦푖푛푔 sin 훾 ≡ 2 (2휇) 휇

In synchronous couplers, δ = 0, leading to 휚 = cos(√2휅퐿퐶) and 휏 = sin(√2휅퐿퐶). In order to switch back to the original basis {E1, E2, E3}, the matrix of basis change can be used:

1 1 0 1 푅 = (0 √2 0 ) √2 1 0 −1

Which is involutory meaning R = R-1. As such, the scattering matrix takes the form:

1 + 휚 푖√2휏 −(1 − 휚) 1 푆 = 푅푆̅푅 = ( 푖√2휏 2휚∗ 푖√2휏 ) 2 −(1 − 휚) 푖√2휏 푖√2휏

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This matrix is unitary and describes the coupler from figure 5.3c. As such, the transfer matrix W from figure 5.2c can be written as follows:

−2 1 + 휚 −푖√2휏 1 푊 = (−(1 + 휚) 2휚∗ −푖√2휏 ) 1 − 휚 푖√2휏 −푖√2휏 −(1 − 휚)

W is unitary with |W| = -1. With this result, the 3x3 transfer matrix for the coupled ring resonators has been completed.

The final step is to impose the boundary conditions of figure 5.2a and calculate the

퐿 퐿 푅 퐿 푅 푖휃 unknown values 퐸푏 , 퐸푑, and 퐸푓 assuming 퐸푓 = 1/√2 and 퐸푏 = 푒 /√2, and assuming a relative phase difference between the two inputs. Explicitly writing the linear equations

휓푅 = 푇푡표푡휓퐿 in terms of matrix components 푇푡표푡 = (푡푖푗) and the field components, the following calculation can be made:

푖휃 퐿 푒 푡33 − 푀12 퐸푏 = 1 푅 퐸푓 √2푀11 푖휃 √2 푖휃 푒 푡32 − 푀12 휓 = , 휓 = 푒 → 퐸퐿 = − 퐿 퐸퐿 푅 푑 푏 √2 √2푀11 퐿 푖휃 퐸푑 푒 푀 + |푇 | ( ) ( 0 ) 푅 21 푡표푡 퐸푓 = { √2푀11

Where 푀 ≡ |(푡 ) | indicates the (i, j) minors of the matrix T . 푖푗 푝푞 푝≠푖,푞=푗 tot

As an example of boundary conditions, the response of the system where light is launched into only one input can be calculated as follows:

푀 퐸퐿 = − 12 푏 푀 1 푅 11 퐸푓 퐿 퐿 푀13 휓 = (퐸푏 ), 휓 = ( ) → 퐸 = 퐿 푅 0 푑 푀 퐸퐿 11 푑 0 | | 푅 푇푡표푡 퐸푓 = { 푀11

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Ultimately, when programmed through MATLAB or similar software, this produces a model in which the following parameters can be changed to produce transmission spectra:  The radius of the ring resonator.  The coupling coefficient between waveguides and rings.  The relative phase of light in each of the input arms.  The path length and losses of light in the ring resonators respectively.

5.4 Comparison between Model and Experimental Data

Running the model from 5.3 through MATLAB, it is possible to determine how each of the factors mentioned (relative phase, effective refractive index, coupling strength and losses) affects the transmitted outputs through the central drop port, the stationary output and the travelling output. The first investigation will be looking at how each factor affects the shape of transmission spectra.

5.4.1 Changes Due to Losses

The first investigation will look at the effect of changing the losses on an arbitrary travelling, stationary and drop port signal. In this observation, A ring resonator radius of 25 μm was used for both rings. The relative phase of light in both input arms was 0, i.e. the light was in phase. The coupling coefficient of each ring resonator was programmed as 0.12. The effective refractive index of each ring was 2.6258 and 2.6244 (i.e. a difference of 0.0014), this was to induce an offsetting of peak positions. In order to observe the effect of losses, a simulation was run for losses of 0, 20, 40, 60, 80 and 100 dB/cm. The aim was to take losses into the extreme and see how effectively the peak shape can be changed through this mechanism. The results of this test can be seen in figures 5.4 and 5.5.

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Change Due to Losses Throughput 0.6

0.5

100 dB/cm 0.4 80 dB/cm 0.3 60 dB/cm

Transmission 0.2 40 dB/cm 0.1 20 dB/cm

0 0 dB/cm 1537 1537.5 1538 1538.5 1539 1539.5 1540 Wavelength (nm)

Figure 5.4: Changes due to losses at one of the throughputs. As shown, losses of approximately 50 dB/cm are required to induce a transmission difference of 20%. As losses increase, the width of the peak shape increases also, as would be expected (higher losses lead to lower Q-Factors).

Change Due to Losses Drop Port 0.6

0.5

100 dB/cm 0.4 80 dB/cm 0.3 60 dB/cm

Transmission 0.2 40 dB/cm 0.1 20 dB/cm

0 0 dB/cm 1537 1537.5 1538 1538.5 1539 1539.5 1540 Wavelength (nm)

Figure 5.5: Changes due to losses at the central drop port. As seen here the change in transmission drops off noticeably faster than the throughput signal for equivalent loss changes. Also of note is how the form of the secondary peak on the right is not affected by losses in the changing peak on the left.

CMOS fabricated single mode strip waveguides were reported in 2004 by Vlasov et al14 with losses of approximately 3.6 ± 0.1 dB/cm. With this in mind, it seems sensible to

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Chapter 5 – Modelling of Double Ring System regard the effect of losses as negligible when modelling these particular double ring systems. From an analytical point of view, the fewer active variables, the easier it will be to draw conclusions on the cause of effects. It is also difficult to justify a significant change in the absorption coefficient of silicon, a material which is optically transparent at 1500 nm wavelength, without it undergoing a substantial material property change.

5.4.2 Changes Due to the Coupling Coefficient

The second observation will look the effect of the coupling coefficient on the form of the peak shapes. For this comparison, ring resonators with a radius of 25 μm were used for both rings. The relative phase of light in both input arms was 0. The loss in both ring resonators is 0. The effective refractive index of each ring was the same at 2.6258 and 2.6244 (i.e. a difference of 0.0014).

In order to explore all possibilities with the coupling coefficients, observations will be made to see what happens if both coefficients are changed by equal amounts (Figures 5.6 and 5.7), and if one coefficient is changed relative to the other (Figures 5.8 – 5.10).

Change Due to Coupling Throughput LHS 0.6

0.5

0.04 - 0.04 0.4 0.06 - 0.06 0.3 0.08 - 0.08

Transmission 0.2 0.10 - 0.10 0.1 0.12 - 0.12

0 0.14 - 0.14 1537 1537.5 1538 1538.5 1539 1539.5 1540 Wavelength (nm)

Figure 5.6: The effect of changing both coupling coefficients on throughput 1 (left hand side). As shown, increasing coupling strength increases the width of the peak, reducing the Q-factor as a result. The right handed peak is a mirrored under the same conditions.

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Change Due to Coupling Drop Port 0.6

0.5

0.04 - 0.04 0.4 0.06 - 0.06 0.3 0.08 - 0.08

Transmission 0.2 0.10 - 0.10 0.1 0.12 - 0.12

0 0.14 - 0.14 1537 1537.5 1538 1538.5 1539 1539.5 1540 Wavelength (nm)

Figure 5.7: The drop port signal when equal but different coupling strengths are used. As shown, the peak shapes are symmetric and the greater coupling strengths have a greater prohibiting effect on the central space between the two peaks than on the outside edges.

Change Due to Coupling Throughput LHS 0.6

0.5

0.4 0.04 - 0.16 0.3 0.06 - 0.14

Transmission 0.2 0.08 - 0.12 0.1 0.10 - 0.10

0 1537 1537.5 1538 1538.5 1539 1539.5 1540 Wavelength (nm)

Figure 5.8: Change due to coupling in the left-hand side throughput peak as differing coupling strengths for each ring are used. As shown, this shape is similar that of figure 5.6.

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Change Due to Coupling Throughput RHS 0.6

0.5

0.4 0.04 - 0.16 0.3 0.06 - 0.14

Transmission 0.2 0.08 - 0.12 0.1 0.10 - 0.10

0 1537 1537.5 1538 1538.5 1539 1539.5 1540 Wavelength (nm)

5.9: Change due to coupling in the right-hand side throughput as differing coupling strengths for each ring are used. Unlike the peaks in figure 5.6, these don’t get broader but instead reduces in amplitude while maintaining the same FWHM values with increasing coupling strength. This is contrary to the case where both coupling strengths increased by equal amounts, where the peak amplitude remains constant but FWHM values increase.

Change Due to Coupling Drop Port 0.6

0.5

0.4 0.04 - 0.16 0.3 0.06 - 0.14

Transmission 0.2 0.08 - 0.12 0.1 0.10 - 0.10

0 1537 1537.5 1538 1538.5 1539 1539.5 1540 Wavelength (nm)

Figure 5.10: The change due to coupling as the left hand side and right hand side change by the amounts stated in the key. As shown, the peak with the lowest coupling strength maintains transmission strength of 0.5, while the side which has a higher coupling strength reduces in amplitude as the difference increases and the peak FWHM value remains equivalent.

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The alternate coupling above is a demonstration where the sum of coupling strength is equal to 0.2; this explains the corresponding peak broadening on the LHS and amplitude shortening on the RHS that is witnessed in figures 5.8-5.10. A final coupling comparison will need to look at a setup where the coupling in one ring remains constant while another one changes. This will be the closest match to what is experience during experimental process. As the coupling region is heated, the effective distance that light needs to couple through will increase slightly, weakening the coupling in one ring as more heater current is applied. Graphs representing the effect of tuning one coupling coefficient relative to a stationary one are shown in figures 5.11 – 5.13.

Change Due to Coupling Throughput LHS 0.6

0.5

0.4

0.3 0.06 - 0.10 0.10 - 0.10

Transmission 0.2 0.14 - 0.10 0.1

0 1537 1537.5 1538 1538.5 1539 1539.5 1540 Wavelength (nm)

Figure 5.11: Changes due to coupling due to tuning of the LHS relative to the RHS peak. As shown, peak amplitude remains relatively constant while peak width increases as the LHS coupling coefficient is increased.

