Design of Erbium-Doped Tellurium Oxide Optical Amplifiers on a Low-Loss Silicon Nitride Waveguide Platform

Design of Erbium-Doped Tellurium Oxide Optical Amplifiers on a

Low-Loss Silicon Nitride Waveguide Platform

Design of Erbium-Doped Tellurium Oxide Optical Amplifiers on a

Low-Loss Silicon Nitride Waveguide Platform

By CHENGLIN ZHANG B.Eng (HIT, Harbin, China) 2016

A Thesis Submitted to the School of Graduate Studies in Partial Fulfillment of the Requirements for the Degree Master of Applied Science

McMaster University © Copyright by Chenglin Zhang, September

2018

MASTER OF APPLIED SCIENCE (2018) (Department of Engineering Physics) McMASTER UNIVERSITY Hamilton, Ontario

TITLE: Design of Erbium-Doped Tellurium Oxide Optical Amplifiers on a Low-Loss Silicon Nitride Waveguide Platform

AUTHOR: Chenglin Zhang, B.Eng. (Harbin Institute of Technology, China)

THESIS SUPERVISOR: Dr. Jonathan Bradley

NUMBER OF PAGES: XCV, 95

Abstract

Research interest in optical amplifiers has remained intensive over the years due to their widespread application in high-speed telecommunication systems. The requirement for amplification arises from the need to strengthen weakened signals as they propagate through optical fibers or through waveguides on chips and in order to meet strict system power budgets. Erbium-doped fiber amplifiers offer high, broadband and low-noise gain for wavelength-division multiplexed systems. Nevertheless, fiber amplifiers are bulky and many applications, including the development of compact transceiver modules for the data center, require an integrated on-chip solution. Erbium-doped waveguide amplifiers

(EDWAs), which are integrated onto silicon chips, could potentially replace EDFAs in many instances. Of prospective materials for EDWAs, erbium-doped tellurium dioxide has a range of advantages including its high refractive index for compact waveguides and bends, large erbium light emission bandwidth, high Er3+ ion solubility and high gain.

However, fabrication of erbium-doped tellurium oxide waveguides has proved challenging, and methods developed to date are not compatible with standard silicon- based photonic integration platforms. Meanwhile, silicon nitride is a standard high- quality light guiding platform due to its fairly high refractive index, high transmission throughout the visible and infrared spectrum and the compatibility of silicon nitride fabrication process with standard CMOS fabrication lines. The combination of erbium- doped tellurium oxide with silicon nitride technology could lead to compact and high performance optical amplifiers that are scalable and compatible with existing photonic

iii integration platforms. This thesis describes research on different designs of erbium-doped tellurium oxide optical amplifiers integrated on a low-loss silicon nitride waveguide platform. Both theoretical and experimental work is described in the context of improving the amplitude, capacity and stability of erbium-doped tellurium oxide optical amplifiers for communications. Specifically, Chapter 2 studies the theory and background of optical waveguides and rare earth dopants and their transitions. Chapter 3 presents the finite element method waveguide mode solver, tellurium oxide-coated silicon nitride waveguide design and amplifier model. In Chapter 4, simulation results on the optimization of the tellurium dioxide-coated silicon nitride waveguides are presented.

Modelling and comparisons between Er-doped Al2O3 and TeO2 waveguides are also described using a MATLAB code that provides predictive results for both of their performance. Fabrication and initial measurements results are generally shown in this chapter as well.

Acknowledgments

First of all, I would like to offer my deepest gratitude to my supervisor Dr. Jonathan

Bradley whose door was always open whenever I ran into a trouble spot or had a question about my research or writing. He consistently helped me in my simulation, lab work, and thesis which gave me a better understanding of silicon photonics field. I would like to thank him for his professional knowledge, kindness, patience, and politeness.

Also, I would like to thank Dr. Andy Knights who continuously offered help in the by weekly optical amplifier group meeting. In the cooperation between Dr. Knights' and Dr.

Bradley's groups, I learned how to work in different teams and met many amazing team members.

I also would like to thank Dr. Peter Mascher, Dr. Jonathan Bradley, Dr. Chang-qing

Xu, and Dr. Ayse Turak who offered me great classes during these two years on various subjects.

I would also want to say think you to all the group members in Dr. Bradley group:

Mengyuan, Dawson, Henry, Khadijeh, Jeremy, Cameron, Josh, Arthur, Caitlin, Daniel and many other people for their assistance and friendships over these two years.

Last but not least, I would like to thank my family far away in China who offered unconditional support and care when I lived alone in another country. Thanks to my mum, dad, and sister who skyped with me every week. Thanks to my friends in China, Canada, and Australia who talked to me once in a while offering me helpful advice and opinions

v about study and life.

Contents

List of Figures...... x

Index of Tables ...... xiii

Chapter 1 Introduction ...... 1

1.1Erbium-Doped Optical Amplifiers for Telecommunications ...... 1

1.2 Integrated Erbium-Doped Amplifiers ...... 3

1.3 Erbium-Doped Tellurium Oxide ...... 6

1.4 Low-Loss Silicon Nitride Waveguide Platform ...... 7

1.5 Thesis Outline ...... 8

Chapter 2 Theory and Background ...... 10

2.1 Waveguide Theory ...... 10

2.1.1 Planar Waveguides ...... 12

2.1.2 Ridge Waveguides ...... 21

2.2 Material Properties ...... 24

2.2.1 Rare Earth Dopants and Their Optical Properties ...... 24

2.2.2 Optical Properties of Erbium ...... 24

2.2.3 Erbium-Doped TeO2 Film Properties ...... 27

vii

2.2.4 Si3N4 Waveguide Properties ...... 28

2.3 Optical Amplifier Theory ...... 29

2.3.1 Loss Mechanisms in Optical Waveguides ...... 29

Chapter 3 Design and Modeling ...... 35

3.1 Waveguide Design ...... 35

3.1.1 Finite Element Method Waveguide Mode Solver...... 35

3.1.2 Optimization of TeO2-Coated Si3N4 Waveguides for Optical Amplifiers39

3.2 Erbium-Doped Amplifier Model ...... 40

Chapter 4 Results ...... 43

4.1 Waveguide Simulation Results ...... 43

4.2 Amplifier Modeling Results ...... 62

3+ 4.2.1 Application of Amplifier Model to Er -doped Al2O3 and TeO2 Waveguides

from Literature ...... 62

3+ 4.2.2 Amplifier Modeling Based on TeO2:Er -Coated Si3N4 Waveguide Design in

this Thesis ...... 67

4.3 Silicon Nitride Mask Layout ...... 70

4.4 Fabrication Results ...... 75

4.5 Measurements ...... 77

Chapter 5 Conclusions and Future Work ...... 80

viii

Appendix: Amplifier Simulation Code ...... 82

References ...... 91

List of Figures:

Figure 1.1: Amplification in an EDFA …………………………………………………3

Figure 1.2: Er-doped waveguide amplifiers and lasers for on-chip applications ………………...……………………………….……………………...……5

Figure 2.1: Planar waveguide……………………………………………………………12

Figure 2.2: Reflection and refraction of light at an interface……………………………13

Figure 2.3: One-dimensional confinement of light propagating in a step-index planar waveguide…………………………………………………………………………....…...14

Figure 2.4: A typical ridge waveguide…………………………………………………..21

Figure 2.5: A typical strip-loaded waveguide…………………………………………...22

Figure 2.6: Energy level diagram and selected transitions for erbium ions relevant to the

3+ 980-nm pumped TeO2:Er doped amplifier……………………………………………..25

Figure 2.7: The radial electric field of a bent waveguide…………..………….………...32

Figure 3.1: Cross-section schematic of the TeO2-coated Si3N4 waveguide structure…………………………………………………………………………………..35

Figure 3.2: Example of node connection in a FEM modesolver………...... ………36

Figure 3.3: Mesh image of grid size 0.1µm ...... ……………...... ……………38

Figure 3.4: Simplified Er3+ energy level diagram and transitions for the 980 nm pumped

3+ TeO2:Er amplifier…………………………………………………………..…………..40

Figure 4.1: Imaginary parts of the effective index of TE signal modes…………..….….44

Figure 4.2: Real part of the effective index of the TE signal modes……………...……..45

Figure 4.3: Mode profiles for TE modes 0, 1 and 2….……………..…………………...49

Figure 4.4: Imaginary parts of effective index of TE pump modes…………………..…50

Figure 4.5: Q factor and confinement for hTeO2 = 0.6µm…………….………………….53

Figure 4.6: Effective mode area………………………………...……………………….56

3+ Figure 4.7: Internal gain in an Al2O3: Er amplifier…………………………...…….…65

3+ Figure 4.8: Internal gain in an TeO2:Er amplifier………………………...…..……….66

3+ Figure 4.9: Internal gain calculated for a TeO2:Er -coated Si3N4 waveguide amplifier………...……….……………………………………………………………….69

Figure 4.10: Overview of the silicon nitride waveguide mask………………….…….…71

Figure 4.11: Layout of straight waveguides with width varying from 0.5 to

2.0µm……………………...…..……………….…….………….………………….…….72

Figure 4.12: Schematic of a taper structure…..……………………….…………...…….73

Figure 4.13: Layout of paperclip waveguides……………………………………….…..74

Figure 4.14: Demonstration of spirals…………………………………………….……..75

Figure 4.15: Sputtering system used to deposit tellurium oxide thin films………….…..76

Figure 4.16: SEM waveguide cross-section pictures…………………………..……...... 77

Figure 4.17: The waveguide transmission measurement setup…………………….....…78

Figure 4.18: Loss measurements for varying waveguide lengths………………….……78

xii

Index of Tables:

Table 3.1: Waveguide parameters varied in Figure 3.1……………………….…..……..39

Table 4.1: Single mode cutoff widths for different Si3N4 and TeO2 heights…………....51

Table 4.2: Waveguide parameters for calculated Q values and confinement factors in

Figure 4.5 …………………………………………….…………………………….….…53

Table 4.3: Minimum 0.98µm pump mode bend radii…….…………….……..…………54

Table 4.4: Minimum 1.55µm signal mode bend radii…...... …………………..55

Table 4.5: Effective 0.98µm pump mode areas……...….…………..…....……………...57

Table 4.6: Effective 1.55µm signal mode areas.………………………………………...58

Table 4.7: TeO2 intensity overlaps at 0.98µm…………………..……………....……….59

Table 4.8: TeO2 intensity overlaps at 1.55µm…………………………………………...60

Table 4.9: Pump-signal mode overlaps for 0.98µm pump wavelength………….…...….61

Table 4.10: Pump-signal mode overlaps for 1.48µm pump wavelength ………….….…62

3+ Table 4.11: Matlab simulation parameters for Er -doped Al2O3 and TeO2 waveguide amplifiers……….……...………………………………………………...……………….64

3+ Table 4.12: Parameters applied for calculation of gain in an Er -doped TeO2-coated

Si3N4 waveguide amplifier.………………………………………………………………68

xiii

Table 4.13: Variations of straight waveguides ………………………………………….72

Table 4.14: Variations of tapers in the mask…….…………….………………………...73

Table 4.15: Variations of paper clip waveguides...……………………………………...74

Table 4.16: Variations of spiral series…………………………………………………...75

iii

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Chapter 1 Introduction

1.1 Erbium-Doped Optical Amplifiers for Telecommunications

Optical amplifiers play the important role of enhancing degraded signals in high-speed telecommunications networks. The optical amplifier is essential because it compensates the inevitable loss during light propagation in fiber and enables long-distance telecommunications. The erbium-doped fiber amplifier (EDFA), which was commercialized in the early 1990s, can provide a signal gain in the range of 10-30dB in the C- and L-bands (1530-1565nm and 1570-1620nm wavelengths, respectively) [1].

Both bands are widely used in fiber-optic communications because they fall in the low- loss window of silica fiber. Thus, the EDFA, which happens to amplify light in this region because of the unique properties of the rare earth element erbium doped into the glass fiber, has become ubiquitous in long-haul communications and is one of the key enabling technologies for the fiber-optic network supporting the worldwide internet.

Generally, the basic working principle of EDFA is stimulated emission. The EDFA is based on silica fiber that is doped with the rare earth element erbium. It contains a laser coupler which couples the pump light into the fiber to excite the erbium atoms. The wavelength of the pump light is usually 980 nm or 1480 nm. After this, signal light will be coupled into the EDFA to trigger the stimulated emission. The excited electrons which are excited by the pump light to the upper level states will go back to lower energy states and emit energy in the form of light. The energy is primarily transferred to energy at the

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

same phase and wavelength as the signal light. In this way, the signal light can be amplified.

There are other types of optical amplifier such as semiconductor optical amplifiers

(SOAs) and Raman amplifiers (RAs). SOAs use a semiconductor as the gain medium and are electrically pumped as opposed to optically pumped. Raman amplifiers work based on

Raman scattering which was discovered by Sir Chandrasekhar Raman in 1928.

Currently, two kinds of Raman amplifiers are widely used in technology. One is the lumped Raman amplifier using DCF (dispersion compensation fiber) or higher nonlinear fiber as the gain medium, while the other one is the distributed Raman amplifier.

Compared to them, EDFA has many advantages. EDFA has lower noise while higher pump power utilization (>50%). The maximum signal gain of an EDFA (>40dB) is also higher than an SOA (30dB) or RA (25dB), as well as the maximum output power.

The most basic property of the EDFA is light amplification. Specifically, as Figure 1.1 shows, pump laser and signal light are coupled into fiber doped with erbium ions (Er3+).

The pump light excites the Er3+ ions to excited states and the energy transition happens when the signal laser stimulates the excited ions back to the ground state. After this process, the signal is amplified and outputted through the other end of the fiber.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Figure 1.1: Amplification in an EDFA [2]

1.2 Integrated Erbium-Doped Amplifiers

Erbium doped amplifiers have been widely researched in these days because they play a significant role in long haul optical communication. In general, the EDFA and the rare earth doped on chip amplifier are the two major types. While both were developed extensively during the early years of the Internet, the EDFA has dominated commercially because of its inherent compatibility with fiber-optic communications systems. However, due to the growing need for cost-effective, highly compact and efficient integrated photonic circuits, driven by the urgent demand for optical solutions for short-reach networks and data centers, the erbium-doped waveguide amplifier (EDWA) is gaining research’s interest again these years [3]. In this thesis, we focus on the integrated on chip erbium-doped waveguide amplifiers which are widely applied to the silicon photonics field.

Er3+is one of the most commonly used doped ions in integrated photonics and the

EDWA is one effective way to amplify light signal at optical communication window between 1500 to 1600nm. The EDWA is similar to the erbium-doped fiber amplifier but

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

uses a small size waveguide instead of several meters fiber to amplify the input signal.

The rapid development of the EDWA allows for the integration of a whole sophisticated amplified system, or integrated optical circuit, on a single small size chip, improving the efficiency and reducing the cost at the same time. A typical structure of an EDWA is shown in Figure 1.2. Light finds its way through the waveguide and amplification takes place in the Er3+ doped layer.

Compared to the EDFA, the EDWA has the primary advantage of size. Because of higher doping concentrations, the length of an EDWA is much shorter than an EDFA.

The higher refractive index difference between waveguide core and cladding in an

EDWA allows the device to have tighter bending radius, so that it takes up a significantly smaller footprint. The index contrast also allows for smaller-core waveguides, enabling higher intensities in the waveguide, thus lower threshold pump power for signal gain. In addition, when integrated on silicon chips, the EDWA can be co-integrated with other silicon photonic circuit elements (e.g. filters, multiplexors, modulators and detectors) to realize ultra-compact photonic microsystems with advanced performance and functionality.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Figure 1.2: Er-doped waveguide amplifiers and lasers for on-chip

applications [3]

A typical fabrication process of an EDWA includes deposition of an erbium-doped thin film by reactive co-sputtering onto a silicon wafer with a thermal silicon dioxide layer on it. The thermal oxide acts as the lower cladding of the waveguide. The erbium- doped film is then structured by lithography and wet chemical or reactive ion etching to form a ridge waveguide core followed by deposition of a SiO2 top-cladding layer. While these steps work for stand-alone devices, if one wishes to integrate such amplifiers into silicon photonic systems, one must ensure compatibility with existing silicon processing methods. This generally requires that the waveguide material be fabricated using silicon- compatible materials (e.g. silicon nitride), and the erbium-doped material be deposited in a post-processing approach onto the pre-fabricated silicon photonic wafer, since rare- earth dopants are not allowed in silicon foundries.

When it comes to the design and performance optimization of EDWAs, there are

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

several challenges. Because shorter device lengths are utilized, larger erbium concentrations are required, leading to solubility issues such as fast-quenching of clustered ions, which is highly dependent on the erbium host material. In addition, significantly higher losses are realized in integrated waveguides vs. fiber, resulting in reduced gain and noise performance. Polarization dependence and fiber-chip coupling loss due to mode mismatch between the integrated waveguide and fiber are additional challenges. Further, for integration within silicon-based photonic systems there is the aforementioned issue of processing and materials compatibility.

1.3 Erbium-Doped Tellurium Oxide

Many materials have been explored for integrated rare earth amplifiers. In this thesis,

3+ Er doped tellurium dioxide (TeO2) has been focused on since it has high erbium solubility, increasing the concentration of PL emission centers. Compared to erbium doped silicates, Er3+doped tellurium dioxide also exhibits a significantly broader emission bandwidth spanning the C and L bands and higher peak gain. TeO2 has a high refractive index (2.1), allowing for highly compact waveguides and integrated devices.

Furthermore, tellurite thin films can be deposited at room temperature and require no post-annealing, ideal for post-processing onto a variety of photonic integrated circuit platforms. Considering all these excellent optical properties, Er3+doped tellurium dioxide is a highly prospective medium for integrated optical amplifiers [4].

However, the etching of Er-doped TeO2 is challenging. One situation may happen is that the surface of the structure become very rough and grassing effects may happen when

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Er-doped film are etched using the Hydrogen/Methane/Argon gas mix. Further, methods to fabricate waveguides to-date result in larger waveguide structures and are not compatible with standard wafer-scale foundry processes [4]. Ideally, we want to develop a post-processing approach to integrate compact erbium-doped TeO2 amplifiers into standard silicon photonic circuit platforms.

1.4 Low-Loss Silicon Nitride Waveguide Platform

Silicon nitride (Si3N4) is known to be an excellent platform for photonic integrated circuits (PICs) [5]. It has extremely low losses throughout the visible and near-infrared, with losses < 0.1 dB/cm demonstrated [6].

The high refractive index of Si3N4 (~2.0) allows it to attain high light confinement, which is essential considering the light propagation situation. Plus, small nonlinear losses, a high Kerr-nonlinearity figure-of-merit, and low dispersion are advantages that worthy of being considered during its application on PICs [7].

Si3N4is also easily used to manufacture waveguides on a wafer scale and within advanced silicon photonic circuits because of its compatibility with CMOS fabrication.

Silicon nitride itself has poor erbium solubility, thus to the best of our knowledge optical gain has not been demonstrated in erbium-doped silicon nitride waveguides. Here, we investigate a novel approach that combines the advantages of silicon nitride waveguide technology with those of erbium-doped TeO2 thin films. Specifically, we study and optimize low-loss Si3N4 waveguides coated in erbium-doped TeO2 films for their application in EDWAs.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

1.5 Thesis Outline

3+ This thesis revolves around the development of Er doped TeO2 amplifiers on a low- loss silicon nitride waveguide platform. Chapter 2 describes the waveguide theory, followed by the description of the material properties. The energy level structure of the erbium ions and associated transitions related to light emission are also described. A review of the loss mechanisms in optical waveguides is provided as well as the requirements for optical gain. The focus is on amplifier modeling. The coupled ordinary differential rate equations used to describe the populations of the electronic levels in the erbium ions and build the model are presented.

The next chapter 3 starts with a brief review on the waveguide design which determines the mode performance in the waveguide. After that, this chapter introduces the finite element method mode solver, which plays a key role in determining the waveguide properties and solving the rate equations of the Er3+ transmission model in the amplifier.

Subsequently, the optimization of waveguides for optical amplifiers is presented.

Furthermore, a discussion introducing the TeO2-Si3N4 waveguide design is presented.

Chapter 4 documents the simulation and fabrication results. Considering different height and width conditions of Er3+ doped tellurium dioxide films, various output optical simulated results are discussed. Chapter 4 also includes all the amplifier modeling based on the erbium-doped waveguides from literature and this thesis. In this chapter, the mask layout with, which contains numerous amplifier structures like straight waveguides, spirals, and paper clips, is presented and their different properties are discussed. The

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

details of initial measurements on the fabricated chips are included, such as the measurement setup diagram, measurement instruments and specific method and process.

Chapter 5 concludes this thesis with a summary of important results of this work and discusses the future direction to be taken. The Matlab code used for optical amplifier calculations is included in the appendix.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Chapter 2 Theory and Background

2.1 Waveguide Theory

Optical waveguides are the optical analog of electrical wires and are used to confine and guide light in a specific direction. They are an essential part of photonic circuits. The theory and technology behind them are well established [8, 9].

According to the number of dimensions in which the light is confined, optical waveguides can be divided as planar waveguides and rib waveguides. A planar waveguide confines the propagating light in one dimension while a rib waveguide confines the propagating light in two dimensions. Because of this, they are called 1D waveguide and 2D waveguides as well.

The first silicon waveguides were reported to on Silicon on Insulator (SOI) in the mid1980s. Since then, the SOI platform is becoming more and more popular in optical integration industry. In it, highly compact silicon waveguides are integrated with electro- optic functionality for high-speed active devices and circuits. Other silicon-based photonic integration platforms, including silica-on-silicon and silicon nitride, have also reached a state of maturity and are widely applied, particularly in applications requiring low loss passive devices.

This chapter briefly introduces the waveguide theory of planar and ridge waveguides followed by the material properties that are used in this thesis. Subsequently, optical amplification theory, mainly covering the loss and gain of the waveguide are presented.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

The propagation of an optical beam in free space or bulk media is accompanied by the diffraction. This phenomenon describes the spatial broadening of optical radiation upon propagation [8]. In order to avoid the divergence associated with this effect and guide light in a proper way over a distance, waveguide structures are used.

As light propagates in a waveguide, only specific transverse field distributions of the electromagnetic field can be propagated. These field distributions are called the modes of the waveguide. Information about the modes is achieved by solving the wave equations which offer us more details. There are many types of waveguides, but the one that will be focused on in this thesis is the rib waveguide.

The propagation of light in bulk media is affected by the refractive index 푛0 of the medium. The dependence of the refractive index on the wavelength is well known as the chromatic dispersion of the material. The effective index can be described as:

훽 푛푒푓푓 = , 푘0

where β is connected to the phase velocity, while k0 is the wavenumber at a specific wavelength.

Propagation loss is another factor that affects the waveguide selection. The propagation loss in integrated optical waveguides has three fundamental linear contributions which are: material absorption, scattering loss and radiation loss.

Furthermore, the polarization of the mode in the waveguide is crucial as well. The electromagnetic wave description assigns a direction of oscillation to the electric and

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

magnetic field components as it propagates in time and space. In isotropic media the propagation behavior, more precisely the refractive index the wave experiences, is independent on the electromagnetic field oscillation. However, in anisotropic media the refractive index is dependent on the orientation of the electric field, leading to effects like polarization-mode dispersion. It is common to define the electric field as the superposition of two polarization states, the TE and the TM polarization modes.

Polarization of the magnetic field component in the propagation direction is zero.

Although the materials forming a waveguide are mostly isotropic, the waveguide itself can show anisotropic optical properties.

2.1.1 Planar Waveguides

Planar optical waveguides are widely used on integrated optical devices due to their reliance on well-established thin film technology, small size and easy interface with fiber optic network [10].

A step-index planar waveguide is the simplest waveguide structure which is shown in

Figure 2.1. It consists of a high refractive index layer 푛푓 with thickness h surrounded by two lower refractive index materials nc and ns. If the ns > nc, we call it asymmetric waveguide; if the ns = nc, we call it a symmetric waveguide. Like the figure shows, the film is infinite in the x and z direction while finite in the y direction.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Figure 2.1: Planar waveguide

The basic working principle of optical waveguide is based on the reflection and refraction of light at the interface between two different media of different refractive indices. As Figure 2.2 shows, the light incident on the interface obeys Snell’s law shown in equation (2.1):

푛1푠푖푛휃1 = 푛2푠푖푛휃2. (2.1)

Figure 2.2: Reflection and refraction of light at an interface

If n2 > n1, the total reflection will happen if the incident angle is bigger than the critical

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

angle θc which is deciding by equation (2.2):

푛1 휃푐 = . (2.2) 푛2

Based on the principle above, in a planar waveguide with a refractive index nf bigger than 푛푐 and 푛푠 , if a light is incident at an angle greater than 휃푐 then the light will be confined to the central region as Figure 2.3 shows . In this case, the light can continuously reflect and propagate through the film. This is the basic working principle for the step- index planar waveguides.

Figure 2.3: One-dimensional confinement of light propagating in a step-index planar

waveguide

To analytical describe the light transport in the waveguide, a series of Maxwell’s equations are used. These four equations 2.3-2.6 can be solved for the given structure to determine how the electrical and magnetic fields of the electromagnetic (EM) wave propagate in the waveguide:

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

∇ ∙ 퐃 = 휌 (2.3)

∇ ∙ 퐁 = 0 (2.4)

휕퐁 ∇ × 퐄 = − (2.5) 휕푡

휕퐃 ∇ × 퐇 = 퐉 + . (2.6) 휕푡

Where D, B, E, H, 휌 and J are the electric flux density, magnetic flux density, electric field vector, magnetic field vector, charge density and current density respectively in the medium.

We can derive the electric and magnetic field vectors from the electric and magnetic flux densities by the following equations:

퐃 = ε퐄 (2.7)

퐁 = 휇퐇. (2.8)

In this work, we assume that the light is propagating through a dielectric, non- magnetic, isotropic and linear medium. So the conductivity σ is equal to 0, the magnetic permeability μ is equal to 휇0, D is equal to εE. In that case equations 2.5 and 2.6 can be written as:

∂퐇 ∇ × 퐄 = −휇 (2.9) 0 ∂t

휕퐄 휕퐄 ∇ × 퐇 = 휀 = 휀 푛2 . (2.10) 휕푡 0 휕푡

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Where 휇0 , 휀 , 휀0 , 푛 are free space permeability, medium permittivity, free space permittivity and medium refractive index, respectively.

∂ ∇ × (∇ × 퐄) = − (∇ × 퐁) (2.11) ∂t

∂ ∇ × (∇ × 퐄) = −휇 (∇ × 퐇). (2.12) 0 ∂t

From equation 2.6 we can derive that:

∂퐉 ∂2퐃 ∂퐉 ∂2퐄 ∇ × (∇ × 퐄) = −휇 ( + ) = −휇 − 휇 휀 푛2 . (2.13) 0 ∂t ∂t2 0 ∂t 0 0 ∂t2

By the relationship ∇ × (∇ × 퐄) = ∇(∇ ∙ 퐄) − ∇2퐄 we can change the equation for inhomogeneous media as follows:

1 ∂2퐄 ∇2퐄 + ∇ ( ∇n2퐄) = 휇 휀 푛2 . (2.14) 푛2 0 0 ∂푡2

Same idea for H we can get:

1 ∂2퐇 ∇2퐇 + ∇푛2 × (∇ × 퐇) = 휇 휀 푛2 . (2.15) 푛2 0 0 ∂푡2

For homogeneous media, equation (2.14) and (2.15) reduce to the well-known wave equations:

∂2퐄 ∇2퐄 = 휇 휀 푛2 (2.16) 0 0 ∂푡2

∂2퐇 ∇2퐇 = 휇 휀 푛2 . (2.17) 0 0 ∂푡2

Equations (2.16) and (2.17) show that the components of the electric and magnetic

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

field vectors are coupled.