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Chapter 5 – Modelling of Double Ring System

Change Due to Coupling Throughput RHS 0.6

0.5

0.4

0.3 0.06 - 0.10 0.10 - 0.10

Transmission 0.2 0.14 - 0.10 0.1

0 1537 1537.5 1538 1538.5 1539 1539.5 1540 Wavelength (nm)

Figure 5.12: Changes due to coupling due to tuning of the LHS relative to the RHS peak. As shown, peak amplitude on the right hand side also remains relatively constant while peak width increases as the LHS coupling coefficient is increased.

Change Due to Coupling Drop Port 0.6

0.5

0.4

0.3 0.06 - 0.10 0.10 - 0.10

Transmission 0.2 0.14 - 0.10 0.1

0 1537 1537.5 1538 1538.5 1539 1539.5 1540 Wavelength (nm)

Figure 5.13: The drop port signal as the LHS peak is tuned relative to the RHS peak. As shown, increased coupling in the LHS leads to peak widening in both sides.

Figures 5.11 – 5.13 show that a difference in coupling can lead to a slight asymmetry. A relevant observation however is that the thermal expansion coefficient for fused silica is 0.55x10-6/°C.15 Corresponding to a heater power of 80 mW, this leads to a change in localised temperature of ~123 °C; this in turn leads to a thermal expansion factor of 6.77x10-5, which, over a 300 nm separation gap is essentially negligible. As such, going

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Chapter 5 – Modelling of Double Ring System forward, to reduce the number of modelling variables the coupling coefficients will remain constant.

5.4.3 Changes Due to the Relative Phase and Effective Refractive Index

As a final look at the model before making direct comparisons with data, it is important to look at the relative phase of light within each input arm, and the effective refractive index of the ring resonators (affecting the observed path length for light within the ring resonators). As one TiN heating element is heated, the input arm on that side is also heated relative to the other. This is expected to lead to a change in the relative phase between the two input arms as the devices are tuned further. The length of input arm directly beneath the heating element leading to the ring resonator is 36 μm long. As demonstrated by Harris et al using a 61.6 μm phase shifter on silicon ridge waveguide, it is possible to achieve heating phase shift of 24.77 ± 0.43 mW/π,16 hence the phase shifting effect shouldn’t be negligible.

To display the effects of effective refractive index and relative phase the following constant parameters were used: A ring radius of 25 μm, zero losses and a coupling coefficient in each ring of 0.12. To simulate the travelling and stationary setup from chapter 4, one ring (stationary) has a constant effective refractive index of 2.6258, while the travelling peak was off-tuned by effective refractive index values of -0.0022, -0.0014, - 0.0010, -0.0006, -0.0004, -0.0002, -0.0001 and zero off-tuning. As the model simulated symmetrically for negative or positive off-tuning, there is no need to present results for positive off-tuning. For each off-tuned value, an observation will be made of how the peaks interact with a relative phase of zero, π/2, π and 3π/2 in order to gain an understanding of how the peaks shape at different phase values.

As there are a lot of graphs to consider, the travelling (the peak being tuned), the stationary (the peak not being tuned) and the central drop port outputs will be viewed individually. These results are shown in figures 5.14 – 5.16.

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Figure 5.14: Relative phase comparisons between travelling peaks with relative phases of zero, π/2, π and 3π/2. The peak off-tuning has values of -0.0022, -0.0014, -0.0010, - 0.0006, -0.0004, -0.0002, -0.0001 and zero, descending from top to bottom. The peaks are offset by intervals of 0.5 for viewing ease.

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Figure 5.15: Relative phase comparisons between stationary peaks with relative phases of zero, π/2, π and 3π/2. The peak off-tuning has values of -0.0022, -0.0014, -0.0010, - 0.0006, -0.0004, -0.0002, -0.0001 and zero, descending from top to bottom. The peaks are offset by intervals of 0.5 for viewing ease. As shown, the plots are symmetric with those from the travelling peak comparison.

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Figure 5.16: Relative phase comparisons between drop port peaks with relative phases of zero, π/2, π and 3π/2. The peak off-tuning has values of -0.0022, -0.0014, -0.0010, - 0.0006, -0.0004, -0.0002, -0.0001 and zero, descending from top to bottom. The peaks are offset by intervals of 0.5 for viewing ease. As seen, the drop port peaks are symmetric.

Key observations from figures 5.14 – 5.16 are as follows:  At perfect peak overlap, a relative phase of π is required to create complete signal cancellation. This may correspond with the drop port CRIT feature which was discovered in chapter 4.  The steepest Fano resonance shapes occur when the relative phase has a value of π/2.  At perfect peak overlap, the spectral shapes at relative phases of π/2 and 3π/2 are perfectly mirrored.

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Chapter 5 – Modelling of Double Ring System

5.4.4 Comparisons to the Experimental Data

To determine the coupling coefficients to be used, peaks were initially fitted to the experimental peak shapes which were far away from resonance overlap. This way the peaks would have the lowest overlap effect on each other, reducing Fano interactions. Fitting like this it was observed that a coupling coefficient of 0.12 matched the peak shapes the best. The assumption that losses are negligible (zero) has been maintained.

Due to the calculation time of the model, the number of potential variables which can be changed and the imperfect background noise signature, all fitting in this section has been completed by hand rather than through the use of least square difference fit optimisation as can be used on single rings. A simple overview of the model under these conditions can be seen in figure 5.17.

Figure 5.17: Typical model results where the travelling peak has an effective refractive index neff1 of 2.62533 and the stationary peak has an effective refractive index neff2 of 2.62604. The different relative phases are noted on the graphs. As shown, the model generates symmetric data.

Comparisons between the travelling and stationary throughput signals from section 4.6 reveal that the peaks appear to have an asymmetric relationship under the same heater current conditions. To satisfy this, the model needs to be fitted to each individual peak separately. A demonstration of this can be seen in figure 5.18.

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Transmission vs Wavelength, Heater Current = 1.1 mA 0.8

0.7

0.6

0.5

0.4 Travelling Peak 0.3 Stationary Peak Transmission 0.2 Travelling Peak Model 0.1 Stationary Peak Model 0 1537 1537.5 1538 1538.5 1539 1539.5 1540 1540.5 1541 Wavelength (nm)

Figure 5.18: Transmission vs Wavelength modelling for travelling and stationary peaks at a heater current of 1.1 mA. Values used for modelling were neff1 = 2.62533, neff2 = 2.62604 in both cases. The relative phase of the travelling peak = 11.5π/8 and the relative phase of the stationary peak = 3π/8.

As a general approach, the same effective refractive indices are used, but the relative phase changes between the travelling and stationary peak models. Figures 5.19 – 5.25 show the best fitting results achieved when applying this model over 1 mA heater current increments.

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Transmission vs Wavelength, Heater Current = 0.1 mA 0.8 0.7

0.6 0.5 0.4

0.3 Travelling Peak

Transmission 0.2 0.1 Stationary Peak 0 1537 1537.5 1538 1538.5 1539 1539.5 1540 1540.5 1541 Wavelength (nm)

Figure 5.19:

Travelling Peak Values: neff1 = 2.62526, neff2 = 2.62604, Relative Phase 11π/8.

Stationary Peak Values: neff1 = 2.62526, neff2 = 2.62604, Relative Phase 3π/8.

Transmission vs Wavelength, Heater Current = 1.0 mA 0.8 0.7

0.6 0.5 0.4

0.3 Travelling Peak

Transmission 0.2 0.1 Stationary Peak 0 1537 1537.5 1538 1538.5 1539 1539.5 1540 1540.5 1541 Wavelength (nm)

Figure 5.20:

Travelling Peak Values: neff1 = 2.62532, neff2 = 2.62604, Relative Phase 11π/8.

Stationary Peak Values: neff1 = 2.62532, neff2 = 2.62604, Relative Phase 3π/8.

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Transmission vs Wavelength, Heater Current = 2.0 mA 0.8 0.7

0.6 0.5 0.4

0.3 Travelling Peak

Transmission 0.2 0.1 Stationary Peak 0 1537 1537.5 1538 1538.5 1539 1539.5 1540 1540.5 1541 Wavelength (nm)

Figure 5.21:

Travelling Peak Values: neff1 = 2.62541, neff2 = 2.62604, Relative Phase 11π/8.

Stationary Peak Values: neff1 = 2.62541, neff2 = 2.62604, Relative Phase 2π/8.

Transmission vs Wavelength, Heater Current = 3.0 mA 0.8 0.7

0.6 0.5 0.4

0.3 Travelling Peak

Transmission 0.2 0.1 Stationary Peak 0 1537 1537.5 1538 1538.5 1539 1539.5 1540 1540.5 1541 Wavelength (nm)

Figure 5.22:

Travelling Peak Values: neff1 = 2.62558, neff2 = 2.62609, Relative Phase 10π/8.

Stationary Peak Values: neff1 = 2.62558, neff2 = 2.62609, Relative Phase π/8.

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Transmission vs Wavelength, Heater Current = 4.0 mA 0.8 0.7

0.6 0.5 0.4

0.3 Travelling Peak

Transmission 0.2 0.1 Stationary Peak 0 1537 1537.5 1538 1538.5 1539 1539.5 1540 1540.5 1541 Wavelength (nm)

Figure 5.23:

Travelling Peak Values: neff1 = 2.62596, neff2 = 2.62618, Relative Phase 9π/8.

Stationary Peak Values: neff1 = 2.62596, neff2 = 2.62618, Relative Phase π/8.

Transmission vs Wavelength, Heater Current = 5.0 mA 0.8 0.7

0.6 0.5 0.4

0.3 Travelling Peak

Transmission 0.2 0.1 Stationary Peak 0 1537 1537.5 1538 1538.5 1539 1539.5 1540 1540.5 1541 Wavelength (nm)

Figure 5.24:

Travelling Peak Values: neff1 = 2.62642, neff2 = 2.62608, Relative Phase 3.8π/8.

Stationary Peak Values: neff1 = 2.62618, neff2 = 2.62647, Relative Phase 0.

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Transmission vs Wavelength, Heater Current = 6.0 mA 0.8 0.7

0.6 0.5 0.4

0.3 Travelling Peak

Transmission 0.2 0.1 Stationary Peak 0 1537 1537.5 1538 1538.5 1539 1539.5 1540 1540.5 1541 Wavelength (nm)

Figure 5.25:

Travelling Peak Values: neff1 = 2.62665, neff2 = 2.62618, Relative Phase 2π/8.

Stationary Peak Values: neff1 = 2.62705, neff2 = 2.62618, Relative Phase 15π/8.