In planar waveguides, we know that the electric and magnetic fields can be written in the following forms:

퐄(퐫, t) = 퐄(푦)e푗(휔푡−훽푧) (2.18)

퐇(퐫, t) = 퐇(푦)푒푗(휔푡−훽푧). (2.19)

The transverse electric (TE) polarization is given by: 퐄 = 퐄x, 퐄y = 퐄z = 0, 퐇x = 0, while the transverse magnetic (TM) is given by: 퐇 = 퐇x, 퐇y = 퐇z = 0, 퐄x = 0. From equation (2.19) we can get:

푗(휔푡−훽푧) 퐇 = 퐇x = 퐻푥(푦)푒 풖푥. (2.20)

Where 풖푥 is a unity vector parallel with the x-axis. From equation (2.15) we can get:

1 ∂2 ∇2[퐻 (푦)푒푗(휔푡−훽푧)퐮 ] + ∇푛2 × [∇ × 퐻 (푦)푒푗(휔푡−훽푧)퐮 ] = μ ε n2 [퐻 (푦)푒푗(휔푡−훽푧)퐮 ] 푥 x 푛2 푥 x 0 0 ∂t2 푥 x (2.21)

푑2퐻 (푦) 1 푑푛2 푑퐻 (푦) 푥 푒푗(휔푡−훽푧)퐮 + 퐮 × [− 푥 푒푗(휔푡−훽푧)퐮 − 푗훽퐻 (푦)푒푗(휔푡−훽푧)퐮 ] − 퐻 (푦)훽2푒푗(휔푡−훽푧)퐮 = 푑푦2 퐱 푛2 푑푦 퐲 푑푦 퐳 푥 퐲 푥 퐱

∂2 −μ ε n2휔2 퐻 (푦)푒푗(휔푡−훽푧)퐮 . (2.22) 0 0 ∂t2 푥 퐱

Therefore:

푑2퐻 (푦) 1 푑푛2 푑퐻 (푦) 푥 푒푗(휔푡−훽푧)퐮 − 푥 푒푗(휔푡−훽푧)퐮 − 훽2퐻 (푦)푒푗(휔푡−훽푧)퐮 + 푑푦2 퐱 푛2 푑푦 푑푦 퐱 푥 퐱

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

∂2 μ ε n2휔2 퐻 (푦)푒푗(휔푡−훽푧)퐮 = 0. (2.23) 0 0 ∂t2 푥 퐱

Finally

푑2퐻 (푦) 1 푑푛2 푑퐻 (푦) 푥 − 푥 + [푘2푛2(푦) − 훽2]퐻 (푦) = 0 (2.24) 푑푦2 푛2 푑푦 푑푦 0 푥

2 2 2휋 2 2 푘0 = |→| = ( ) = 휇0휀0휔 . (2.25) 푘 휆0

In a region of constant refractive index, the TM wave equation becomes:

푑2퐻 (푦) 푥 + [푘2푛2(푦) − 훽2]퐻 (푦) = 0. (2.26) 푑푦2 0 푥

Same idea for the TE wave equation:

푑2퐸 (푦) 푥 + [푘2푛2(푦) − 훽2]퐸 (푦) = 0. (2.27) 푑푦2 0 푥

If the propagation constant 훽 is designated as:

훽 = 푘0푁. (2.28)

Where N is the effective refractive index of the mode, and we assume

푘0푛푐 < 푘0푛푠 < 훽 < 푘0푛푓.

So we have:

푛푐 < 푛푠 < 푁 < 푛푓.

With these assumptions we can try to solve Equation (2.26):

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

푑2퐻 (푦) 푑2퐻 (푦) 푥 − (훽2 − 푘2푛2)퐻 (푦) = 푥 − 훾2퐻 (푦) = 0, 푦 ≥ 0 (2.27) 푑푦2 0 푐 푥 푑푦2 푐 푥

푑2퐻 (푦) 푑2퐻 (푦) 푥 + (푘2푛2−훽2)퐻 (푦) = 푥 + 푘2퐻 (푦) = 0, 0 > 푦 > −ℎ (2.28) 푑푦2 0 푓 푥 푑푦2 푓 푥

푑2퐻 (푦) 푑2퐻 (푦) 푥 − (훽2 − 푘2푛2)퐻 (푦) = 푥 − 훾2퐻 (푦) = 0, 푦 ≤ −ℎ. (2.29) 푑푦2 0 푠 푥 푑푦2 푠 푥

Where 훾푐, 훾푠 and kf are positive real numbers. So the solutions of the three different

Equations (2.27-2.29) can be expressed as:

−훾푐푦 퐻푥(푦) = 퐴푒 , 푦 ≥ 0 (2.30)

퐻푥(푦) = 퐵푐표푠(푘푓푦) + 퐶푠푖푛(푘푓푦), 0 > 푦 > −ℎ (2.31)

훾푠(푦+ℎ) 퐻푥(푦) = 퐷푒 , 푦 ≤ −ℎ. (2.32)

With the boundary conditions we can obtain the relation between coefficients A and B:

−훾푐∙0 퐴푒 = 퐵푐표푠(푘푓 ∙ 0) + 퐶푠푖푛(푘푓 ∙ 0) (2.33)

A = B. (2.34)

Same idea for the relation between A and C:

1 1 −훾푐∙0 − 2 퐴훾푐푒 = 2 [−퐵푘푓푠푖푛(푘푓 ∙ 0) + 퐶푘푓푐표푠(푘푓 ∙ 0)] (2.35 푛푐 푛푓

2 훾푐 푘푓 훾푐 푛푓 −퐴 2 = 퐶 2 → 퐶 = −퐴 2 ∙ (2.36) 푛푐 푛푓 푛푐 푘푓

훾푠∙0 퐵푐표푠(푘푓 ∙ ℎ) − 퐶푠푖푛(푘푓 ∙ ℎ) = 퐷푒 (2.37)

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

2 훾푐 푛푓 퐷 = 퐴[푐표푠(푘푓 ∙ ℎ) + ∙ 2 푠푖푛(푘푓 ∙ ℎ)] (2.38) 푘푓 푛푐

1 푑퐻푥 1 푑퐻푥 2 |(푥 = −ℎ) = 2 |(푥 = −ℎ) (2.39) 푛푓 푑푦 푛푠 푑푦

1 1 훾푠∙0 2 [퐵푘푓푠푖푛(푘푓ℎ) + 퐶푘푓푐표푠(푘푓ℎ)] = 2 훾푠퐷푒 (2.40) 푛푓 푛푠

2 2 1 훾푐 푛푓 훾푠퐴 훾푐 푛푓 2 [퐴푘푓푠푖푛(푘푓ℎ) − 퐴 2 푐표푠(푘푓ℎ)] = 2 [푐표푠(푘푓ℎ) + 2 푠푖푛(푘푓ℎ)] (2.41) 푛푓 푘푓 푛푐 푛푠 푘푓 푛푐

2 2 2 2 훾푐 푛푓 훾푠 푛푓 훾푠 푛푓 훾푐 푛푓 tan(푘푓ℎ) − 2 = 2 + 2 2 ∙ tan(푘푓ℎ) (2.42) 푘푓 푛푐 푘푓 푛푠 푘푓 푛푠 푘푓 푛푐

4 2 2 훾푐훾푠푛푓 훾푐 푛푓 훾푠 푛푓 tan(푘푓ℎ) [1 − 2 2 2] = 2 + 2 (2.43) 푘푓푛푐 푛푠 푘푓 푛푐 푘푓 푛푠

2 2 2 2 훾푐 푛푓 훾푠 푛푓 훾푐 훾푠 푛푓 tan(푘푓ℎ) = [ ( ) + ( ) ⁄1 − ( ) ] (2.44) 푘푓 푛푐 푘푓 푛푐 푘푓 푘푓 푛푐푛푠

훾푐 훾푠 훾푐 훾푠 tan(푘푓ℎ) = ( + )⁄(1 − ). (2.45) 푘푓 푘푓 푘푓 푘푓

From above equations we can get the Poynting vector, Pz, which describes the direction of energy flux of the EM wave:

1 ∞ 훽 ∞ 2 푃푧 = ∫ 퐸푥퐻푦푑푦 = ( ) ∫ |퐸푥| 푑푦 (2.46) 2 −∞ 2휔휇0 −∞

−훾푐푦 퐻푥(푦) = 퐴푒 , 푦 ≥ 0

2 훾푐 푛푓 퐻푥(푦) = 퐴[푐표푠(푘푓푦) − ∙ 2 푠푖푛(푘푓푦)], 0 > 푦 > −ℎ (2.47) 푘푓 푛푐

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

2 훾 푛 푐 푓 훾푠(푦+ℎ) 퐻푥(푦) = 퐴[푐표푠(푘푓 ∙ ℎ) + ∙ 2 푠푖푛(푘푓 ∙ ℎ)]푒 , 푦 ≤ −ℎ. (2.48) 푘푓 푛푐

As we can see from these equations, the magnetic field decreases exponentially in the cover and substrate, whilst its dependence is sinusoidal in the film.

Also, as the mode number m increases, the field penetration into the cover and substrate is deeper resulting more leakage of higher order modes.

If the waveguide thickness decreases, there is a certain value of h for which the coefficient is 훾푠 = 0. This is the cut-off point for that mode.

When 훾푠 becomes imaginary, the evanescent field in the substrate region becomes a radiation mode in the waveguide and the light is no longer confined in the film, but can leak to the substrate and that explains the occurrence of leaky modes.

2.1.2 Ridge Waveguides

The ridge waveguide is widely used for passive devices and semiconductor components [9]. It has many advantages due to its special structure geometry, for example strong optical confinement.

A typical ridge waveguide structure is shown in Figure 2.4. A rectangular ridge which acts as the core of the waveguide with refractive index n1, width w and thickness d is on top of a lower cladding. Usually the ridge is topped with air or a cladding material that has lower refractive index.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Figure 2.4: A typical ridge waveguide

Figure 2.5: A typical strip-loaded waveguide

Figure 2.5 shows a typical geometry of a strip-loaded waveguide. A strip with width w, refractive index 푛3 < 푛1 is loaded on the planar waveguide. The core of the waveguide includes the n1 layer with the thickness d and n3 strip. As we introduced previously, the planar waveguide confine the propagating modes in x direction. The strip on top of it can confine the mode in y direction in order to reduce the propagating loss.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

In this thesis, we analyze the fundamental mode on geometry, confinement, effective areas sides. In later Rsoft simulation part, we are using FemSIM which is a generalized mode solver based on the Finite Element Method (FEM) that can calculate any number of transverse or cavity modes of an arbitrary structure on a non-uniform mesh.

Modes of the waveguide are the specific transverse field distributions of the electromagnetic field that can be propagated in a waveguide [10]. The solutions of wave equations define the specific modes achieved in waveguide.

One factor that affects the number of the modes is the geometry of the waveguide.

When specific geometry requirements are achieved, only the fundamental mode can propagate in the waveguide which is called single mode. In another word, the core of the waveguide has to be small enough. Solution of the wave equation propagating in z direction can represent the single mode distribution in the waveguide:

퐸(푥, 푦, 푧) = 퐸(푥, 푦)exp (푖훽푧), (2.49) where β indicates the propagation constant of the mode and 퐸(푥, 푦) represents the field distribution transverse to the light propagation direction.

The effective area parameter 퐴푒푓푓is used to describes the cross-sectional size of the mode:

∞ ∞ 2 2 (∫−∞ ∫−∞ |퐸(푥,푦)| 푑푥푑푦) 퐴 = ∞ ∞ , (2.50) 푒푓푓 | ( )|4 (∫−∞ ∫−∞ 퐸 푥,푦 푑푥푑푦) where 퐸(푥, 푦)is the field distribution.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

As we analysed before, the waveguide geometry together with the refractive index contrast between the core and the cladding dictate the mode field distribution. We obtain larger effective areas when increasing the mode order and wavelength, but for larger intensities and more efficient optical pumping we might prefer smaller effective mode areas [11].

2.2 Material Properties

2.2.1 Rare Earth Dopants and Their Optical Properties

Research about rare earth ions has been popular since Becquerel observed the energy transmission of these elements in doped compounds.

The rare earth elements are the 17 elements which are vital to modern technology, networks and computers. Fifteen of the rare earth elements are in the lanthanide series, while the other two, scandium and yttrium, share similar chemical properties. When exposed to incident light of specific frequencies, electrons of rare earth ions on a low energy level transfer to a high energy level, and a series of energy transmissions happen, which emit light at specific wavelengths. The most commonly used rare earth ions in optical devices include Yb3+, Nd3+, Pr3+, Er3+ etc. Among these, Er3+ is widely applied to lasers and amplifiers in fibers and waveguides as it offers an emission around 1550nm, which is a useful optical window in fiber communication.

2.2.2 Optical Properties of Erbium

When doped into a material such as TeO2 erbium ions offer the opportunity for

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

electrons transfer between different energy levels. As Figure 2.6 shows, the energy levels of Er3+ consist of the ground state (level 0) and upper levels (levels 1-6). The highest level

4 in this figure is F7/2. Different levels are labeled by using Russell-Saunders notation

2S+1 LJ, where 2S+1 stand for the spin angular momentum, L denotes the orbital angular momentum and J represents the total angular momentum. In energy transmission, the ground state absorption (GSA) and stimulated emission are major energy transfer process

3+ 4 in Er doped TeO2.Ground state electrons can be excited to upper energy levels like I13/2

4 4 and I11/2. On energy level 3, the upper energy level I9/2, electrons can decay directly to the next lower energy level or be excited to higher lying F energy levels. The fluorescent

4 3+ lifetimes of level 2, another upper energy level I11/2, and 3 in Er -doped TeO2 have been measured to be 2.6ms and 0.24ms, respectively [4].

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Figure 2.6: Energy level diagram and selected transitions for erbium ions relevant to the

3+ 980-nm pumped TeO2:Er doped amplifier

In figure 2.6, GSA stands for the ground state absorption, ESA stands for the excited state absorption, ETU stands for the energy transfer up-conversion, and CR stands for the cross-relaxation. When a 980nm wavelength incent light is input, a stimulated emission from level 2 occurs. Electrons on the ground state (level 0) can be pumped to the upper

4 4 energy level I13/2. Sometime electrons can be pumped to I11/2 level as well but

4 spontaneous emission of a photon can happen quickly causing the electrons back to I13/2 or ground energy state level. The fourth and fifth transitions can be triggered by the 1550

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

nm wavelength signal light. There are also up conversions happen on level 2 and 3.The

3+ transition time for Er in TeO2 is long enough to take into consideration.

2.2.3 Erbium-Doped TeO2 Film Properties

Tellurium dioxide (chemical form as TeO2) is one of the most popular materials used in both scientific and technological fields due to its elastic, thermal, electrical and optical properties. Particularly, it is widely applied in optical telecommunication, fiber devices, sensing and photonics glasses. TeO2-based glasses were reported to be applicable to nonlinear optical technology because their nonlinear refractive indices are up to 100 times higher than those of SiO2 [12]. Since the optical properties of TeO2 based glasses are strongly related to their composition and structure, it is important to understand the influence of glass composition and structure on the nonlinear response. The properties of the pure material (i.e. tellurite glass without other components), TeO2, are relatively well understood. In this thesis, we study the properties of waveguides based on rare-earth ion doped pure TeO2 films.

TeO2 can exist in an amorphous or glassy form or has two different crystalline forms.

One is the yellow orthorhombic mineral tellurite, β-TeO2; the other one is the synthetic, colorless tetragonal (paratellurite), α-TeO2 [13]. In this thesis we investigate the amorphous, glass-like form of TeO2. The physical properties of TeO2 are represented by how fast sound travels in it, which is 4250m/s. It can react with acids fabricating tellurides. The structural and the physical characteristics of TeO2 thin films strongly depend on their fabrication method and annealing conditions. In addition, TeO2 thin films

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

exhibit different optical characteristics depending on their chemical compositions. Most researchers have investigated the properties of TeO2 thin films with a specific composition (TeO2) [14]. Therefore, evaluating the effects of various chemical compositions on the characteristics of thin films is important.

Erbium as an important dopant has been widely applied to tellurite glasses. Related literature emerged recently concerning the structure, optical, mechanical, thermal, and electrical properties. Especially the excellent optical properties of Er3+ doped tellurite glasses in laser and amplifier material areas were widely studied. For instance, it was demonstrated that good gain can be attained in C and L bands in Erbium doped tellurite fiber amplifiers (EDFA) [15]. They are also good options for photonic devices since its high refractive index and good transmittance over a wide wavelength region of ~0.35-

5μm [16].

In a previous report, the optical loss of TeO2 was found to be below ~0.05dB/cm on the NIR spectrum and ~0.10dB/cm at 1550nm has been achieved, the lowest ever reported by more than an order of magnitude, and clearly suitable for planar integrated devices [17]. Erbium doped films were generally observed to have a refractive index of

0.01-0.04 lower than un-doped material, depending on Er3+ concentration and O/Te ratios. In previous study, a peak internal gain of 14dB was obtained at 1530nm in a 5-cm- long single-mode Er-doped tellurium oxide waveguide [18].

2.2.4 Si3N4 Waveguide Properties

Recently, silicon nitride (Si3N4) has emerged as an alternative to silicon on insulator

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

(SOI) platforms for integrated photonic circuits because of its low loss throughout the visible and infrared, moderate refractive index contrast and CMOS compatibility. The moderately high index contrast (between a silicon nitride waveguide core and a silicon oxide cladding, 2 vs. 1.45) enables the fabrication of complex circuits on a small footprint and, hence, the fabrication of many chips per wafer. Furthermore it allows for the implementation of functions such as wavelength-sized cavities, photonic crystal structures, high-efficiency grating couplers, etc. Si3N4 films have always been considered as potential optical waveguide materials for various optical devices in passive planar light and multifunctional circuits. Because of its low loss and standardized fabrication methods, silicon nitride serves as good prospective base waveguide material for integrated optical amplifiers. Nevertheless, rare-earth doped silicon nitride has not exhibited gain because of erbium’s poor solubility in Si3N4, leading to ion clustering and quenching. Thus a combined approach using both Si3N4 and erbium-doped TeO2, with its excellent erbium host properties, is desirable.

2.3 Optical Amplifier Theory

2.3.1 Loss Mechanisms in Optical Waveguides

Loss mechanisms should be understood thoroughly if we want to investigate and optimize optical waveguides and amplifiers. In general, optical loss is the loss of light when the light is propagating through the optical waveguide. It usually consists of three types, which are scattering loss, material absorption and radiation loss [19]. In this section we will discuss these three fundamental contributions to better offer a clearer image of

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

loss mechanisms in optical waveguides.

All loss contributions are summarized in the loss parameter α that leads to an exponential power decay along propagation distance z according to:

푃 = 푃0exp (−훼푧), (2.51)

where 푃0 is the initial power before propagation. Similarly, the intensity (power per area) at any point (position z) along the waveguide is given by

−αz 퐼(푧) = 퐼0e , (2.52)

where I0 is the initial intensity at z = 0.

There are two types of scattering loss in an optical waveguides: volume scattering and surface scattering. Volume scattering is caused because of the imperfections, such as voids, doped atoms and crystalline defects in the waveguide. The number of the imperfections is proportional to the loss per unit length. Plus, the size of the imperfections like the size of the doped atoms also affects the volume scattering. Because the imperfections tend to be much smaller than the wavelength in the waveguide, the volume scattering loss is typically negligible compared to surface scattering loss.

The surface scattering loss is significant in scattering loss even when the light is traveling in a smooth surface waveguide, especially for the higher-order modes, because the propagating waves interact strongly with the surface of the waveguide. The fabrication imperfections in the deposition and etching processes can lead to rough sidewalls or rough surface waveguides which occurring a higher scattering loss.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Waveguides with very thin sidewalls of only 40-50 nm lead to record low propagation loss [20].

Another major loss that happens in waveguide is the absorption loss. The basic idea for the material absorption is the interaction of optical waves with the medium during propagation which leads to energy transfer from the wave to the material. The absorption loss happens due to photons annihilated in materials. The absorption is frequency dependence since different wavelengths interact differently with charges and bonds in various materials. Usually, the absorption loss includes the inter-band absorption and intra-band absorption. The inter-band absorption relates to the electron and hole pairs and photodetector is made based on it. Intra-band absorption relates to the free carrier scattering commonly happens in metal.

When it comes to our focus in this thesis we wish to design waveguides integrated on silicon substrates. One of the properties of Si that should consider is its high absorption in the visible range. To reduce its impact on traveling light in waveguide, isolation between the substrate and the waveguide is important. The popular approach is to put a low index buffer layer between them. Suitable waveguide core and buffer materials are Si3N4 with a refractive index of 2.0 and SiO2 with a refractive index of 1.45, respectively [21].

Although Si3N4 films are considered as a potential candidate as optical waveguide materials for various optical devices, they also suffer from additional absorption loss due to hydrogen bonds. Especially, the N-H bonds can lead to undesirable absorption in the range of 1510-1565nm [21]. This loss can be removed by annealing out the hydrogen at

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

high temperature (~1000 °C).

Radiation loss is another type of loss relevant to the bent waveguides. In a curved waveguide, the optical field of the propagating light is distorted in comparison to a straight waveguide which can cause the radiation of optical energy into radiating modes.

Figure 2.8 shows a sample radial electric field profile of a bend waveguide mode.

Figure 2.7: The figure represents the radial electric field of a bent waveguide with radius

150um; It shows a Si3N4 with TeO2 coating and air top-cladding; The scale bar at right

showing the mode intensity described by different color; R is the bend radius while Y is

the vertical axis of mode Si3N4: width 1µm, height 0.2µm ,TeO2: 0.6µm.

The light confinement and the bend radius are two important factors that affect the ideal size of a mode. The former affects the peak intensity in the waveguide as well as the overlap of the light with the erbium-doped material, both important for amplifiers as will

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

be discussed. The latter determines how small waveguides can be bent on the chip, thus the minimum footprint of devices such as amplifiers, which typically utilize a spiral layout. Therefore, when it comes to the bend waveguide designs in this thesis, the minimum achievable bending radius are discussed in detail. To conveniently analyze the radiation loss, the velocity approach developed by Marcatili and Miller is mostly used

[22].

The effective area parameter 퐴푒푓푓is used to describe how well the optical field is confined inside the core area:

∞ ∞ 2 2 (∫−∞ ∫−∞ |퐸(푥,푦)| 푑푥푑푦) 퐴 = ∞ ∞ , (2.53) 푒푓푓 | ( )|4 (∫−∞ ∫−∞ 퐸 푥,푦 푑푥푑푦) where 퐸(푥, 푦)is the field distribution.

We define the overlap factor (Γ) in the active medium by the following equation:

(푝) (푠) ∫ 퐼푝퐼푠푑퐴 ∑푔푎푖푛(푖푗) 퐼푖푗 퐼푖푗 훤푆/푃 = = , (2.54) √ 퐼2푑퐴 퐼2푑퐴 ∑ 2(푝) ∑ 2(푠) ∫ 푝 ∫ 푠 √ 푔푎푖푛(푖푗) 퐼푖푗 √ 푔푎푖푛(푖푗) 퐼푖푗 where I denotes the intensity of the mode and s and p denote the signal and pump laser wavelength respectively. The indices i and j are used to discretize the integral.

2.3.2 Optical Gain

To achieve the optical gain in a waveguide structure, it is vital to generate photon more than photons that are lost in absorption or due to other loss mechanisms. As we

3+ show in the energy transmission levels, in a Er doped gain material TeO2 , more

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

electrons should be pumped to the higher energy level so that stimulated emission occurs which leads to more photons emission. To achieve this, a population inversion is required

4 4 between the I13/2 and I15/2 states. The percentage of ions that excited to the higher energy level should at least 50% in case the absorption and emission cross sections are similar for the ions [3].

In this thesis, we can use the internal net gain as an important factor to measure the gain of the amplifier. We can calculate the internal net gain γ(λ)(dB/cm) by using following equation:

10∙푙표푔 [퐼 (휆)/퐼 (휆)] γ(λ) = 10 푂푛 푂푓푓 − 훼 (휆), (2.55) 퐿 푇표푡푎푙

where Ion and IOff are the optical signal intensity measured at the detector in the pumped and un-pumped case, respectively, and L is the amplifier length (cm). 훼푇표푡푎푙(휆) stands for the measured total propagation loss.

In following parts of the thesis we will discuss the rate equations for different ions population densities on Er3+ levels which used to determine the theoretical gain and performance.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Chapter 3 Design and Modeling

3.1 Waveguide Design

In this thesis, the optical properties of the rib structure, Si3N4 waveguide topped with a

TeO2 coating, is studied. An illustraion of a typical structure used in this thesis is shown in Figure 3.1, where the wSiN, hSiN,hTeO2 ,hSiO2 stand for the width of waveguide Si3N4, the height of waveguide Si3N4, the height of cladding TeO2, and the depth of substrate SiO2 respectively.

Figure 3.1: Cross-section schematic of the TeO2-coated Si3N4 waveguide structure

3.1.1 Finite Element Method Waveguide Mode Solver

To analyse the light modes transportation and discribution in an optical waveguide, a

Finite Element Method (FEM) modesolver is a popular option due to its flexibility to any

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

waveguide geometry. This part introduces the main idea of FEM and demonstrates the process of its applicaion by using this thesis waveguide design.

FEM is a numerical method to solve problem in mathematics and engineering areas.

The main idea behind FEM is to divide working region into many small parts and then apply analytical funtions to every element. After this, the results are summed up to global matrixes in order to produce an eigenvalue matrix equation. After solving the eigenvalue matrix equation, the propagation modes together with corresponding propagation constants are obtained [23].

The impletation of the FEM to the waveguide can be explained in several steps. First the waveguide is created based on the input parameters like the refractive index of the core, wavelength, core width, core height etc. The next step is to perform meshing in many small elements consisting of nodes. Many algorithms could be used for this pupose.

For example, a simple custom meshing algorithm is used to connect every point as the

Figure 3.2 shows:

Figure 3.2: Example of node connection in a FEM modesolver

When we examine the node i, the triangles ( i, j ) - ( i+1, j ) - ( i , j+1 ) and ( i+1 , j ) -

( i+1 , j+1 ) - ( i , j+1 ) are created by the meshing engine which produces two arrays. The

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

first array holds the node data and the element data goes to the second array. In this way, the node values and the refractive index of every element are stored. Figure 3.3 shows an example mesh of the Si3N4 strip waveguide topped with TeO2 coating. The waveguide and coating regions are shown in purple and green color. As Figure 3.3 shows, the mehsing of the area is performend with different densities for the strip and the coating so as to better show the mode file. Grid sizes are also different depending on the accuracy requirement.

The last step is to apply the FEM functions and offer the creation of the eigenvalue matrix equation and the solution. Each element is applied by the analytical funtions. A global matrix contains all results while the eigenvalue matrix equation is created:

([퐴] − 휆2[퐵]){휙} = 0 (3.1)

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Figure 3.3: Mesh image of grid size 0.1µm, Si3N4 height: 0.2µm, width: 1um; TeO2

height 0.4µm with grid grading ratio 1.25; grid edge size 0.1µm

In (3.1), A and B are global matrix, the λ is the unknown eigenvalue which we derive from the solution of the system, in our case the propagation constants, and 휙 is the distribution of the field for the corresponding eigenvalue.

The number of propagation constants shows the number of supported modes for the waveguide. The solutions of the eigenvalue equation are not all acceptable. We accept only those which meet the necessary criteria. More specifically, the 푛푒푓푓 (the effective index) has to satisfy the following inequality:

푛푠 < 푛푒푓푓 < 푛푐

Where neff is defined as:

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

2 2 2 푛푒푓푓 = √푏(푛푐 − 푛푠 ) + 푛푠 (3.2)

where b is the propagation constant which has been calculated from the solution of equation (3.1). After deriving the accepted propagation constants, then the corresponding field values are retrieved.