The figures above show that the model works reasonably well when the peaks don’t overlap significantly. It breaks down at points when the peaks do overlap though, as shown in figure 5.24. It becomes difficult to match the amplitudes of the model to those measured in the experimental data. This suggests that there may be more to the reality of the situation during peak overlap than the current model accounts for.

In order to better understand the unexplained asymmetries and mismatching amplitudes encountered close to peak overlap, a novel approach was adopted, swapping the values of neff1 and neff2 around while keeping the relative phase the same. Physically, this is the same as heating the other ring resonator and re-labelling the respective travelling and stationary peaks. A demonstration of this effect can be seen in figure 5.26

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Figure 5.26: The only conditions that have changed are the values of neff1 and neff2, which have been switched around, as shown; the shapes of all peaks have changed. Physically, this is the same as heating the other ring resonator and re-labelling the respective travelling and stationary peaks. On first impression this is unexpected.

On further investigation, it was discovered that the same results could be achieved if the relative phase was reversed about zero, keeping neff values constant but using values of π/16 and -π/16. Thinking about this analytically, when the ring resonators are perfectly overlapping, light coupling with them would see a path similar to an S shape rather than the O ring shape it normally encounters, passing from one input arm through to the other. By definition light coupling the other way would have an opposite relative phase around zero to the one used for calculations. As such the throughput signals would have two signal contributions, their original signal input and one crossing over the double ring arrangement with an opposite relative phase.

Using this construction of two states, one with an original relative phase value (the original ring contribution to signal) and the other with a negative relative phase value (The S-shaped contribution from the other arm). The total contribution from each signal is then shared between each contributor by proportional amounts to produce a new balanced output which represents both spectral states. Figure 5.27 Shows a demonstration of this two peak combination model functioning.

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Figure 5.27: The original peak models are slightly transparent. The peak on the left hand side is referred to as peak 1, the peak on the right hand side is referred to as peak 2. In this case when 25% of peak 1 and 75% of peak 2 are combined, they create the merged fit. Using this adapted model, it is possible to fit the data much better than could otherwise be achieved using single peaks.

Applying the double peak fitting model, fits have been completed for the data between 4.0 mA and 6.0 mA, in 0.2 mA steps, for both the travelling and stationary peaks. These fits are presented in the graphs below.

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Figure 5.28: The double peak fitting between 4.0 and 6.0 mA tuning currents. The travelling peak data is displayed on the left in blue. The stationary peak data is displayed on the right in green. Raw data is displayed with a lighter colour; the base peaks which combine for the merged fit are faded in the background while the merged fit is a darker shade of blue for travelling and green for stationary.

As shown in the graphs of figure 5.28, while the model may not achieve a perfect fit in all instances, it fits very closely and much better than the standard fit in figures 5.23 – 5.25. The effective refractive index values, relative phase values and % signal contribution values required to produce these signals are shown in graph format in the figures below.

Predicted Effective Refractive Index vs Applied Current for Travelling Peak Fit

2.6274

2.6272 Travelling signal neff1

2.627 Stationary signal neff2 2.6268

2.6266

2.6264

2.6262

2.626 Effective Refractive Index Refractive Effective 2.6258 4.0 4.5 5.0 5.5 6.0 Applied Current (mA) Figure 5.29: The effective refractive index values used for the travelling signal (heated ring) and the stationary signal (non-heated ring). As seen, the travelling signal gradually increases while the stationary signal remains fairly stable.

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Relative Phase vs Applied Current for Travelling Peak fit 8

4 π/8)

2 Travelling Peak

0 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 -2

-4

Relative Phase (x Phase Relative -6

-8 Applied Current (mA)

Figure 5.30: The relative phase divided by π/8 for the travelling peak signal. These values are used for the first signal of the combined peak model while their negative counterparts are used to form the secondary signal contribution.

Double Peak signal % vs Applied Current for Travelling Peak

100

80 70 Travelling Peak 1 60 50 Travelling Peak 2 40 30

20 % Signal Contribution Signal % 10 0 4.0 4.5 5.0 5.5 6.0 Applied Current (mA)

Figure 5.31: The percentage of signal contributing to the merged peak at each corresponding applied current value. As can be seen, there is a significant switch between 5.2 and 5.4 mA.

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Predicted Effective Refractive Index vs Applied Current for Stationary Peak Fit

2.6274

2.6272 Travelling signal neff1

2.627 Stationary signal neff2 2.6268

2.6266

2.6264

2.6262

Effective Refractive Index Refractive Effective 2.626

2.6258 4.0 4.5 5.0 5.5 6.0 Applied Current (mA)

Figure 5.32: The effective refractive index values used for the travelling signal (heated ring) and the stationary signal (non-heated ring). As can be seen, the travelling signal gradually increases while the stationary signal remains fairly stable.

Relative Phase vs Applied Current for Stationary Peak fit 8

4 Stationary Peak π/8) 2

0 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 -2

-4 Relative Phase (x Phase Relative -6

-8 Applied Current (mA)

Figure 5.33: The relative phase divided by π/8 for the stationary peak signal. These values are used for the first signal of the combined peak model while their counterparts (multiplied by -1) are used to form the secondary signal contribution.

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Double Peak signal % vs Applied Current for Stationary Peak

100

80 70

60 Stationary Peak 1 50

40 Stationary Peak 2 30

20 % Signal Contribution Signal % 10 0 4.0 4.5 5.0 5.5 6.0 Applied Current (mA)

Figure 5.34: The percentage of signal contributing to the merged peak at each corresponding applied current value. As can be seen in this case too, there is a significant switch between 5.2 and 5.4 mA.

Figures 5.29 and 5.32 suggest that there is never really a point at which the two effective refractive index values for the peak overlap, but rather that the energy switches between 5.2 and 5.4 mA in the ‘double peak’ state instead. This suggests that when the two peaks are far from overlapping, they act independently in a way which can be modelled fairly well by the conventional model, but when they come into close proximity, they enter a “super-state” where light no longer sees just a ring resonator with an additional drop port to interact with, but also an S-shaped path through both ring resonators towards the other waveguide arm. As a result the peak power switches between these two states as the peaks overlap. It is interesting to note how the two peaks appear to never truly overlap in this state, this result is similar to the squeezing effect reported by Lipson et al in 2016.17

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Unfortunately the model for the central drop port only offers symmetric solutions when only adjusting the relative phase and effective refractive index values. It is quite easy to manipulate the model using coupling coefficients and losses as seen in figure 5.35, but to adopt this approach requires a justification for the massive losses required in one ring relative to the other, or a sudden change in coupling coefficients. Each requirement is difficult to justify.

Drop Port Modelling 4.5 mA 0.6

0.5

Real Data

0.4 Coupling Modification

0.3 Loss modification

0.2 Transmission

0.1

0 1546.5 1546.7 1546.9 1547.1 1547.3 1547.5 1547.7 1547.9 1548.1 1548.3 1548.5 Wavelength (nm)

Figure 5.35: Modelling of the drop port signal at 4.5 mA. In the blue fitted curve, the coupling coefficients were modified, the coefficients used were C1 = 0.08 and C2 = 0.013, with losses of 0.5 dB/cm in both rings, neff1 = 2.62135 and neff2 = 2.62019 and a relative phase of 15π/16. In the green curve, losses were modified with the coupling coefficients being C1 = 0.09 and C2 = 0.08, with losses in ring one of 0.5 dB/cm and 39 dB/cm in ring two, neff1 = 2.62135 and neff2 = 2.62019 and a relative phase of 15π/16.

5.4.5 Discussion

In summary, the 3x3 Matrix works well for modelling when the peaks aren’t overlapping, and behave like standard Lorentzian peak shapes. When the peaks do start to overlap, the basic model breaks down, but the throughput signals can be adapted to incorporate a

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‘double state’ peak which fits the data very closely. Unfortunately it becomes difficult to model the central drop port signals once the peaks begin to overlap due to the clear asymmetry which can only be matched through incurring huge losses without an explanation. As the material properties don’t change during testing and accurate modelling can be achieved in the throughput outlets without the addition of losses it seems unlikely that this is the case. A possible cause is that the model assumes nearest neighbour coupling only with zero losses during its derivation. If there are any second- order coupling effects or additional losses, this may affect the outcome of the model.

In order to further investigate these double peak tuning effects, a new modified chip design has been made which features the design modifications (shown in figure 5.36) made to the Y-Splitting configurations.

By the time these new ring design chips have been fabricated, they will be a platform for future researchers to study; these designs should offer more information about the phenomena encountered so far and the factors which really affect the modelling results.

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Figure 5.36: New double ring designs for the next chip for testing. The top left configuration has the heating elements moved away from the input arms, it is hoped that this will reduce systematic noise on the relative phase factor of light coupling to the ring resonators. The top right configuration has also had the central drop port removed, it is hoped that this will help to deduce the effect that this component plays on the overarching spectral behaviour. The bottom left image features two rings of differing diameter, where one is double that of the other, it is hoped that the spectra will overlap on half of the peaks generated by the smaller ring, but the other half will be unaffected. The configuration on the bottom right is the same but with heaters moved away from the input waveguides.

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5.5 Conclusion

In this chapter the transfer matrix method of modelling ring resonators has been explored with both single ring 2x2 transfer matrix cases and novel double ring 3x3 transfer matrix cases.

The double ring system is significantly more complex than the single ring model and collaboration with Matteo Cherchi from VTT was required to derive a working transfer matrix model. Working with the model, it was decided to neglect the effect of losses and changing coupling coefficients as they weren’t expected to make a significant contribution to the output.

By only tuning the effective refractive indices and relative phase between input arms, it was possible to demonstrate reasonable modelling accuracy when the two peaks in the double peak system didn’t overlap. When they started overlapping however, the throughput signals began to form shapes which couldn’t be matched by the basic model. Having noticed an effect from the negative relative phase contribution, the model was adapted into a ‘double-state’ combined peak system, which included signal contribution from standard phase and negative phase contributions. This double state peak was able to match the experimentally measured data very closely as the peaks overlap. When looking at the effective refractive index values required for a close fit, it becomes obvious that the peaks never actually overlap, but that a squeezing effect is seen, similar to the effects reported by Lipson et al in 2016.17

The double ring model was harder to fit against the central drop port signal due to the inherent asymmetries which could only be achieved by using inexplicably high loss effects or differing coupling coefficients.

In order to gain more information about the causes of the unusual effects encountered in the double ring tuning work, a new chip has been designed which should mitigate systematic sources of noise and offer more information about the nature of the double ring tuning process.