3.1.2 Optimization of TeO2-Coated Si3N4 Waveguides for Optical

Amplifiers

For waveguides, different structural parameters affect the optical amplification.

In particular, we will analyze the influence of these design parameters with respect to the changes of the Si3N4 waveguide height, Si3N4 waveguide width and TeO2 cladding height.

We try to optimize the confinement in the Er-doped TeO2 cladding, the effective mode area, the pump-siganl intensity overlap so that we can use these parameters in the later simulation trying to get the gain of the energy level model. These parameters and their investigated ranges are shown in Table 3.1.

Table 3.1: Waveguide parameters varied in Figure 3.1

Variable Symbol Range (μm)

Waveguide Width 푊푆푖푁 0.1:5.0

Waveguide Height ℎ푆푖푁 0.2;0.3

TeO2 Height hTeO2 0.3:0.6

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

3.2 Erbium-Doped Amplifier Model

Figure 3.4: Simplified Er3+ energy level diagram and transitions for the 980 nm

3+ pumped TeO2: Er amplifier

Different energy transitions associated with Er3+ are shown in figure 3.4. The rate equations describing these transitions are given below:

푑푁 = −푅 푁 + 푅 푁 + 퐴 푁 + 퐴 푁 + 퐴 푁 + 퐴 푁 + 퐶 푁2 + 퐶 푁2,(1) 푑푡 13 1 31 3 21 2 31 3 41 4 51 5 22 2 33 3

푑푁 2 = −퐴 푁 + 퐴 푁 + 퐴 푁 + 퐴 푁 − 2퐶 푁2, (2) 푑푡 21 2 32 3 42 4 52 5 22 2

푑푁 3 = 푅 푁 − 푅 푁 − 푅 푁 −퐴 푁 − 퐴 푁 + 퐴 푁 + 퐴 푁 − 2퐶 푁2,(3) 푑푡 13 1 31 3 36 3 31 3 32 3 43 4 53 5 33 3

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

푑푁 4 = −퐴 푁 − 퐴 푁 − 퐴 푁 + 퐴 푁 + 퐶 푁2 , (4) 푑푡 41 4 42 4 43 4 54 5 22 2

푑푁 5 = −퐴 푁 − 퐴 푁 − 퐴 푁 − 퐴 푁 + 퐴 푁 , (5) 푑푡 51 5 52 5 53 5 54 5 65 6

푑푁 6 = 푅 푁 − 퐴 푁 + 퐶 푁2 , (6) 푑푡 36 3 65 6 33 3

푁1 + 푁2 + 푁3 + 푁4 + 푁5 + 푁6 = 푛0 (7)

-3 In these equations, N1 –N6 stand for different ion population density (cm ) on energy level 1 to 6. R (cm3/s) stands for the transmission rate between different levels. For

3 example, R13 represents the rate from ground state to level 3. A (cm /s) stands for the spontaneous emission rate, for instance, A21 represents for the ions spontaneous emission from level 2 to ground state. Equation (2) describes the total population density on different energy levels equal to the density. Other equations stand for the rate of the population density considering the actions between different levels. When solving these rate equations, we can get different ions distributions when the energy state is stable. In this case, the gain of the whole system can be predicted.

Compare to traditional host materials, some differences of the rate equations for Er- doped TeO2 should be noticed. For silica, silicate, or phosphate glasses, the excited state absorption (ESA) can be neglected because of the short lifetime of the level 3 in these glasses. However this approximation will not be justified in tellurite or fluoride glasses because of their long lifetime at the level 3.

For the same reason, stimulated emission at the 980-nm pump wavelength should also

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

be properly accounted for as included in rate equation by the term 푅31. Rate equations on level 6 and level 5 are included in the whole rate equation group.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Chapter 4 Results

4.1 Waveguide Simulation Results

A waveguide is the most fundamental passive structure in integrated optics since it is used in one way or another in almost all micro-optic devices from modulators, to directional couplers [24]. In a waveguide structure, insuring the single mode condition

(SMC) is vital since the fundamental mode carries the majority of optical power. Also, the fundamental mode is the most well confined field distribution in a waveguide structure. In this thesis, we focus on the wavelengths 0.98μm and 1.55μm which are the pump and signal wavelength, respectively. In order to design devices in which single mode can occur, we perform FemSIM simulation for the structure shown in Figure 3.1.

First, we look at the single mode situation for different waveguide parameters. For example, we look at a structure with 0.2μm Si3N4 height and 0.3μm TeO2 height. In the

Figure 4.1 the imaginary part of the effective Index stands for the loss of different modes.

We select the TE0, TE1 and TE2 representing the fundamental mode, mode 0, and higher order modes, mode 1 and mode 2. As the figure shows, the value of the imaginary parts of the effective index of the TE0 mode is zero for different waveguide widths ranging from

-5 0.5 to 1.5μm; while the value of TE1mode changes from around 2.4e at 0.5μm to 0 at

1.2μm. The value of TE2 stays above 0 for all waveguide widths in the range. The result shows the single mode cutoff width is at 1.2μm. From the picture, only the TE0 mode exists before the cutoff width 1.2μm of the waveguide. After the cutoff width, the TE1

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

mode shows up and mixes with the fundamental mode. Higher order modes are still lossy since the value is above zero. If we look at the real parts of the effective index, in figure

4.2, the turning away point for different modes is also located at the width 1.2 μm. In conclusion, the cutoff waveguide width for this waveguide design is 1.2μm. In this thesis simulation, the refractive indices of SiO2, Si3N4, and TeO2 at 0.98μm and 1.55μm are

푛푆푖푂2 =1.47, 1.45; 푛푆푖3푁4 =2.01, 1.98; 푛푇푒푂2 =2.10, 2.08, respectively. We study the waveguide properties for Si3N4 film heights of 0.2 and 0.3μm and TeO2 film heights of

0.3, 0.4, 0.5 and 0.6μm.

Figure 4.1: Imaginary part of the effective index of TE modes 0, 1, and 2 at 1.55µm

wavelength, ℎ푆푖푁 = 0.2µm, ℎ푇푒푂2 = 0.3µm

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Figure 4.2: Real part of the effective index of TE modes 0, 1, and 2 at 1.55µm

wavelength, ℎ푆푖푁 = 0.2µm, ℎ푇푒푂2 = 0.3µm

The modes before the cutoff width 1.2μm, at the cutoff width and after the cutoff width are shown in Figure 4.3.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

(a) Before 1.2μm

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

(b) At 1.2μm

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Figure 4.3: Modes profiles for mode 0, 1 and 2 for structure ℎ푆푖푁 = 0.2µm, ℎ푇푒푂2 =

0.3µm with cutoff width 1.2μm at wavelength 1.55µm; the x axis stands for the horizontal

extension of the structure while the y axis stands for the vertical extension. The colour

scale indicates the electric field magnitude.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Similarly, since the wavelength of the pump laser is 0.98μm, as illustrated in Figure

4.4, we look at different imaginary parts of effective index of SiN height hSiN = 0.2µm

and cladding TeO2 height ℎ푇푒푂2 changing from 0.4µm to 0.6 um at 0.98μm laser wavelength.

Figure 4.4: Imaginary parts of effective index of TE modes 0, 1, and 2 at wavelength

0.98µm, hSiN = 0.2µm, ℎ푇푒푂2= 0.4µm

For pump wavelength 0.98μm and signal wavelength 1.55μm we simulated different

Si3N4 heights and TeO2 heights ranging from 0.3-0.6μm. Different single mode results are shown in table 4.1.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Table 4.1: Single mode cutoff widths for different hSiN and ℎ푇푒푂2 at 0.98μm and 1.55μm wavelengths

Single mode Wavelength cutoff width ℎ푆푖푁(μm) ℎ푇푒푂2(μm) (μm) (μm)

0.2 0.3 0.95 0.2 0.4 0.9 0.2 0.5 0.9

0.2 0.6 1.2 0.98 0.3 0.3 0.95 0.3 0.4 0.95 0.3 0.5 1.2 0.3 0.6 1.15 0.2 0.3 1.2 0.2 0.4 1.2 0.2 0.5 1.4

0.2 0.6 1.4 1.55 0.3 0.3 1.2 0.3 0.4 1.5 0.3 0.5 1.2 0.3 0.6 1.2

In the next step, we look at the Q factor and confinement of different waveguide geometries. The Q factor (the quality factor) is the key characteristic parameter in waveguides used to measure the energy loss. It can be expressed by:

퐸푛푒푟푔푦 푆푡표푟푒푑 푄 = 2휋푓 × , 푟 푃표푤푒푟 퐿표푠푠

where 푓푟 is the resonant frequency. From the equation we can see that, with stable

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

resonant frequency, higher Q indicates a lower rate of energy loss.

Another important parameter to describe waveguide performance is the confinement factor, which stands for the fraction of the total power residing in the core of the waveguide. A higher confinement of the fundamental mode can cause a smaller portion of the light field leaking to the outside of the core so as to minimize losses from sidewall interface scattering [24].

In this thesis, we look into the Q factor and confinement for different bend radii of the waveguide to select the best radius range in which Q <107 while maintaining confinement > 0.5. The mode loss is acceptably low and most of the propagating light energy is stored in the waveguide in these ranges.

For example, we look into the structure with Si3N4 waveguide width 1µm, height

0.3µm and TeO2 height 0.6μm. The geometry parameters are shown in Table 4.2 and results are shown in figure 4.5.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Table 4.2: Waveguide parameters for calculated Q values and confinement factors in

Figure 4.5

Variable Symbol Range(μm) Waveguide Width wSiN 1.0 Waveguide Height hSiN 0.3 TeO2 Height hTeO2 0.6 Bend Radius r 150:500

Figure 4.5: Q factor and confinement for ℎ푇푒푂2 = 0.6µm

For the 0.98μm pump wavelength, the minimum bend radius is shown in Table 4.3 below.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Table 4.3: Minimum bend radii at minimum waveguide width and waveguide cutoff

width for different ℎ푆푖푁 and ℎ푇푒푂2, at the 0.98µm pump wavelength

Min. bend radius (Q < 107) Single mode ℎ (μm) ℎ (μm) cutoff width 푆푖푁 푇푒푂2 At waveguide At waveguide (μm) minimum width cutoff width 0.5μm 0.2 0.3 0.95 166 94 0.2 0.4 0.9 378 233 0.2 0.5 0.9 566 455 0.2 0.6 1.2 1373 788 0.3 0.3 0.95 130 70 0.3 0.4 0.95 305 172 0.3 0.5 1.2 568 300 0.3 0.6 1.15 1111 622

For the 1.5μm signal wavelength, the minimum bend radii are shown in Table 4.4 below.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Table 4.4: Minimum bend radii at minimum waveguide width and waveguide cutoff

width for different ℎ푆푖푁 and ℎ푇푒푂2, at the 1.55µm signal wavelength

Single Min. bend radius (Q < 107) ℎ ℎ mode cutoff 푆푖푁 푇푒푂2 At waveguide At waveguide (μm) (μm) width minimum width cutoff width (μm) 0.5μm 0.2 0.3 1.2 247 93 0.2 0.4 1.2 415 173 0.2 0.5 1.4 710 294 0.2 0.6 1.4 1166 500 0.3 0.3 1.2 173 62 0.3 0.4 1.5 289 105 0.3 0.5 1.2 489 216 0.3 0.6 1.2 777 366

As we analyzed before, the waveguide geometry together with the index contrast between the core and the cladding dictate the mode field distribution. In fact, we get smaller effective areas, thus higher pump intensities, by selecting the fundamental mode and a sufficiently thin TeO2 layer [11].

For instance, we look at the 0.2μm SiN height, 0.3μm TeO2 height, at the cut-off width

1.2μm and the 1.55μm signal wavelength. The effective mode area is shown in Figure 4.6.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

2 Figure 4.6: Effective mode area in µm (1.55μm, 0.2μm Si3N4 height, 0.3μm TeO2 height, cutoff width 1.2μm)

Simulations were carried out for 0.98μm and 1.55μm wavelengths and the effective mode area results are shown in Tables 4.5-4.6.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Table 4.5: Effective mode areas at minimum waveguide width and single-mode cutoff

width for different ℎ푆푖푁 and ℎ푇푒푂2, 0.98 μm pump wavelength

Effective mode area (μm2) Single mode ℎ (μm) ℎ (μm) cutoff width 푆푖푁 푇푒푂2 At waveguide At single-mode (μm) minimum width cutoff width 0.5μm

0.2 0.3 0.95 0.63 0.60 0.2 0.4 0.9 0.80 0.73 0.2 0.5 0.9 0.98 0.96 0.2 0.6 1.2 1.41 1.33 0.3 0.3 0.95 0.57 0.54 0.3 0.4 0.95 0.90 0.77 0.3 0.5 1.2 0.98 1.06 0.3 0.6 1.15 1.28 1.29

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Table 4.6: Effective mode areas at minimum waveguide width and single-mode

cutoff width for different hSiN and ℎ푇푒푂2, 1.55μm signal wavelength

Effective mode area (μm2) Single mode ℎ (μm) ℎ (μm) cutoff width 푆푖푁 푇푒푂2 At waveguide At single-mode (μm) minimum width cutoff width 0.5μm

0.2 0.3 0.95 0.98 1.00 0.2 0.4 0.9 1.40 1.19 0.2 0.5 0.9 1.77 1.51 0.2 0.6 1.2 1.98 1.79 0.3 0.3 0.95 0.91 0.95 0.3 0.4 0.95 1.23 1.28 0.3 0.5 1.2 1.48 1.41 0.3 0.6 1.15 1.78 1.68

3+ Since TeO2:Er acts as the amplifier material in our structure, it is also important to look at the TeO2 intensity overlap. Simulations were carried out for 0.98μm and 1.55μm wavelength laser and the TeO2 intensity overlap results are shown in Table 4.7-4.8.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Table 4.7: TeO2 intensity overlap at minimum waveguide width and single-mode cutoff

width for different ℎ푆푖푁 and ℎ푇푒푂2, 0.98μm pump wavelength

TeO2 intensity overlap (%) Single mode ℎ (μm) ℎ (μm) cutoff width 푆푖푁 푇푒푂2 At waveguide At single-mode (μm) minimum width cutoff width 0.5μm

0.2 0.3 0.95 0.47 0.25 0.2 0.4 0.9 0.66 0.49 0.2 0.5 0.9 0.73 0.63 0.2 0.6 1.2 0.84 0.75 0.3 0.3 0.95 0.43 0.07 0.3 0.4 0.95 0.53 0.30 0.3 0.5 1.2 0.68 0.43 0.3 0.6 1.15 0.79 0.57

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Table 4.8: TeO2 intensity overlap at minimum waveguide width and single-mode cutoff

width for different ℎ푆푖푁 and ℎ푇푒푂2, 1.55μm signal wavelength

TeO2 intensity overlap (%) Single mode ℎ (μm) ℎ (μm) cutoff width 푆푖푁 푇푒푂2 At waveguide At single-mode (μm) minimum width cutoff width 0.5μm

0.2 0.3 0.95 0.49 0.23 0.2 0.4 0.9 0.54 0.42 0.2 0.5 0.9 0.66 0.55 0.2 0.6 1.2 0.78 0.65 0.3 0.3 0.95 0.39 0.06 0.3 0.4 0.95 0.55 0.23 0.3 0.5 1.2 0.60 0.41 0.3 0.6 1.15 0.77 0.53

The pump-signal mode overlap decides what is the fraction of energy transfer from the pump laser to the signal laser. Simulations were carried out for 0.98μm and 1.48µm pump wavelengths and the pump-1.55µm-signal intensity overlap results are shown in Table

4.9-4.10.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Table 4.9: Pump-signal mode overlap at minimum waveguide width and single-mode

cutoff width for different ℎ푆푖푁 and ℎ푇푒푂2, 0.98µm pump wavelength

Pump (0.98µm) - signal (1.55µm) Single mode mode overlap cutoff width (%) ℎ푆푖푁(μm) ℎ푇푒푂2(μm) (μm) At waveguide At single-mode minimum width cutoff width 0.5μm

0.2 0.3 0.95 97.09 97.91 0.2 0.4 0.9 98.16 98.68 0.2 0.5 0.9 98.71 99.08 0.2 0.6 1.2 98.93 99.26 0.3 0.3 0.95 97.38 98.28 0.3 0.4 0.95 98.40 98.94 0.3 0.5 1.2 98.81 99.07 0.3 0.6 1.15 99.05 99.23

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Table 4.10: Pump-signal mode overlap at minimum waveguide width and single-mode

cutoff width for different ℎ푆푖푁 and ℎ푇푒푂2, 1.48µm pump wavelength

Pump (1.48µm)-signal (1.55µm) Single mode mode overlap cutoff width (%) ℎ푆푖푁(μm) ℎ푇푒푂2(μm) (μm) At waveguide At single-mode minimum width cutoff width 0.5μm

0.2 0.3 0.95 99.81 99.90 0.2 0.4 0.9 99.88 99.93 0.2 0.5 0.9 99.92 99.95 0.2 0.6 1.2 99.93 99.96 0.3 0.3 0.95 99.83 99.93 0.3 0.4 0.95 99.89 99.95 0.3 0.5 1.2 99.93 99.95 0.3 0.6 1.15 99.94 99.96

4.2 Amplifier Modeling Results

3+ 4.2.1 Application of Amplifier Model to Er -doped Al2O3 and TeO2

Waveguides from Literature

In this thesis the Matlab code is used to simulate the light propagating process based

3+ on Figure 2.6 for Er -doped Al2O3 and TeO2 in order to compare the signal gain from in

3+ amplifiers based on these two materials. Er -doped Al2O3 was selected as a good comparison material because of its well-established application in integrated amplifiers.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

First we did the comparison for Er-doped TeO2 and Al2O3. Parameters from literature

3+ 3+ are shown in Table 4.11. The pump wavelength for both Al2O3:Er and TeO2:Er is

0.977µm while the signal laser wavelength is 1.533µm. The amplifier length in this comparison is 5cm; the pump focus radius is the radius of the pump light mode, and the signal focus radius is the radius of the signal light. The Er3+ concentrations, pump and signal light absorption and emission cross sections, excited state absorption cross sections and background losses are all from the literature. The radius of the active medium was chosen for a circular Gaussian profile with equivalent 1/e2 area to the calculated mode area for each amplifier.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

3+ Table 4.11: Matlab simulation parameters for Er -doped Al2O3 and TeO2 waveguide

amplifiers: [4][25][26]

Parameters Al2O3:Er3+ TeO2:Er3+ Pump wavelength (μm) 0.977 0.977 Signal wavelength(μm) 1.533 1.533 Amplifier length(cm) 5 5 Radius, pump focus(cm) 1.15 1.21 Radius, signal focus(μm) 1.39 1.30 Launch signal power(μW) 1 1 Confinement factor , pump 96% 73% wavelength Confinement factor, 89% 84% Signal wavelength Radius, active medium(μm) 1 µm ~1.05*(Radius, signal 1 focus) Er concentration(cm-3) 3.0 1020 3.0 1020 −21 −21 Pump absorption cross 2.0 10 5. 2 10 section(cm2) −21 −21 Signal absorption cross 5.7 10 8.0 10 section(cm2) −21 −21 Pump emission cross 2.0 10 5. 2 10 section(cm2) −21 −21 Signal emission cross 5.7 10 8.0 10 section(cm2) −21 −21 Excited State Absorption 0.8 10 7.04 10 cross section(cm2) Fluorescent lifetimes(ms) τ1=6.7 τ1=2.6 τ2=0.1 τ2=0.24 3 −18 −18 ETU parameter(cm /s) 8 = 10 2.74 = 10 Pump background 0.17 0.6 loss(dB/cm) Signal background 0.11 0.4 loss(dB/cm)

The internal net gain vs. signal wavelength and at a signal wavelength of 1532 nm for varying pump powers are shown in Figures 4.7 (a) and (b) and 4.8 (a) and (b) for

3+ 3+ Al2O3:Er and TeO2:Er amplifiers, respectively.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

(a)

(b)

3+ Figure 4.7: (a) Internal gain calculated for a 5-cm-long Al2O3:Er amplifier, the x axis stands for the signal wavelength, the y axis stands for the gain of the input signal; (b)

3+ Internal gain for the Al2O3:Er amplifier at 1533nm, the x axis stands for the launched

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

pump power while the y axis stands for the internal gain at this wavelength

(a)

(b)

3+ Figure 4.8: (a) Internal gain calculated for a 5-cm-long TeO2:Er amplifier, the x axis

stands for the signal wavelength, the y axis stands for the gain of the input signal; (b)

3+ Internal gain for the TeO2:Er amplifier at 1533nm, the x axis stands for the launched

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

pump power while the y axis stands for the internal gain at this wavelength

3+ As the figure 4.7 (b) shows, the peak amplification for the 5cm-long Er doped Al2O3 amplifier is about 12dB, which agrees with the results in the literature [25], verifying the simulation model.

3+ Figure 4.8 (b) shows the amplification for the 5cm-long Er doped TeO2 amplifier, which is around 15dB, about 3dB/cm, and agrees with the result in the paper [26]. The

3+ simulation shows the Er doped TeO2 amplifier exhibits higher gain per unit length than

3+ the Er doped Al2O3 amplifier.

3+ 4.2.2 Amplifier Modeling Based on TeO2:Er -Coated Si3N4 Waveguide

Design in this Thesis

Based on the RSoft simulations we selected favourable waveguide geometry parameters with which we can obtain high gain, high efficiency and a small device

3+ footprint. As the table 4.12 shows, a TeO2:Er coating height of 0.6µm was selected

3+ because it provides a good compromise between mode size, bend radius and TeO2:Er intensity overlap. The nitride width of 1.2µm was selected to ensure single mode operation at the pump and signal wavelengths. The confinement factors of the pump and signal light were chosen based on the simulations in Table 4.7 and 4.8. The radius in the table is the radius of the approximated mode, assuming an equivalent Gaussian mode

[25]. The Gaussian radii of the pump and signal focus were calculated using the effective mode areas in Table 4.5 and 4.6.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

3+ Table 4.12: Parameters applied for calculation of gain in an Er -doped TeO2-coated

Si3N4 waveguide amplifier

Parameters TeO2:Er3+

TeO2 coating height(μm) 0.6 SiN height, width(μm) 0.2, 1.2 Pump wavelength (μm) 0.977 Signal wavelength(μm) 1.533 Amplifier length(cm) 5 Radius, pump focus(cm) 1.05 Radius, signal focus(μm) 1.19 Launch signal power(μW) 1 Confinement factor , pump 84% wavelength Confinement factor, 78% Signal wavelength Radius, active medium (μm) 1 Er3+ concentration(cm-3) 3.0 1020 Pump absorption cross 5. 2 10−21 section(cm2) −21 Signal absorption cross 8.0 10 section(cm2) Pump emission cross 5. 2 10−21 section(cm2) −21 Signal emission cross 8.0 10 section(cm2) −21 Excited State Absorption 7.04 10 cross section (cm2) Fluorescent lifetimes (ms) τ1=2.6 τ2=0.24 3 −18 ETU parameter(cm /s) 2.74 10 Pump background 0.6 loss(dB/cm) Signal background 0.4 loss(dB/cm)

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

(a)

(b)

3+ Figure 4.9: (a) Internal gain calculated for a 5-cm-long TeO2:Er -coated Si3N4

waveguide amplifier, the x axis stands for the signal wavelength, the y axis stands for the

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

gain of the input signal (b) internal gain for the amplifier at a wavelength of 1533 nm, the

x axis stands for the launched pump power while y axis stands for the internal gain at this

wavelength

From Figure 4.9 (a) and (b) we can see that the peak gain for a 5-cm-long Er3+ doped

3+ TeO2-coated Si3N4 amplifier is about 19dB, which compares favourably with TeO2:Er waveguide amplifier results in the literature.

4.3 Silicon Nitride Mask Layout

In this section, various amplifier waveguide structures are described based on the results from various simulations. We used the layout software Pyxis to design a high- resolution silicon nitride mask. Structures including straight waveguides, paper clips

(bend waveguides), large S bends (bend waveguides), spirals and tapers were included in the design. The fabrication service was provided by the company LioniX International.

The Lionix silicon nitride platform was fabricated on 10-cm-diameter Si wafers with 8um thermal oxide lower cladding layer, ~0.1-0.3µm thick Si3N4 waveguide layer which is patterned and etched using stepper lithography and using the designed mask layout. Its limitations and constraints include a maximum Si3N4 thickness of 300nm to avoid stress and cracking of the nitride films and a minimum feature width based on the stepper lithography process of 0.5 µm. An overview of the mask is presented in figure 4.10.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Figure 4.10: Overview of the silicon nitride waveguide mask. Region I includes rings, straight waveguides, tapered waveguide fiber-chip coupling test structures, directional couplers and Sagnac interferometers. Region II contains long straight waveguides and large 6-cm long S bends to for testing longer amplifiers. Region III has spirals, paper clips and straight waveguides for testing a variety of amplifier lengths and formats.

Next, the separate components of the mask are presented with their parameter variations. The purpose of the various structures is testing different waveguide widths, amplifier lengths and for cut-back loss measurements.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Figure 4.11: Layout of straight waveguides with width varying from 0.5 to 2.0 µm

Table 4.13 : Variations of straight waveguides

Block I,IIШ Block Variation

Width 0.5,0.6,0.7,0.8,0.9,1.0,1.2,1.4,1.6,1.8,2.0(Repeat Straight [μm]: five times per width) Waveguide Length[cm]: 0.6; 1.0;2.2

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Figure 4.12: Schematic of a taper structure for testing fiber-chip coupling loss

Table 4.14 : Variations of tapers

Block I Block Variation

Width w1[μm]: 1

0.5,0.6,0.7,0.8,0.9,1.0,1.1,1.2,1.3,1.4,1.5, Width w2 [μm]: 1.6,1.7,1.8,1.9,2.0 Tapers l2[μm]: 200

l1[mm]: 6

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Figure 4.13: Layout of paperclip waveguides for amplifier and cut-back loss

measurements

Table 4.15 : Variations of paper clip waveguides

Block II,III Block Variation

Width [μm]: 0.6;0.8;1.0;1.2;1.4 600,630,….,990,1020; Paper Clips Radius [μm]: 1000,1030,…,1390,1420 Length [104 μm]: 2.5;3;3.5;4.0;5.5

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Figure 4.14: Layout of spiral waveguides

Table 4.16 : Variations of spirals series

Block Ш Block Variation

Width [μm]: 0.8;1.0

Length [cm]: 5;10 Spiral

Minimum radius [μm]: 100; 200;300;400;500

4.4 Fabrication Results

The silicon nitride waveguides were fabricated as described in section 4.3 [27]. An illustration of the reactive sputtering system used to deposit TeO2 is shown in Figure 4.15.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

The system was used to deposit undoped TeO2 for the initial waveguide measurements in this thesis. In future a second sputtering gun with an Er target will be used in the system

3+- in order to deposit Er doped films. In the system, oxygen (O2) and argon flow are injected. The oxygen is in a constant mass flow rate, while argon flow is adjusted in order to maintain chamber pressure. The target is driven by a radio frequency (RF) power supply [28]. A SEM image of a Si3N4 waveguide with and without TeO2 top-coating is shown in Figure 4.16, after focused-ion-beam milling of the end-facet.

Figure 4.15: Sputtering system used to deposit tellurium oxide thin films onto the

chips containing silicon nitride waveguides [28]

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

(a) (b) Figure 4.16: (a) SEM cross-section of an uncoated Si3N4 waveguide. (b) SEM cross-

section of a Si3N4 waveguide coated with a 0.3-µm-thick TeO2 film [27].