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5.6 References

1. A. Yariv, Electronics letters, 2000, 36, 321-322. 2. A. Yariv, IEEE Photonics Technology Letters, 2002, 14, 483-485. 3. J. K. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang and A. Yariv, Optics express, 2004, 12, 90-103. 4. L. Zhou, R. Soref and J. Chen, Optics Express, 2015, 23, 13488-13498. 5. F. Wang, X. Wang, H. Zhou, Q. Zhou, Y. Hao, X. Jiang, M. Wang and J. Yang, Optics express, 2009, 17, 7708-7716. 6. T. Y. Ang and N. Q. Ngo, JOSA B, 2012, 29, 1094-1103. 7. M. Cherchi, 2017. 8. M. Born and E. Wolf, Cambridge University, Cambridge, 1999. 9. M. Cherchi, Applied optics, 2003, 42, 7141-7148. 10. H. A. Haus and W. Huang, Proceedings of the IEEE, 1991, 79, 1505-1518. 11. W.-P. Huang, JOSA A, 1994, 11, 963-983. 12. K. Iwasaki, S. Kurazono and K. Itakura, Electronics Communications of Japan, 1975, 58, 100-108. 13. H. Haus and C. Fonstad, IEEE Journal of Quantum Electronics, 1981, 17, 2321-2325. 14. Y. A. Vlasov and S. J. McNab, Optics express, 2004, 12, 1622-1631. 15. Accuratus, Fused Silica, SiO2 Glass Properties, http://accuratus.com/fused.html, Accessed 27/07/2017, 2017. 16. N. C. Harris, Y. Ma, J. Mower, T. Baehr-Jones, D. Englund, M. Hochberg and C. Galland, Optics express, 2014, 22, 10487-10493. 17. A. Dutt, S. Miller, K. Luke, J. Cardenas, A. L. Gaeta, P. Nussenzveig and M. Lipson, Opt. Lett., 2016, 41, 223-226.

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6.1 Introduction

Moving on from the topic of double ring tuning and its spectral effects, investigations into sensing with ring resonators were also conducted during this project, targeting applications in healthcare and pathological testing. As the spectral behaviour of single ring resonators is far easier to predict and spectral measurements are easier to take on the single ring systems, in this part of my project only simple single ring examples have been considered.

This chapter is written to give an insight into the practical requirements for biosensing, difficulties encountered and methods adopted to overcome these difficulties. Inventive approaches to sensing with novel materials will also be introduced through a project collaboration.

The aims of this chapter are to:  Investigate basic ring resonator sensing.  Introduce surface functionalisation techniques.  Introduce microfluidics and an adapted method of fabrication.  Introduce up conversion nanoparticles and inkjet printing to ring resonator sensing.

6.2 Basic Ring Resonator Sensing

The aim of this investigation is to explore the use of the ring resonator chips as basic sensors by assessing their spectral response to various surface coatings, including air, PMMA, NaCl and glucose.

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6.2.1 Method

Single ring resonators without any additional drop ports are easier to analyse for basic sensing applications. Twelve single ring resonators (Seen in figure 6.1) on the chip were assessed using the experimental setup described in chapter 3 section 4 (i.e. offset but focussed light source and offset spectrometer, chip based on a 3D moving platform). The light source was a Thorlabs fibre coupled superluminescent diode (SLD) source centred around 1550 nm and the spectrometer was the 1.0 – 2.6 μm Thorlabs optical spectrum analyser OSA 203B.

Figure 6.1: A compressed view of the single ring resonators and their corresponding labels. The ring resonators have been given positional labels based on their order in terms of input grating. G1 = bottom, G14 = top on the chip layout. G1 and G8 are both plain straight waveguides. G2-G7 have 25 μm radius ring resonators. G9-G14 have 50 μm radius ring resonators. G3, G5, G7, G10, G12 and G14 have windows etched into the silicon over the ring resonators; these can be used for biosensing. G2, G4, G6, G9, G11 and G13 are situated under a 1.6 μm layer of SiO2, making them more suitable as a stable reference or thermal tuning. The ring resonators of G2, G3, G9 and G10 are 200 nm away from their input waveguides. The ring resonators of G4, G5, G11 and G12 are 250 nm away from their input waveguides. The ring resonators of G6, G7, G13 and G14 are 300 nm away from their input waveguides.

The microchips come with a pre-packaged PMMA layer on their surface. Initial base spectral measurements are taken with this, and then the sample is cleaned. In the cleaning process:

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 The sample is placed into a container of acetone for 15 minutes to dissolve the PMMA layer.  The sample is placed in a second acetone bath for 15 minutes to remove any residue from the first bath.  A third bath using either ethanol or IPA is used for 15 minutes.  A final bath in de-ionised water is used to dissolve and remove any further material.

During initial cleaning tests, a sonic bath was used, however it was quickly determined that the resulting spectra has greatly reduced Q-factors. It is assumed that the sonic baths were damaging the exposed ring resonators, leading to additional systematic losses.

Following the cleaning process the sample is left to dry in a covered area (to reduce dust collection). After the initial cleaning process, all of the waveguide systems G3, G5, G7, G10, G12 and G14 were measured to gain a baseline measurement for comparison. In order to detect substances, droplets from a micropipette over the active region of the chip can be used to apply material. This is shown in figure 6.2. The solution (for example glucose or NaCl dissolved in deionised water) can either be left on to dry, revealing further crystallised properties, or washed away using the same cleaning cycle as stated above. As this was a probing investigation to see what was possible, the amounts, types and concentrations of solution used were varied and will be stated in the results section.

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Figure 6.2: Using a micropipette and careful manipulation, the user can apply μl quantities of solution exclusively over the active region of the ring resonators, avoiding the input and output gratings of the waveguide. Due to the miniscule amounts of liquid being applied, the solution would evaporate quite quickly, which in turn caused a change over time of the refractive indices of the solutions used (as water would reduce, but NaCl and glucose would remain in the solution). The user can either leave the drop to completely evaporate, leaving crystallised residue, or can add additional droplets of water to dilute the solution again, making it easier to clean after the experiment.

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6.2.2 Results

Initial Sensing Test for G5

5.00E-08

1. PMMA

5.00E-09 2. Straight after Clean

Power(mW) 3. PBS Droplet 4. PBS Crystallised

5.00E-10 1514 1516 1518 1520 1522 1524 Wavelength (nm)

Figure 6.3: Transmission spectra for ring resonator G5 (25 μm radius, with window and 250 nm separation between bus and ring resonator) under different conditions. 1. An initial reading was taken of the ring resonator while it was coated in shipping condition PMMA. 2. After the PMMA was cleaned off, exposing the waveguide to laboratory air, the lateral position of the spectrum changed and the resonant valleys saw drastic reduction in their depths and quality, this will be due to the effect of the sonic bath. 3. A droplet of phosphate buffered saline (PBS), a water-based salt solution commonly used in the field of biological research, was applied to the ring resonator and a measurement of the transmission spectrum was taken while the PBS was in liquid form. As shown, the resonant minima have moved laterally again and the quality of the spectrum has improved. 4. The PBS was left to dry and crystallise onto the surface, leaving a residue of crystallised salts. The transmission spectrum of the crystallised PBS has been shifted even further (due to increased concentration of salts) and quality of the spectrum is similar to the hydrated PBS droplet (3).

Figure 6.3 indicates that the position of resonant peaks changes with increasing concentrations of salts in water based solution. Taking this further, a second investigation

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Chapter 6 – Sensing with Ring Resonators was conducted using the process described in figure 6.2 and the Labview OSA software that tracks the movement of spectral peaks or valleys over time. Figure 6.4 shows the results of this investigation.

Shift of Resonant Minimum Over Time With Increasing Glucose Concentration - G10

1522

Introduced a 6 μl 1521.5 drop of 10% weight glucose solution to waveguides 1521 Added a 3 μl drop of deionised water Added another 3 μl drop of

Wavelength Wavelength (nm) deionised water, this one 1520.5 caused an overlap of the output diffraction grating, skewing output signal 1520 0 500 1000 1500 2000 Time (seconds)

Figure 6.4: A graph showing the tracked position of a resonant minimum (based around 1521 nm) as it is exposed to a 10% weight glucose/ deionised water solution.

As shown in figure 6.4, the position of spectral peaks and valleys can be tracked over time using the customised Lorentzian peak fitting software to print the position of their maxima (or minima) against the time the result was taken. The focussed beam setup (rather than the fibre optic input setup) was used for this experiment along with the semiconductor optical amplifier broadband light source and the optical spectrum analyser. In this experiment, the 50 μm radius waveguide G10 was exposed to air for 180 seconds before a 6 μl drop of glucose solution was added to the top using a micropipette. It is important to make sure that the droplet doesn’t overlap the output or input gratings as refraction through the droplet may prevent optical alignment.

Over time, the water from the solution evaporates, increasing the concentration of the solution, leading to a shift in the resonant wavelength. After 1200 seconds a 3 μl droplet

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Chapter 6 – Sensing with Ring Resonators of pure deionised water was also added to the glucose solution droplet. As the solution mixed and diluted the glucose, the position of the peak shifted back towards its original position, before stabilising and increasing again with further evaporation. A second 3 μl droplet of deionised water was added at 2340 seconds, but this caused the droplet to overlap the output diffraction grating, ending the experiment.

6.2.3 Discussion

The results in figure 6.3 confirm that there are two transmission spectra parameters that can be used for biosensing applications: the amplitude of resonant peaks and their position. Expanding on the findings of figure 6.3, figure 6.4 shows that by tracking the position of resonant peaks over time, the ring resonators can be used to monitor the concentration of basic chemicals such as glucose or salt.

Using simple solutions with known refractive indices, such as glucose or NaCl in water, it will be possible to make a direct correlation between the refractive index change of a solution and the corresponding wavelength shift detected by the ring resonators. This would provide a baseline ring resonator calibration that could be used for a range of more complex biosensing investigations. This train of thought will be taken further in section 6.4.

6.3 Drop Testing Streptavidin

Several research groups have published reports of biosensing with ring resonator type devices.1-7 The surface functionalisation technique typically adopted by these groups is to silanize the ring surface, leaving vacant NH2 sites; attach a layer of biotin to these sites, a layer of streptavidin and finally a biotinylated coating. Using the technique reported by Lapin and Chabal,8 it is hoped that the ring resonators being studied in this thesis will be suitable for functionalising in a similar manner. The sensitivity of ring resonator biosensors decays exponentially as target material is further from the surface of the waveguide. As discussed in chapter 1, modelling predicts that the ‘active region’ of a

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Chapter 6 – Sensing with Ring Resonators silicon-on-insulator ring resonator biosensor is of the order of 100 nm. If the functionalised layer is thicker than this, the devices will lose useful functionality.