In this thesis, we used radio frequency (RF) reactive sputtering process to deposit the tellurium oxide coating layer. In details, we sputtered a 3 inch metallic tellurium target in an argon/oxygen ambient in order to deposit the tellurium oxide. To reduce the loss, a stoichiometry 2:1 ratio for oxygen to tellurium was used. The Argon flow was 12 sccm.

We also deposited onto a piece of 6 inch thermally oxidized silicon witness sample.

During sputtering, the power applied to the Te target was 150W and a 7.5 to 8.3 sccm flow of oxygen flow was applied to obtain a low loss film. The deposition rate for films was between 22 and 25nm/min resulting in a refractive index of 2.08 at 1550nm wavelength. The film loss ranged from 0.5dB/cm to less than 0.1dB/cm at a wavelength of 1550nm. By using the prism coupling method, the film loss was measured to be ≤ 0.1 dB/cm at 1550 nm [27].

4.5 Measurements

Waveguide transmission measurements were carried out using the setup shown in

Figure 4.17, which consists of either a 980, 1310, 1550 or 2000 nm tunable laser, lensed fibers, polarizers, and XYZ alignment stages. During the measuring, the laser light is

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

coupled into different waveguide structures using the XYZ stages through the lensed tapered fibers. The paddle-based polarization controller is used to adjust the polarization of the incident light to TE polarization as the figure shows. Results of light transmission in four different paperclip lengths are shown in Figure 4.18.

Figure 4.17: The waveguide transmission measurement setup [29]

Fig. 4.18: Loss measurements for varying waveguide lengths from 2.5cm to 4cm

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

for four different wavelengths [27]

In the waveguide loss measurement we used cut-back method which is a common way to separate the waveguide propagation loss from the fiber-chip coupling losses that occur at the input and output. We applied the method on waveguides by changing the length of the waveguide and observing the change in loss [27]. In Figure 4.18, the propagation losses of different waveguide lengths ranging from 2.5cm to 4cm at 980nm, 1310nm

1550nm and 2000nm wavelengths are shown. For 1550nm wavelength, the propagation loss is 0.67dB/cm.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Chapter 5 Conclusions and Future Work

3+ This thesis studied the optical properties of a novel TeO2:Er -coated Si3N4 waveguide platform. Possible gain was predicted by the amplifier model using Matlab code. A mask layout with different amplifier designs was fabricated based on the simulations and gain predictions.

Specifically, chapter one introduced the current background of erbium-doped optical amplifiers. We focused on erbium-doped tellurium oxide due to its excellent optical properties. Low-loss silicon nitride waveguide platforms were also discussed offering a general idea of the thesis. Chapter 2 summarized the waveguide theory and material properties. The loss and gain mechanisms in waveguides were also introduced. In chapter

3, the waveguide design and amplifier modeling methods involving RSoft modesolver software and a Matlab-based rate equation solver were introduced. In chapter 4 the simulations results were presented, including the specific waveguide parameters for single mode conditions, small bending radius, high intensity overlap with the gain medium and small effective mode areas. Amplifier modeling results were also shown in chapter 4 predicting the gain in the designed waveguide structures. Furthermore, initial experimental results were reported, including Si3N4 waveguide fabrication, reactive sputtering deposition of the TeO2 coating layer and cut-back loss measurements showing low waveguide propagation loss.

3+ In the future, TeO2:Er films can be deposited onto Si3N4 chips and the gain on the different amplifier structures can be measured and compared to the predicted theoretical

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

values. These modeling and waveguide simulation results can be applied to optimize the footprint, gain and efficiency of integrated erbium-doped waveguide amplifiers. This work serves as a basis for the development of high-performance erbium-doped optical amplifiers utilizing this promising platform.

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

Appendix: Amplifier Simulation Code

The code below was adapted from the amplifier model developed in [25]. The sections of code which have been modified or added as part of this thesis work are indicated in bold.

%Erbium-doped aluminum oxide amplifier simulation %Analytical steady state solution to rate equations based on 3-level approximation %Pump and signal intensity profiles determined separately by modesolver

%======tic; format short; close all; clear all; clc; %======%Constants h = 6.626068e-34; %Planck's constant [m^2kg/s] c = 299792458.; %Speed of light [m/s] e = 2.718281828; %e pi = 3.141592654; %Pi %======%Define signal, pump and Er spectroscopic properties num_wavelengths = 301; %Number of signal wavelengths in simulation wavelength_signal = zeros(num_wavelengths,1); %Initialize signal wavelengths array abs_cross_signal = zeros(num_wavelengths,1); %Initialize signal absorption cross sections array em_cross_signal = zeros(num_wavelengths,1); %Initialize signal emission cross sections array wavelength_signal = dlmread('Cross_Sections.txt', '\t', 'A1..A301'); %Signal wavelengths [nm] abs_cross_signal = dlmread('Cross_Sections.txt', '\t', 'B1..B301'); %Signal absorption cross sections [cm^2] em_cross_signal = dlmread('Cross_Sections.txt', '\t', 'C1..C301'); %Signal emission cross sections [cm^2]

loss_signal = 0.40; %goes up, gain decreases %Signal background loss [dB/cm] loss_coeff_signal = loss_signal/4.34294482; %Signal background loss coefficient [cm^-1] launched_power_signal = 1.e-3;%doesn't affect the gain %Launched signal power [mW] wavelength_pump = 976.; %Pump wavelength [nm] abs_cross_pump = 5.1e-21; %affects the gain %Pump absorption cross section [cm^2]

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

em_cross_pump = 5.1e-21; %reversely affects the gain %Pump emission cross section [cm^2] esa_cross_pump =7.04e-21; %doesn't affect the gain %Pump excited state absorption cross section [cm^2]

loss_pump = 0.60;%affects the gain %Pump background loss [dB/cm] loss_coeff_pump = loss_pump/4.34294482; %Pump background loss coefficient coefficient [cm^-1] launched_power_pump = [0.3;1.0;10.0;25.0;171.0;300.0]; %Launched pump powers array [mW] num_powers = length(launched_power_pump); %Number of launched pump powers in simulation doping_concentration = 3.0e20;%affects the gain %Erbium ion concentration [cm^-3]

upconversion_coeff_11 = 2.74*1e-18;%(2.01*(doping_concentration/1e20)+1.9703)*1e-18;%it affects the gain (2.01*(doping_concentration/1e20)+1.9703)*1e-18; %4I13/2->4I9/2 macroscopic upconversion parameter [cm^3s^-1] upconversion_coeff_22 = 0; %2.0e-18; doesn't affect the gain %4I13/2->4I9/2 macroscopic upconversion parameter [cm^3s^-1] lifetime_1 = 2.6e-3; % 2.6e-3; doesn't affect the gain %First excited state lifetime [s] lifetime_2 = 240e-6; % 240.0e-6;it reversely affects the gain a lot %Second excited state lifetime [s]

%======

%Define amplifier modes and active medium dimensions L = 5.0; %Amplifier length [cm] numZ = 20; %Number of discretizations in the longitudinal direction dZ = L/numZ; %Longitudinal step size [cm] solvertype = 0; %0=3-level analytical solutions (no fast quenching), 1=3-level solved by Matlab ODE (including fast quenching) beamtype = 0; %0=flat-top, 1=Gaussian, 2=user-defined

%Parameters for flat-top or Gaussian mode profiles: radius_gain_medium = 1.0; %affects the gain %Radius of the gain medium [µm] confinement_signal = 0.9;%0.5 %Fraction of signal confined in the gain medium confinement_pump = 0.92; %0.5 %Fraction of pump confined in the gain medium

%0)Flat top profile: if beamtype==0 numX = 2; %Number of discretizations in the X direction numY = 1; %Number of discretizations in the Y direction dA=zeros(numX,numY); %Initialize area of each mesh element dA(:,:) = pi*radius_gain_medium^2; %Area of each mesh element [µm^2] norm_power_signal=zeros(numX,numY); %Initialize signal intensity profile norm_power_pump=zeros(numX,numY); %Initialize pump intensity profile 83

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

doping_profile = zeros(numX,numY); %Initialize doping profile norm_power_signal(1,1) = confinement_signal; %Set percentage of signal in active region norm_power_signal(2,1) = 1-confinement_signal; %Set percentage of signal outside active region norm_power_pump(1,1) = confinement_pump; %Set percentage of signal in active region norm_power_pump(2,1) = 1-confinement_pump; %Set percentage of signal outside active region doping_profile(1,1) = 1; %Set doped region doping_profile(2,1) = 0; %Set undoped region end

%1)Circular Gaussian beam: if beamtype==1 numX = 20; %Number of discretizations in the X direction numY = 1; %Number of discretizations in the Y direction dX = radius_gain_medium/(numX-1); dA = zeros(numX,numY); %Initialize area of each mesh element norm_power_signal=zeros(numX,numY); %Initialize signal intensity profile norm_power_pump=zeros(numX,numY); %Initialize pump intensity profile confined_power_signal = 0; %Initialize confined signal power confined_power_pump = 0; %Initialize confined pump power doping_profile = zeros(numX,numY); %Initialize doping profile radius_signal = sqrt(-2*radius_gain_medium^2/(log(1-confinement_signal))); %Fraction of signal confined in the gain medium radius_pump = sqrt(-2*radius_gain_medium^2/(log(1-confinement_pump))); %Fraction of pump confined in the gain medium for i =1:(numX-1) dA(i,1) = pi*(dX*i)^2-pi*(dX*(i-1))^2; %Area of each mesh element [µm^2] norm_power_signal(i,1) = (1-e^(-2*(i*dX)^2/radius_signal^2))-(1-e^(-2*((i-1)*dX)^2/radius_signal^2)); norm_power_pump(i,1) = (1-e^(-2*(i*dX)^2/radius_pump^2))-(1-e^(-2*((i-1)*dX)^2/radius_pump^2)); confined_power_signal = confined_power_signal + norm_power_signal(i,1); confined_power_pump = confined_power_pump + norm_power_pump(i,1); doping_profile(i,1) = 1; %Set doped region end dA(numX,1) = dA(numX-1,1); %Set area seen by signal/pump outside the active region (arbitrary) norm_power_signal(numX,1) = 1-confined_power_signal; %Set percentage of signal outside active region norm_power_pump(numX,1) = 1-confined_power_pump; %Set percentage of signal outside active region doping_profile(numX,1) = 0; %Set undoped region disp(['Percentage signal power confined in active region = ',num2str(confined_power_signal)]); disp(['Percentage pump power confined in active region = ',num2str(confined_power_pump)]); end

%2)User-defined profile: if beamtype==2 load amplifier_mode_profiles_Al2O3_fivenitride_CW.mat; %Load values from signal intensity profile file norm_power_signal = (1/sum(sum(signal_mode_profile))).*signal_mode_profile; %Create normalized signal intensity profile from Poynting vector norm_power_pump = (1/sum(sum(pump_mode_profile))).*pump_mode_profile; %Create normalized pump intensity profile from Poynting vector numX = length(norm_power_signal(:,1)); %Number of discretizations in the X direction numY = length(norm_power_signal(1,:)); %Number of discretizations in the Y direction dX = DX; %X step size [µm] dY = DY; %Y step size [µm] dA=zeros(numX,numY); %Initialize area of each mesh element 84

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

dA(:,:) = dX*dY; %Area of each mesh element [µm^2] %top_undoped = zeros(numX,410); %Undoped portion above Er %er_doped = ones(numX,90); %Er-doped region %bottom_undoped = zeros(numX,400); %Undoped portion below Er %doping_profile = horzcat(top_undoped,er_doped,bottom_undoped); %Doping profile -> ones where Er:Al2O3 doping_profile = NNlogic; end %======%Amplifier calculation %Initialize arrays for storing pump and signal power and gain total_power_signal=zeros(numZ+1,num_wavelengths,num_powers); %Initialize total signal power at each launched pump power, wavelength and z-step total_power_pump=zeros(numZ+1,num_wavelengths,num_powers); %Initialize total pump power at each launched pump power, wavelength and z-step gain = zeros(numZ+1,num_wavelengths,num_powers); %Initialize total gain at each launched pump power, wavelength and z-step %Initialize arrays for storing power, flux and population densities at each %X, Y and Z location and each pump power and wavelength power_signal = zeros(numX,numY,numZ+1,num_wavelengths,num_powers); %Initialize signal power at each coordinate in the waveguide power_pump = zeros(numX,numY,numZ+1,num_wavelengths,num_powers); %Initialize pump power at each coordinate in the waveguide flux_signal = zeros(numX,numY,numZ,num_wavelengths,num_powers); %Initialize signal photon flux at each coordinate in the waveguide flux_pump = zeros(numX,numY,numZ,num_wavelengths,num_powers); %Initialize pump photon flux at each coordinate in the waveguide CONST = zeros(numX,numY,numZ,num_wavelengths,num_powers); QUADC = zeros(numX,numY,numZ,num_wavelengths,num_powers); QUADB = zeros(numX,numY,numZ,num_wavelengths,num_powers); QUADA = zeros(numX,numY,numZ,num_wavelengths,num_powers); N_0 = doping_concentration.*ones(numX,numY,numZ,num_wavelengths,num_powers); %Initialize ground state population density matrix [cm^-3] N_1 = zeros(numX,numY,numZ,num_wavelengths,num_powers); %Initialize 4I13/2 level population density matrix [cm^-3] N_2 = zeros(numX,numY,numZ,num_wavelengths,num_powers); %Initialize 4I11/2 level population density matrix [cm^-3]

%1) Start outer loop for incrementing pump power for index_powers = 1:num_powers %Initialize signal and pump powers and photon fluxes and population %densities at each coordinate in the waveguide total_power_signal(1,:,index_powers) = launched_power_signal; total_power_pump(1,:,index_powers) = launched_power_pump(index_powers,1);

%2) Start loop for incrementing wavelength %Establish total signal and pump power at the input and fill launched pump %power array (the launched signal array is constant). for index_wavelengths=1:num_wavelengths power_signal(:,:,1,index_wavelengths,index_powers)=launched_power_signal.*norm_power_signal; power_pump(:,:,1,index_wavelengths,index_powers)= launched_power_pump(index_powers,1).*norm_power_pump;