6.3.1 Method

The method used for this investigation is an adaptation of the approach proposed by Lapin and Chabal.8 In this technique, a 3-aminopropylsiloxane (APS) film is applied to the oxidised surface of the silicon chip using 3-aminopropyltriethoxysilane (APTES). 3-sulfo-N- hydroxysuccinimide ester sodium salt (biotin-NHS) is then attached to the APS film, leaving an exposed biotinylated film for the attachment of streptavidin. Following this, any biotinylated biomolecule is able to be attached to the streptavidin. A visual diagram of this process can be seen in figure 6.5.

Figure 6.5: The functionalisation of a silicon substrate using (1) APTES, (2) Biotin-NHS and (3) Streptavidin. Any biotinylated biomolecules (4) can be bound to the streptavidin layer, making this process highly versatile from a biosensing point of view.8

This method used this investigation differs from that used by Chabal and Lapin as different techniques are used to apply each layer to the surface.

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Initially a new chip is selected to apply a functionalised layer. This is cleaned to remove the protective PMMA layer which coats the chip. The initial cleaning process involves soaking the chip in two acetone baths for approximately five minutes. Following this, the chip is soaked in an ethanol bath for a further five minutes to remove any acetone residue.

Following the initial cleaning process, the twelve single ring resonators (Seen in figure 6.1) on the chip were assessed using the same experimental setup described in chapter 3 section 4.

Once base spectra had been read for the clean chip, the chip was then further subjected to surface functionalisation. Initially a UV cleaner was used to give 3 x 15 minute exposures to the chip. This reduces the effect of carbon trapping on the surface, making the chip ready for silanization.

Following this, APTES was coated onto the chips surface. To do this, the chip was placed in an aluminium foil tray inside a sealed desiccator, adjacent to another foil tray containing 10 droplets of APTES. The desiccator chamber was evacuated with a vacuum pump for 5 minutes; the sample was then left to sit in the evacuated chamber for 30 minutes. During this time, evaporated APTES coated all surfaces with an approximate monolayer of APTES. Following this, air was slowly released into the chamber (to prevent the chip from blowing around), and the microchip was removed from the desiccator and placed inside a 110 °C oven for 30 minutes to anneal the surface. Once the chip had cooled, the 12 single ring resonators were assessed and their transmission spectra were recorded.

The next layer in the functionalisation process was Biotin-NHS. Before applying this, the chip was cleaned with deionised water and acetone under a flowing argon tube to remove any residual material. 2.3 mg of Biotin-NHS was mixed with 0.8 ml of deionised water. This mixture was then applied to the chip surface using 100 μl pipette droplets and left in a hydrated atmosphere for 53 minutes. The chip was then gently rinsed with

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Chapter 6 – Sensing with Ring Resonators deionised water and dried with argon gas. Once the chip had dried, the 12 single ring resonators were once again assessed for their transmission spectra.

The final step in functionalising was to coat the surface with streptavidin. To do this, a 100 μl/ml mixture of streptavidin and phosphate buffer saline (PBS) was prepared and left on the surface of the chip for one hour under a hydrated atmosphere.

In a subsequent experiment, fluorescent streptavidin-alexa488 was used instead of streptavidin to give a visual indication of surface adsorption.

Following the binding of streptavidin, the surface of the chip was cleaned using a 0.05% volume solution of Tween20 (cleaning agent) in PBS. After approximately four minutes of rinsing the chip with the Tween20 solution under a pipette, the chip was rinsed in deionised water and dried off using a nitrogen gas tap. Once the layer of streptavidin had been applied and rinsed, the chip was assessed for its transmission spectra. A visual image of the chip during the streptavidin coating stage can be seen in figure 6.6.

The additional test using fluorescent streptavidin-alexa488 was conducted on plain silicon wafer for viewing under a fluorescence microscope. Once the streptavidin had been applied, a thin glass slide with a droplet of water underneath it was used to keep the streptavidin proteins hydrated while images were taken using the microscope. Unfortunately the imaging software on the microscope used on the day was broken on the day the microscope was booked, so images had to be taken using a digital camera through the eyepiece.

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Figure 6.6: the chip during the streptavidin coating stage. The area circled in red is where the single ring resonators are based on the chip. As can be seen, these are located close to the edge which may affect the consistency of results. At the bottom of the image are two plain pieces of silicon wafer, primarily used for testing application volumes and comparison.

6.3.2 Results

When assessing the spectral shifting of the ring resonators, it was noted that G10, G12 and G14 showed consistent shifting when applying biotin and streptavidin, G3, G5 and G7 showed inconsistent shifting when applying biotin and streptavidin. There were no consistent shifts when applying the APTES, possibly due to varying thicknesses of the APTES layer. A spectral result for G10 can be seen in figure 6.7. A comparison between the different ring resonators can be seen in figure 6.8.

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Spectra for G10 1.00E-06

1.00E-07 Pre Aptes Post Aptes Biotin

Power(mW) 1.00E-08 Streptavidin

1.00E-09 1545 1547 1549 1551 1553 1555 Wavelength (nm)

Figure 6.7: The transmission spectra for ring resonator G10, a 50 μm radius ring resonator that has a 200 nm separation from its input waveguide. As can be seen, the quality factor of spectra is relatively consistent, suggesting that there aren’t substantial losses caused by this coating process. The magnitude of shifts suggests that this surface coating method can be extended further while retaining sensitivity.

Figure 6.8: The relative peak shift of each ring resonator with an open window above it (G3, G5, G7, G10, G12 and G14). Stage 1 represents after APTES coating, 2 is after biotin- NHS coating and 3 is after streptavidin coating. As can be seen, ring resonators G10, G12 and G14 show more consistent peak shifting, while G3, G5 and G7 are inconsistent.

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It should be noted that using this method of analysis, it is impossible to determine whether the resonant peaks have been shifted by more than a whole free spectral range, hence comparisons can only be made in relative terms.

Figure 6.8 shows that the shifts experienced by ring resonators G3, G5 and G7 are inconsistent when compared to G10, G12 and G14.

Reasons for this may be because they are located closer to the edge of the chip, meaning that they may not have been coated as homogeneously as the ring resonators which are located more centrally (G10, 12 and 14). This may have resulted in coatings of biotin-NHS and streptavidin with lower uniformity. The ring resonators G3, 5 and 7 are also 25 μm in diameter, meaning that they also have a proportionately smaller surface exposed to the binding molecules; hence any discrepancies will be amplified when compared to the larger G10, 12 and 14 ring resonators.

The additional test results using fluorescent streptavidin-alexa488 can be seen in figure 6.9.

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Figure 6.9: An image taken through the lens of a fluorescence microscope. Magnification was 100 times. Unfortunately the image is poor quality but two clear boundaries can be seen (highlighted in red) where two droplets of fluorescent material are separated by a space which had no streptavidin-alexa488 applied. This image suggests that the streptavidin coats evenly when applied to a flat surface. The additional glowing spots may be from clustered areas of fluorescent streptavidin which weren’t cleaned off sufficiently before viewing.

6.3.3 Discussion

The results from this investigation show promise. Ring resonators G10, 12 and 14 show relatively consistent shifting and in all cases, the ring resonators were able to retain sensitivity after applying the functionalised layer. It is also clear that this method of application does not produce repeatable results. As mentioned, it is impossible to determine exactly how much shift has been generated using the snapshot method of spectroscopy. Real time measurements will be needed for effective monitoring of peak movements. The application of binding material via micropipette droplets works fine for

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Chapter 6 – Sensing with Ring Resonators large areas and rough, proof-of-principle investigations, but a reliable method of applying functionalised material is needed for further investigations. As such, microfluidic channels will be introduced to the surface of the chip, enabling constant surface hydration, real- time measurements and greater control of the amounts of material applied. The method of functionalisation introduced by Iqbal et al2 is a good starting point for taking this line of work further.

6.4 Microfluidics Integration

As demonstrated in section 6.3, the chip configuration explored is capable of being functionalised, and therefore capable of being converted into a more sophisticated biosensor, targeting specific biomolecules within a solution. The problem with drop casting layers and leaving them to dry is that they can lead to inconsistent coverage and the drying process can denature the proteins involved. The required step of removing the chip to add additional sensing layers makes it so that a continuous sensing run cannot be achieved, making real time sensing impossible. In order to overcome this obstacle a progressive investigation has been conducted on how to incorporate microfluidics onto the base microchip. The aims of this section are to walk the reader through the developed method, showing the crucial steps and some basic testing.

6.4.1 Method

In this experiment, microfluidics channels were made out of PDMS as it is relatively flexible and rubbery, allowing it to mould around uneven surface topography if required. It is also reasonably transparent around 1500 nm wavelength. There are several guides in the literature9, 10 on how to use this material for microfluidics and the approach reported here is adapted from these.

The first step for PDMS casting is to create a microfluidic master template mould over which the PDMS can be set to produce copies. To do this a piece of silicon wafer was etched away using photolithography and reactive Ion etching to form channels of 200 μm width and 150 μm height. An image of the mould can be seen in figure 6.10.

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Figure 6.10: The silicon mould for PDMS casting. It was glued into a Petri dish using superglue to ensure it stayed in place when casting. The ridge design is 150 μm tall with a channel width of 200 μm. The slight kink at the end of the left hand side of the channel is to ensure that the output waveguides gratings are not affected by the microfluidics channel. In this image, a rectangular block of PMMA had also been glued next to the channel in order to provide a hard edge to mould against.

The next step is to silanize the surface, making it hydrophobic so it’s easier to peel back the PDMS cast once it sets over the mould. In order to do this, the silicon surface was washed with IPA, then deionised water to remove any surface grease and dust. The surface was then UV cleaned for one minute as this makes the silicon surface wetting (i.e. hydrophilic) in nature. Following the wetting stage, the silicon mould was placed in a desiccator with 40 μl of trichloro(1H,1H,2H,2H-perfluorooctyl)silane 97% (purchased from Sigma Aldritch) placed in an aluminium tray next to it. The desiccator was evacuated to 5 inHg of pressure and left for 1 hour, and then the silicon mould was removed to a standard laboratory environment. Droplets of water can be used at this stage to ensure that the silanization has worked and the surface is now hydrophobic.

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In order to create the PDMS for casting, silicone Sylgard 184 was used, purchased from Scientific Laboratory Supplies. A 10:1 ratio of PDMS to crosslinking curing agent was used to produce the syrupy PDMS mixture. This was then thoroughly mixed with a spatula, leading to the formation of bubbles within the mixture, as shown in figure 6.11. If the bubbles set into the mixture, they could affect the optical path of light travelling through the PDMS, so must be removed before casting.

Figure 6.11: Bubbles in the PDMS after mixing. These can be popped by evacuating the mixture in a desiccator, then re-evacuating the desiccator chamber. This puts strain on the walls of the bubbles, leading them to pop at a faster rate.

Once the bubbles have been removed, the PDMS mixture can be cast over the mould. During the casting process, more bubbles may form, but these can also be removed using the air evacuation technique described above. It can be useful to place an anchor into the mould to aid with the removal of PDMS once it has set. A slightly bent paperclip was used for this purpose as shown in figure 6.12. The PDMS cures at room temperature over a 24 hour period, but this process can be accelerated by heating the mixture to ~ 60 °C, causing it to set in approximately one hour. The PDMS is cured when it is no longer sticky to the touch. Once set, the PDMS can be shaped using a Stanley knife to cut it into a suitable sized shape for sticking to the surface of the chip.

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Figure 6.12: A PDMS cast after setting. A blue paperclip anchor has been used in this instance to aid in the removal of the PDMS. Once set, it is rubbery in texture and appears transparent like glass.

The surface of the ring resonator microchip features several raised Al contact pads for thermal tuning experiments. If these are not removed, they act like tent-poles, pitching up the PDMS and degrading the final surface seal. To remove the Al contact pads, an aluminium chemical etch was used for one hour. The chip was then cleaned in acetone, deionised water and IPA to remove any residue then left to dry. This removes the raised Al contact pads and leaves a flush flat silicon oxide surface (minus the etched windows for sensing) over which to stick the PDMS microfluidics mould to.

As a final stage, to ensure that the PDMS forms a good seal with the SiO2 surface of the chip, both surfaces were UV Cleaned before being placed together. UV cleaning is used because it is energetic enough to decompose the methyl side chains but not energetic enough to react with the Si-O backbone. It is also able to help remove surface stored carbon. While 3x15 minute bursts of UV cleaning were used here to prime the surfaces for adhesion, plasma etching is often used as a popular alternative.

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With this processing complete, the silicon chip surface and PDMS microfluidic cast can be placed together. This was done by hand and eye co-ordination under a far field optical microscope in this instance, but an automated system may provide higher accuracy. Once the PDMS and silicon chip have been placed together, they should hold together, but a further anneal of 100 °C for an hour was conducted to ensure a strong surface bonding. An image of a bonded microfluidic chip can be seen in figure 6.13

Figure 6.13: The PDMS microfluidic channel after bonding to the surface of the microchip. Needles can be used to inject and eject fluid through these channels accessed through the raised bubbles on the right hand side. The yellow dots represent where the input and output diffraction gratings are.

In order to test the microfluidic channel, syringe needles were used for a sequence of flushing the channels with deionised water, flowing glucose dissolved into deionised water (8.4% weight), and rinsing again with deionised water. This was to ensure that repeatable rinses were possible and that the system doesn’t easily get contaminated. Spectral measurements were taken at each stage using the broadband light source and OSA 302B spectrometer.

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Unfortunately the chip needed to be removed at each stage of the flushing sequence, hence only snapshot spectra could be obtained, rather than real time measurements.

6.4.2 Results

The positioning of the microfluidic channel lined up best with ring resonators G10 and G12, both 50 μm radius rings, with 200 nm and 250 nm separation gaps. Offset spectral results can be seen in figures 6.14 and 6.15. These have been flattened to remove the Gaussian signal contribution from the broadband light source. Each peak has had a Lorentzian curve fitted which in turn provides accurate measurements of peak position and Q-factor.

50 μm, 200 nm Gap, Microfluidics Glucose Test

4.5 4 3.5 3 2.5 Deionised Water 2 2 Glucose Sol (8.4% wt) 1.5 Deionised Water 1 1 Starting Position 0.5 Transmission(Arbitrary Units) 0 1547 1548 1549 1550 Wavelength (nm)

Figure 6.14: Results from the microfluidics glucose test for ring resonator G10, a 50 μm radius ring resonator with a 200 nm separation gap. Wavelength Stage Wavelength (nm) Q-Factor Difference from deionised water 1 Starting Position 1548.35 4200 -0.20 Deionised Water 1 1548.55 6700 0 Glucose Solution 1549.01 8500 0.46 Deionised Water 2 1548.58 5200 0.03

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50 μm, 250 nm Gap, Microfluidics Glucose Test 4.5

4 3.5 3 2.5 Deionised Water 2 2 Glucose Sol (8.4% wt) 1.5 Deionised Water 1 1 Starting Position Intensity(Arbitrary Units) 0.5 0 1548 1549 1550 1551 Wavelength (nm)

Figure 6.15: Results from the microfluidics glucose test for ring resonator G12, a 50 μm radius ring resonator with a 250 nm separation gap.

Wavelength Stage Wavelength (nm) Q-Factor Difference from deionised water 1 Starting Position 1549.59 6000 -0.05 Deionised Water 1 1549.64 7300 0 Glucose Solution 1549.96 6800 0.31 Deionised Water 2 1549.68 5200 0.03

6.4.3 Discussion

It should be noted that the shift in figures 6.14 and 6.15 due to the 8.4% weight glucose solution is different for each ring resonator, at 0.46 nm (G10) and 0.31 nm (G12). The reasoning for this may be due to poorer mixing of the liquid solutions over G12, which in turn is due to bad placement of the microfluidic channel. This could be improved by placing the microfluidics channels mechanically rather than by hand, as was conducted in this experiment.

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We can use the shift measured on ring resonator G10 to calibrate the sensitivity of the windowed ring resonators. We calculate a shift of 0.0545 nm/% glucose. According to research by Tan et al, the refractive index of a 10% weight glucose solution is 1.3475 at 25°C.11 At 1500 nm and 25°C, distilled water has a refractive index of 1.3190.12 As such the difference is calculated to be 0.0285, which corresponds with a 0.545 nm shift leaving us with a device bulk sensitivity of 19.12 nm/RIU. Comparing these results with figure 6.4, there is a measured a shift of 1.19 nm between the 10% weight starting point and point of dilution, this indicates that the solution would have increased to 31% weight glucose in in that time, suggesting that the volume of water in the solution in figure 6.4 reduced in volume by 67.7 %. This approach of evaporating glucose in a solution could be used for making highly sensitive volumetric measurements on a small scale, increasing the versatility of ring resonators as a sensing tool.

In order to take the microfluidics work further, it would be useful to further develop the pumping system so that the chip can remain stationary while different fluids are flowed through it. This would allow real time measurements with the microfluidics, which in turn would be of great value in surface functionalisation experiments as we could monitor over time, the adsorption of particles to the surface of the ring resonator. Unfortunately this project ended before automated microfluidics could be investigated.

6.5 Upconverting Nanoparticles

Moving away from conventional sensing and ring resonator applications, during this project, work was conducted in a collaborative project with Dr Chloë Oakland within the NOWNANO doctoral training centre, of which I also studied within. As she researched the synthesis of upconverting nanoparticles, and I worked on ring resonator sensing, we decided to combine our research and collaborate in an attempt to stimulate the emission of upconversion nanoparticles using the evanescent field of light confined within a ring resonator. The images used for figures in this section have also been used in Dr Chloë Oakland’s thesis,13 as they are a result of our collaborative efforts.

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Upconversion nanoparticles (UCNPs) are essentially quantum dots which merge two photons to produce upconversion, releasing a single photon with half the wavelength.14 These particles have particular applications in the field of biosensing, where they can replace traditional quantum dot and fluorophore luminescence. Both of these technologies typically require UV radiation for luminescence. Over time, the UV energies can damage the samples being studied or cause mutations. By using upconversion to stimulate emission, it is possible to illuminate using wavelengths which are less invasive and less damaging to living tissue.

Upconverting nanoparticles are lanthanide-doped nanomaterials. These particles give low Stokes emission upon low levels of irradiation in the near infrared spectrum, where many biomolecules are optically transparent. UCNPs also have sharp emission bandwidths, long lifetimes, tuneable emission, high photostability and low cytotoxicity,15, 16 making them ideal for bio-imaging and sensing applications.

Conventional luminescence processes typically involve one ground state and one excited emitting state. UCNPs use multiple intermediate states in order to accumulate low energy excitation photons. The processes responsible for upconversion are typically excited state excitation, photon avalanche and energy transfer upconversion.17 These processes occur via sequential absorption of two or more photons by a doped ion within the crystalline nanoparticle. Luminescent materials including f and d ions can be used to generate upconverting luminescence18, but the most efficient upconversion processes use trivalent lanthanide ions as they have extremely long lived intermediate energy states.19, 20

UCNPs are usually made of an inorganic host with lanthanide dopant ions embedded within. UC emissions can be expected from most lanthanide ions, but visible emissions under low pumping power are only generated using Er3+, Tm3+ and Ho3+ activators. These dopants are used because they have equally spaced energy levels that accommodate photon absorption and energy transfer as required for upconversion.14 To make the upconversion efficient, the properties of the host material is important. Ideally it should be transparent at the wavelengths of interest. Excited energies of the doped ions can also be absorbed through lattice vibrations.21, 22 Changes to the crystal structure in the host

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Chapter 6 – Sensing with Ring Resonators materials can also alter the crystal field around the dopant ions, leading to different optical properties.23-25 Ideally the host material should also have low phonon energy and high optical damage threshold. They should also have close lattice constants to the dopant ions in order to achieve higher doping levels. Meeting these criteria, the most suitable host materials are inorganic compounds of rare earth ions, alkaline earth ions and several transition metal ions.14

Nanoparticles with good structural crystallinity produce a strong crystal field around the doped ions, reducing the energy loss due to crystal defects. Small particle size is also advantageous to biosensing and similar applications. Typical synthesis techniques for UCNPs with high crystallinity, well controlled size, dispersity, and well defined crystal phase require careful control over factors such as reaction temperature and reaction time.26 These processes can lead to particle aggregation, enlarging particle size.

In literature, other research groups have started to look at merging waveguide ring resonator technologies and upconversion technologies as they both operate in the NIR 27 regime. In 2010 Dong et al reported the use of Er3+ to dope the surface of silica microspheres. The result was the ability to visualise the whispering gallery mode in the visible spectrum around the microspheres. Using an excitation wavelength of 780 nm, observable emissions were measured at 1550 and 550 nm.

In 2007, Morgan and Mitchell28 also investigated the evanescent coupling of an erbium doped waveguide to an absorbed fluorophore and characterised the luminescence from the erbium dopant. The erbium emission was highly structured with well separated bands of violet, green and red spectral regions. The intensity of the bands was dependent on the power density of infrared excitation, with the green emission dominating at lower power densities and the red emission increasing more as power density increased. They also detected a surface monolayer of fluorescent protein R-phycoerythrin which was bound to the upconverting waveguide. The waveguide was made from Yaglass (a ceramic glass made mostly with lead fluoride), so it wasn’t CMOS compatible like the systems investigated here, and it didn’t incorporate ring resonators, as proposed here.

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6.5.1 Method

In order to combine upconversion nanoparticles with ring resonators, compatible particles and ring resonators were required, which would have a corresponding excitation wavelength. Si3N4 slotted ring resonators were chosen, as donated by Professor Roel Baets at Ghent University in association with the nanoelectronic company Imec. These ring resonators are transparent at 980 nm, which is also the excitation wavelength of many UCNPs. In theory it was expected that this would enable excitation within both the ring resonators and UCNPs. Several approaches were adopted in attempts to illuminate the UCNPs over the ring resonators. In the first case, A PMMA mask was created with the help of Dr Scott Lewis from the University of Manchester; the mask had windows opened over the ring resonators. Using a drop casting method, the surface of the PMMA mask 3+ and ring resonators was coated with commercially available PTIR545 UCNPs (Gd2O2S:Yb , Er3+) using a micro nib. The PMMA coating was then washed away with acetone using 3 immersions in a beaker of acetone for 2 minutes, leaving the remaining UCNPs localised over the ring resonator specifically.

With the help of Professor Stan Botchway and Dr Andy Ward in the lasers for Science Facility (LSF) at the Harwell Research Complex, the waveguides and ring resonators were excited.

To do this, a 980 nm Ti:Sapphire laser was used in conjunction with a Becker and Hickl (B&H) scan head to align the position of the laser with respect to the waveguides. Using a Semrock FF705-Di01-25x36 dichroic fluorescence lifetime image mapping (FLIM) detector, which transmits ~90% at 980 nm and reflects below 705 nm and transmits above 750 nm, the laser was aligned.

This filter was then switched to a Semrock FF01-750/SP-25. This transmits between 380 nm and 720 nm, reflecting above 720 nm. Using this new filter it was possible to image the emission from UCNPs, while preventing any reflected laser light, protecting the camera. Unfortunately it was not possible to acquire a spectrometer that would function at 980 nm. Hence no measurements of the transmission spectra of the ring resonator

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Chapter 6 – Sensing with Ring Resonators were made. Assumptions were made about the bandwidth of the light source and coupling with the ring resonators as shown in figure 6.16.

Figure 6.16: Going into testing, the specific wavelengths would be required for coupling to the ring resonator were unknown. It was assumed that through the use of a reasonable bandwidth Ti:Sapphire laser light source and tuning through wavelengths, it would be possible to couple to the ring resonator in at least one wavelength setting around 980 nm.

As can be expected, this testing approach was coarse, but the UCNPs were illuminated using this technique as seen in figure 6.17. The problem was that it was difficult to determine whether the illumination was due to the ring resonators or scattering from the laser against the surface at this point.

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Figure 6.17: Brightfield images of the ring resonators with UCNPs drop cast onto their surface. b), c) and d) show the UCNP emission when the laser was focussed onto positions 1, 2 and 3. As can be seen, the emission changes based on laser position, but isn’t limited to the localised region of the ring resonators. This suggests that the UCNPs may be illuminated by surface scattering. If any illumination was caused by the ring resonator itself, it would be masked by the surface scattering illumination. The ring resonators used were approximately 150 μm in diameter but the coupling length varied slightly with each ring.13

The results in figure 6.17 suggested that further experimental refinement was required in order to determine whether direct stimulation of the UCNPs via the ring resonators was being observed.

With the assistance and training of Dr Adam Parry and Professor Stephen Yeates from the University of Manchester, the use of inkjet printing was explored to deposit the UCNPs in a controlled, precise manner to the surface of the ring resonators. Using a 1 mg/mL

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3+ 3+ dispersion of UCNPs (NaYF4:20 %Yb , 0.2% Tm ) in a 1:1 mixture of H2O: ethylene glycol as an ink and a Super Inkjet SIJ-S050 inkjet printer, the printing was conducted. In order to eject the UCNP suspension ink, a nozzle working distance of 40 μm was used, with an 800V potential between the nozzle and substrate. To switch the nozzle on and off, a pulsed sinusoidal waveform of 75V was used. A pattern to match the ring resonator shape was designed using the inkjet printers CAD software and printing was repeated 40 times over each ring resonator tested, in order to deposit a satisfactory layer of UCNPs over the ring resonators. The resulting printing can be seen in figure 6.18

Figure 6.18: Brightfield images of the UCNP inkjet printing using a Leica DM 2700M microscope. a) and b) show the ring resonators beforehand at a 300 μm scale and 60 μm scale. c) and d) show the ring resonators after inkjet printing. As shown, the nanoparticles are represented by the dark spots, which are over the ring resonator waveguide.13

As can be seen in figure 6.18, the inkjet printing method has greater precision and accuracy than the drop casting method we initially used.

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Using the facilities at LSF, the newly inkjet-printed UCNPs were tested. The same Ti:Sapphire laser was used, adjusting its position using the B&H scan head. The light source was aligned to the input waveguides using a Chroma Zt1064rdc dichroic filter which reflects ~95% at 980 nm while transmitting below 940 nm and a Thorlabs FGS600 KG5 filter which transmits ~95% at 980 nm while transmitting 80% between 330 nm – 665 nm. When monitoring the emission of the UCNPs, filters which transmitted between 380 and 720 nm were used, reflecting above 720 nm. This time, a more sensitive iXon Ultra 897 electron multiplying charged coupled device (EMCCD) camera was used to raise the chance of capturing the low intensity emission of UCNP excited by the ring resonator.

6.5.2 Results

Images of the ring resonators and inkjet-printed UCNPs, can be seen in figure 6.19.

Figure 6.19: a) The Ti:Sapphire laser 980 nm illumination, with the output grating highlighted by red circles. b) the output grating under a 980 nm input grating illumination. c) The signal after the 330 nm – 665 nm window filter has been applied. As can be seen, the UNCPs based around the ring resonator are illuminating. Figures a – c are shown with a white light illuminating the chips surface, allowing a view of where signals are coming from. Figures d), e) and f) show the equivalent results without white light illumination.13

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In order to determine whether the UCNP illumination was due to the ring resonator or surface scattering of the light source, the light source target was changed to directly illuminate the ring resonators and compare results. These can be seen in figure 6.20.

Figure 6.20: a) The original ring resonator based illumination. b) UCNP illumination when the 980 nm laser is incident over the top left of the ring resonator. c) UCNP illumination when the 980 nm laser is incident over the bottom of the ring resonator. d) UCNP illumination when the 980 nm laser is incident over the right of the ring resonator. As can be seen, the footprint of UCNPs is drastically different when directly illuminated when compared to stimulation via the ring resonator.13

As a final check, the input wavelength was tuned at values of 960 nm and 970 nm for a comparison and the emission results were imaged. The results of this comparison are shown figure 6.21.

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Figure 6.21: The output grating (circled in red) when stimulated by a) 960 nm, b) 970 nm and c) 980 nm input signal. As shown, the waveguide transmits at each of these wavelengths. d), e) and f) show the corresponding UCNP emission signals. The only stimulant wavelength that leads to UCNP emission is 980 nm.

Figure 6.21 shows that the input wavelength can have an impact on UCNP emission. The reason for this may be due to light not coupling into the ring resonator, or the wavelength not being high enough in energy to stimulate the upconverting process.

6.5.3 Discussion

As shown in this section, evidence suggests that direct stimulation of the UCNPs has been achieved using the evanescent field from light confined within a ring resonator. This is the first time in literature that this has been reported. It should be noted that the signal was weak and the more sensitive iXon Ultra 897 EMCCD camera with appropriate filters was required to detect this signal. This experiment is proof of principle that it is possible to merge UCNPs with ring resonator technology. Merging these two technologies, it may be

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Chapter 6 – Sensing with Ring Resonators possible to develop a dual mechanism biosensor on a micro-scale with each technology compensating for the shortfalls of the other.

Inkjet printing directly onto waveguides as a method of surface functionalisation was also introduced. The use of inkjet printing could be taken further as follows: UCNPs could be printed over the double ring resonator systems from chapters 4 and 5, illumination would give a better look at how light propagates through the ring resonators as they are tuned relative to each other. This would give more information on how the light was behaving as the peaks overlap and the induced transparencies and Fano resonances take effect. This in turn would lead to a better understanding of the physics involved.

The majority of anti-body to antigen surface functionalisation techniques occur under wet conditions, it may be possible to use inkjet printing to specifically upscale targeted printing of targeting antibody or protein surfaces to the ring resonators, as has already been demonstrated by several research groups.29-31 With a goal of commercialising these technologies, the use of inkjet printing could greatly improve the versatility of sensing chips without the need for highly complex micro-fluidics systems. Instead, just a single channel could be used to flow over several ring resonators, each functionalised with inkjet printing before a basic form of microfluidics is applied.

6.6 Conclusion

To summarise, in this chapter initially some basic drop cast sensing was conducted with single ring resonators, targeting PMMA, phosphate buffer saline (PBS), glucose and deionised water. During these initial investigations, the movement of resonant peaks was also investigated as a glucose solution increased in concentration with droplet evaporation on the surface.

Surface functionalisation techniques were then investigated, applying a surface layer of APTES, biotin-NHS and streptavidin to the surface of the ring resonators. In this investigation, it was found that the ring resonators closer to the edge of the chip had lower cohesion in their peak shifting during each stage of application. The ring resonators

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Chapter 6 – Sensing with Ring Resonators closer to the centre of the chip showed more consistent shifting. As such, it was determined that microfluidics may be more reliable for surface functionalisation than drop casting with pipettes.

Following these initial surface functionalisation tests, a microfluidic system was developed in a bid to observe more consistent peak shifting behaviour, removing environmental factors which could contribute to noise. Using PDMS silicone to cast over a microfluidic mould, a repeatable system was created for applying microfluidics to the surface of the chip.

Testing the microfluidics system with deionised water and glucose resulted in a calibration of the sensitivity of a 50 μm radius single ring resonator, measuring it at 19.12 nm/RIU change. When flushing the system back through with deionised water, the spectral peaks reverted back to their original position, proving the repeatability of this method for future biosensing and surface functionalisation investigations. Using these new calibrations, it was possible to further analyse the glucose droplet evaporation from the initial sensing investigations. Unfortunately time on the project ran out before a more sophisticated automated delivery system could be developed, which would have enable real time microfluidics measurements.

As a final alternative investigation, collaborating with Dr Chloë Oakland, the optical emission of upconverting nanoparticles (UCNPs) was achieved using the evanescent field from some silicon nitride ring resonators. To achieve this it was necessary to attempt both drop casting the nanoparticles and inkjet printing them. Notably greater precision was achieved when depositing with the inkjet printer. Using a Ti:Sapphire laser and several filters and cameras at the Lasers for Science Facility (LSF) at the Harwell Research Complex it was possible to excite the ring resonator and stimulate emission from the upconverting nanoparticles. This proof of principle investigation showed how UCNPs could be used in principle to image the intensity of light within waveguides. The idea of using inkjet printing was introduced, to further increase the sensing versatility of ring resonator systems.

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6.7 References

1. N. Trummer, N. Adányi, M. Váradi and I. Szendrö, Fresenius' journal of analytical chemistry, 2001, 371, 21-24. 2. M. Iqbal, M. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey and L. C. Gunn, Selected Topics in Quantum Electronics, IEEE Journal of, 2010, 16, 654-661. 3. A. L. Washburn, L. C. Gunn and R. C. Bailey, Analytical chemistry, 2009, 81, 9499-9506. 4. A. L. Washburn, M. S. Luchansky, A. L. Bowman and R. C. Bailey, Analytical chemistry, 2009, 82, 69-72. 5. H. Li and X. Fan, Applied Physics Letters, 2010, 97, 011105. 6. X. Jiang, Y. Chen, F. Yu, L. Tang, M. Li and J.-J. He, Opt. Lett., 2014, 39, 6363-6366. 7. J. S. del Río, T. Steylaerts, O. Y. Henry, P. Bienstman, T. Stakenborg, W. Van Roy and C. K. O’Sullivan, Biosensors and Bioelectronics, 2015, 73, 130-137. 8. N. A. Lapin and Y. J. Chabal, The Journal of Physical Chemistry B, 2009, 113, 8776-8783. 9. M. Lake, C. Narciso, K. Cowdrick, T. Storey, S. Zhang, J. Zartman and D. Hoelzle, Protoc. Exch, 2015, 10. 10. Y. Temiz, R. D. Lovchik, G. V. Kaigala and E. Delamarche, Microelectronic Engineering, 2015, 132, 156-175. 11. C.-Y. Tan and Y.-X. Huang, Journal of Chemical & Engineering Data, 2015, 60, 2827-2833. 12. G. M. Hale and M. R. Querry, Applied optics, 1973, 12, 555-563. 13. C. Oakland, in Science and Engineering, The University of Manchester, 2016. 14. F. Wang, D. Banerjee, Y. Liu, X. Chen and X. Liu, Analyst, 2010, 135, 1839-1854. 15. W. M. Yen and M. J. Weber, Inorganic phosphors: compositions, preparation and optical properties, CRC press, 2004. 16. G. Blasse and B. Grabmaier, in Luminescent materials, Springer, 1994, pp. 1-9. 17. S. Sivakumar, F. C. M. van Veggel and P. S. May, Journal of the American Chemical Society, 2007, 129, 620-625. 18. F. Auzel, Chemical reviews, 2004, 104, 139-174. 19. J. Suyver, A. Aebischer, D. Biner, P. Gerner, J. Grimm, S. Heer, K. Krämer, C. Reinhard and H.-U. Güdel, Optical Materials, 2005, 27, 1111-1130. 20. F. Wang and X. Liu, Chemical Society reviews, 2009, 38, 976-989. 21. S. Heer, O. Lehmann, M. Haase and H. U. Güdel, Angewandte Chemie International Edition, 2003, 42, 3179-3182. 22. S. Heer, K. Kömpe, H. U. Güdel and M. Haase, Advanced Materials, 2004, 16, 2102-2105. 23. A. Patra, C. S. Friend, R. Kapoor and P. N. Prasad, Applied physics letters, 2003, 83, 284- 286. 24. G. Yi, H. Lu, S. Zhao, Y. Ge, W. Yang, D. Chen and L.-H. Guo, Nano letters, 2004, 4, 2191- 2196. 25. K. W. Krämer, D. Biner, G. Frei, H. U. Güdel, M. P. Hehlen and S. R. Lüthi, Chemistry of Materials, 2004, 16, 1244-1251. 26. F. Wang, Y. Han, C. S. Lim, Y. Lu, J. Wang, J. Xu, H. Chen, C. Zhang, M. Hong and X. Liu, nature, 2010, 463, 1061. 27. C. Dong, Y. Yang, Y. Shen, C. Zou, F. Sun, H. Ming, G. Guo and Z. Han, Optics Communications, 2010, 283, 5117-5120. 28. C. Morgan and A. Mitchell, Biosensors and Bioelectronics, 2007, 22, 1769-1775. 29. J. T. Delaney, P. J. Smith and U. S. Schubert, Soft Matter, 2009, 5, 4866-4877. 30. I. McWilliam, M. C. Kwan and D. Hall, Protein Microarrays: Methods and Protocols, 2011, 345-361. 31. B. Derby, Journal of Materials Chemistry, 2008, 18, 5717-5721.

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7.1 New Contribution to Knowledge

While similar work has been conducted in literature, as cited and referenced in this thesis, to my knowledge, I have managed to make a new and original contribution to knowledge in the field in the following ways:  The experimental characterisation of single ring resonators with the specific manufactured designs has been achieved as highlighted in chapter 4.1, gaining values of their Q-factors at separation distances of 200 nm, 250 nm and 300 nm. The spectral characterisations of equivalent single ring resonators with additional drop ports were also measured.  Using the thermal on-chip TiN heating elements, the spectral shifting performance of the single ring resonator configurations was also achieved, testing against a general background hot plate heating effect for calibration. These characterisations can be applied to equivalent systems in the future.  The spectral responses of the more complex double ring resonator Mach-Zehnder and Y-splitting configurations with a central drop port were measured to a very high resolution at different on-chip heater values. In doing so, the generation of Fano type resonances were observed in the throughputs and a coupled resonance induced transparency (CRIT) features were observed in the central drop port when the peaks from both ring resonators overlap. These behaviours were then characterised, revealing that the CRIT feature had an improved device sensitivity of 2.7 times compared to an equivalent single ring resonator and the Fano resonance shape, when tuned translationally, had a sensitivity of 2.0 times the single ring equivalent.  Working with the model developed by Matteo Cherchi of VTT in Finland, his novel 3x3 transfer matrix model was compared against the more complex double ring resonator Mach-Zehnder and Y-splitting configurations with a central drop port. In doing so, it was discovered that the model breaks down as the peaks overlap. An adapted model was proposed which combined peaks, providing an alternative

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which fitted the experimentally measured data very effectively for throughput signals. Using The modified model suggested that the reason for the unusual breakdown close to overlap was because of light travelling through an S-shape configuration across the double ring setup, rather than being confined to just the ring resonators.  Developing a PDMS based microfluidic system, the single ring resonators (50μm radius) were characterised as bulk refractive index sensors using glucose in deionised water for calibration.  Working in collaboration with Dr Chloë Oakland from the University of Manchester’s school of chemistry, the excitation of upconversion nanoparticles was achieved by directly using the evanescent field of single silicon nitride ring resonators, using inkjet printing as a nanoparticle deposition method.

7.2 Progress towards meeting the Thesis Aims

The original aims of this project were to test and characterise the ring resonator devices developed by Dr Joseph Lydiate during his time as a PhD student, and also to explore their potential applications as a biosensing technology. Through the work presented, I believe that these aims have been achieved, referencing the new contributions to knowledge listed above as a justification. It would have been good to develop the biosensing portion of this project further, but new discoveries in the double ring characterisation and modelling portion of this project required more time than originally expected as the complexity of the system became clear.

7.3 Future Continuation of this Research

While significant progress has been made in this project, there are also several ways in which this work can be developed and taken further. These are listed as follows:

 The novel double ring resonator designs (section 5.4.5) which will be fabricated soon will need testing. These will hopefully offer new insights into the relationship between double ring resonators with a central channel, allowing the combination

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of mismatching ring resonator sizes, the ability to thermally tune the rings only, and the ability to characterise the devices without a central drop port channel. This will provide a substantial amount of new data which will need modelling in the future.  The 3x3 transfer matrix model developed by Matteo Cherchi needs further modification before it will be able to model the drop port signal reliably without inexplicably requiring huge losses in one ring relative to the other.  The ground work which was conducted with the microfluidics needs automating, and some real time calibration measurements and tests need to be conducted. Following this, it will be possible to further develop this technology into a fully- fledged biosensor. This could also be merged with the inkjet printing technology which was explored, allowing easier automation and the development of more versatile biosensing arrays.  If the upconverting nanoparticles can be fabricated to work with the double rings, it will be possible to visually see how light flows through the rings as they overlap and interact with each other. If not, a silicon nitride double ring resonator system could be developed which would be compatible with the UCNPs.  Finally, a system which throws it all together is yet to be realised. A double ring resonator system can be imagined, with a central drop port, with two microfluidic channels and thermal tuning. One window could be used as a reference window while the second which could be functionalised using liquid deposition or inkjet printing. These could be used to adsorb biomolecules targeted for their relevance towards specific diseases. The use of two ring resonators would reduce environmental temperature noise contributions, and the use of the double ring setup with a central drop port would enable the more efficient CRIT tuning sensing mechanism.

While this list is quite long, it demonstrates how this trail of investigation is far from concluded. If developed far enough, it may ultimately lead to commercial industrialisation and a revolution in diagnostic and pathological healthcare. Professor Matthew Halsall has

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Chapter 7 – Conclusions and Future Outlook arranged for a Post-doctoral researcher to look further into the thermal tuning side of this research, so it should be possible for this work to be developed further.

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