%3) Start loop for determining power along amplifier length %Propagate in Z direction, solving population equations for each Z step: %Fill signal and pump arrays at each step, redistributing the 85

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

%total power in a Gaussian profile. for index_Z=1:numZ if solvertype==0 %Determine photon fluxes (in cm^-2): flux_signal(:,:,index_Z,index_wavelengths,index_powers) = power_signal(:,:,index_Z,index_wavelengths,index_powers).*1e- 3.*wavelength_signal(index_wavelengths,1).*1e-9./(dA(:,:)*1e-12*h*c)*1e-4; flux_pump(:,:,index_Z,index_wavelengths,index_powers) = power_pump(:,:,index_Z,index_wavelengths,index_powers).*1e-3.*wavelength_pump.*1e- 9./(dA(:,:)*1e-12*h*c)*1e-4; %Solve for population densities: CONST(:,:,index_Z,index_wavelengths,index_powers) = 1./(1/lifetime_2+em_cross_pump.*flux_pump(:,:,index_Z,index_wavelengths,index_powers)+abs_cross _pump.*flux_pump(:,:,index_Z,index_wavelengths,index_powers)); QUADC(:,:,index_Z,index_wavelengths,index_powers) = abs_cross_signal(index_wavelengths,1).*flux_signal(:,:,index_Z,index_wavelengths,index_powers).*do ping_concentration+(1/lifetime_2- abs_cross_signal(index_wavelengths,1).*flux_signal(:,:,index_Z,index_wavelengths,index_powers)).*C ONST(:,:,index_Z,index_wavelengths,index_powers).*abs_cross_pump.*flux_pump(:,:,index_Z,index_ wavelengths,index_powers).*doping_concentration; QUADB(:,:,index_Z,index_wavelengths,index_powers) = - (1/lifetime_1+em_cross_signal(index_wavelengths,1).*flux_signal(:,:,index_Z,index_wavelengths,index _powers)+abs_cross_signal(index_wavelengths,1).*flux_signal(:,:,index_Z,index_wavelengths,index_p owers)+(1/lifetime_2- abs_cross_signal(index_wavelengths,1).*flux_signal(:,:,index_Z,index_wavelengths,index_powers)).*C ONST(:,:,index_Z,index_wavelengths,index_powers).*abs_cross_pump.*flux_pump(:,:,index_Z,index_ wavelengths,index_powers)); QUADA(:,:,index_Z,index_wavelengths,index_powers) = (1/lifetime_2- abs_cross_signal(index_wavelengths,1).*flux_signal(:,:,index_Z,index_wavelengths,index_powers)).*C ONST(:,:,index_Z,index_wavelengths,index_powers).*upconversion_coeff_11- 2*upconversion_coeff_11; N_1(:,:,index_Z,index_wavelengths,index_powers) = ((- QUADB(:,:,index_Z,index_wavelengths,index_powers)- sqrt(QUADB(:,:,index_Z,index_wavelengths,index_powers).*QUADB(:,:,index_Z,index_wavelengths,in dex_powers)- 4.*QUADA(:,:,index_Z,index_wavelengths,index_powers).*QUADC(:,:,index_Z,index_wavelengths,inde x_powers)))./(2.*QUADA(:,:,index_Z,index_wavelengths,index_powers))).*doping_profile(:,:); N_2(:,:,index_Z,index_wavelengths,index_powers) = (CONST(:,:,index_Z,index_wavelengths,index_powers).*(abs_cross_pump.*flux_pump(:,:,index_Z,inde x_wavelengths,index_powers).*(doping_concentration- N_1(:,:,index_Z,index_wavelengths,index_powers))+upconversion_coeff_11.*N_1(:,:,index_Z,index_w avelengths,index_powers).*N_1(:,:,index_Z,index_wavelengths,index_powers))).*doping_profile(:,:); N_0(:,:,index_Z,index_wavelengths,index_powers) = (doping_concentration- N_1(:,:,index_Z,index_wavelengths,index_powers)- N_2(:,:,index_Z,index_wavelengths,index_powers)).*doping_profile(:,:); %Determine powers remaining after propagation through Z-step in %each element and keep running total of total power remaining after Z-step power_signal(:,:,(index_Z+1),index_wavelengths,index_powers) = power_signal(:,:,index_Z,index_wavelengths,index_powers).*e.^((em_cross_signal(index_wavelengths ,1).*N_1(:,:,index_Z,index_wavelengths,index_powers)- abs_cross_signal(index_wavelengths,1).*N_0(:,:,index_Z,index_wavelengths,index_powers)- loss_coeff_signal).*dZ); power_pump(:,:,(index_Z+1),index_wavelengths,index_powers) = power_pump(:,:,index_Z,index_wavelengths,index_powers).*e.^((em_cross_pump.*N_2(:,:,index_Z,ind

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

ex_wavelengths,index_powers)-esa_cross_pump.*N_2(:,:,index_Z,index_wavelengths,index_powers)- abs_cross_pump.*N_0(:,:,index_Z,index_wavelengths,index_powers)-loss_coeff_pump).*dZ); %Determine total pump and signal powers and total signal gain after propagating through Z-step. %Establish signal and pump power arrays for input into the next section %by redistributing the power in the mode distribution. total_power_signal(index_Z+1,index_wavelengths,index_powers) = sum(sum(power_signal(:,:,(index_Z+1),index_wavelengths,index_powers))); total_power_pump(index_Z+1,index_wavelengths,index_powers) = sum(sum(power_pump(:,:,(index_Z+1),index_wavelengths,index_powers))); gain(index_Z+1,index_wavelengths,index_powers)=10.*log10(total_power_signal(index_Z+1,index_wa velengths,index_powers)./total_power_signal(1,index_wavelengths,index_powers)); power_signal(:,:,index_Z+1,index_wavelengths,index_powers)=total_power_signal(index_Z+1,index_w avelengths,index_powers).*norm_power_signal; power_pump(:,:,index_Z+1,index_wavelengths,index_powers)= total_power_pump(index_Z+1,index_wavelengths,index_powers).*norm_power_pump; end if solvertype==1 % %Determine photon fluxes (in cm^-2): % flux_signal(:,:,index_Z,index_wavelengths,index_powers) = power_signal(:,:,index_Z,index_wavelengths,index_powers).*1e- 3.*wavelength_signal(index_wavelengths,1).*1e-9./(dA(:,:)*1e-12*h*c)*1e-4; % flux_pump(:,:,index_Z,index_wavelengths,index_powers) = power_pump(:,:,index_Z,index_wavelengths,index_powers).*1e-3.*wavelength_pump.*1e- 9./(dA(:,:)*1e-12*h*c)*1e-4; % %Solve for population densities: % N_1(:,:,index_Z,index_wavelengths,index_powers) = ; % N_2(:,:,index_Z,index_wavelengths,index_powers) = ; % N_0(:,:,index_Z,index_wavelengths,index_powers) = ; % %Determine powers remaining after propagation through Z-step in % %each element and keep running total of total power remaining after Z-step % power_signal(:,:,(index_Z+1),index_wavelengths,index_powers) = power_signal(:,:,index_Z,index_wavelengths,index_powers).*e.^((em_cross_signal(index_wavelengths ,1).*N_1(:,:,index_Z,index_wavelengths,index_powers)- abs_cross_signal(index_wavelengths,1).*N_0(:,:,index_Z,index_wavelengths,index_powers)- loss_coeff_signal).*dZ); % power_pump(:,:,(index_Z+1),index_wavelengths,index_powers) = power_pump(:,:,index_Z,index_wavelengths,index_powers).*e.^((em_cross_pump.*N_2(:,:,index_Z,ind ex_wavelengths,index_powers)-esa_cross_pump.*N_2(:,:,index_Z,index_wavelengths,index_powers)- abs_cross_pump.*N_0(:,:,index_Z,index_wavelengths,index_powers)-loss_coeff_pump).*dZ); % %Determine total pump and signal powers and total signal gain after propagating through Z-step. % %Establish signal and pump power arrays for input into the next section % %by redistributing the power in the mode distribution. % total_power_signal(index_Z+1,index_wavelengths,index_powers) = sum(sum(power_signal(:,:,(index_Z+1),index_wavelengths,index_powers))); % total_power_pump(index_Z+1,index_wavelengths,index_powers) = sum(sum(power_pump(:,:,(index_Z+1),index_wavelengths,index_powers))); % gain(index_Z+1,index_wavelengths,index_powers)=10.*log10(total_power_signal(index_Z+1,index_wa velengths,index_powers)./total_power_signal(1,index_wavelengths,index_powers)); % power_signal(:,:,index_Z+1,index_wavelengths,index_powers)=total_power_signal(index_Z+1,index_w avelengths,index_powers).*norm_power_signal; % power_pump(:,:,index_Z+1,index_wavelengths,index_powers)= total_power_pump(index_Z+1,index_wavelengths,index_powers).*norm_power_pump; end 87

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

end %End Z-propagation loop (3) end %End loop for incrementing wavelength (2) end %End loop for incrementing launched pump power (1) %======

%Plotting:picture of the whole gain that I am working on %Plot gain vs wavelength for different launched pump powers figure; grid on; box on; xlabel('wavelength (nm)','FontSize',16); axis([1400 1700 -38 16]); ylabel('internal net gain (dB)','FontSize',16); set(gca,'FontSize',16); hold on; lambda_plot = zeros(num_wavelengths, num_powers); gain_plot = zeros(num_wavelengths, num_powers); for i=1:num_powers lambda_plot(:, i) =wavelength_signal(:,1); gain_plot(:, i) = gain(numZ+1,:, i); end plot(lambda_plot,gain_plot,'Linewidth',3.0); %Continue to plot measured gain data: %measured_lambda1 = dlmread('Measured_Loss_190312.txt', '\t', 'A1..A16271'); %Wavelengths [nm] %measured_loss = dlmread('Measured_Loss_190312.txt', '\t', 'B1..B16271'); %Loss [dB] (unpumped) %measured_lambda2 = dlmread('Measured_Gain_190312.txt', '\t', 'A1..A16271'); %Wavelengths [nm] %measured_gain = dlmread('Measured_Gain_190312.txt', '\t', 'B1..B16271'); %gain [dB] %plot(wavelength_signal,0,'Linewidth',1); %plot(measured_lambda1,measured_loss,'Linewidth',1); %plot(measured_lambda2,measured_gain,'Linewidth',1); legend(strcat(num2str(launched_power_pump(:,1)),' mW'),'Location','SouthEast'); %legend boxoff; hold off;

%Plot peak gain vs pump power (at 1532 nm) figure; grid on; box on; xlabel('launched pump power (mW)','FontSize',16); ylabel('internal net gain at 1532 nm (dB)','FontSize',16); set(gca,'FontSize',16); hold on; launched_power_plot = zeros(num_powers, 1); gain_peakwl_plot = zeros(num_powers, 1); for i=1:num_powers launched_power_plot(i, 1) =launched_power_pump(i,1); gain_peakwl_plot(i, 1) = gain(numZ+1,132,i);%132@1532nm 88

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

end plot(launched_power_plot,gain_peakwl_plot,'Linewidth',3.0); hold off;

%Plot average population densities vs. z distance for different pump powers %and peak wavelength (1532 nm) for j=num_powers:num_powers figure; title(strcat('Launched Pump Power = ',num2str(launched_power_pump(j,1)),' mW'),'FontSize',16); grid on; box on; xlabel('propagation distance (cm)','FontSize',16); ylabel('population density (cm^-^3)','FontSize',16); axis([0 L 0 doping_concentration]); set(gca,'FontSize',16); hold on; propagation_distance_plot = zeros(numZ, 1); N0_plot = zeros(numZ, 1); N1_plot = zeros(numZ, 1); N2_plot = zeros(numZ, 1); for i=1:numZ propagation_distance_plot(i, 1) =i*dZ-dZ*0.5; N0_plot(i, 1) = N_0(1,1,i,132,j); N1_plot(i, 1) = N_1(1,1,i,132,j); N2_plot(i, 1) = N_2(1,1,i,132,j); end plot(propagation_distance_plot,N0_plot,propagation_distance_plot,N1_plot,propagation_distan ce_plot,N2_plot,'Linewidth',3.0); legend('N0','N1','N2','Location','Best'); hold off; end

%Plot transmitted and absorbed pump power vs. propagation distance for j=num_powers:num_powers figure; grid on; box on; xlabel('propagation distance (cm)','FontSize',16); ylabel('pump power (mW)','FontSize',16); set(gca,'FontSize',16); hold on; propagation_distance_plot = zeros(numZ, 1); transmitted_pump_power_plot = zeros(numZ, 1); absorbed_pump_power_plot = zeros(numZ, 1); for i=1:numZ+1 propagation_distance_plot(i, 1) =(i-1)*dZ; transmitted_pump_power_plot(i, 1) = total_power_pump(i,132,j); absorbed_pump_power_plot(i, 1) = total_power_pump(1,132,j)- total_power_pump(i,135,j);%132@1532nm end plot(propagation_distance_plot,transmitted_pump_power_plot,propagation_distance_plot,abso rbed_pump_power_plot,'Linewidth',3.0); legend('transmitted pump power','absorbed pump power','Location','Best'); 89

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

hold off; end toc; %======

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

References

[1] P. M. Becker, A. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers:

Fundamentals and Technology (Academic Press, 1999).

[2] “Comparison Of Different Optical Amplifiers,” http://www.fiber-optic- tutorial.com/comparison-of-different-optical-amplifiers.html

[3] J. D. B. Bradley and M. Pollnau, "Erbium-doped integrated waveguide amplifiers and lasers," Laser & Photonics Reviews 5, 368–403 (2011).

[4] K. T. Vu and S. Madden, “Tellurium dioxide erbium doped planar rib waveguide amplifiers with net gain and 2.8dB/cm internal gain,” Optics Express 18, 19192–19200

(2010).

[5] C. G. H. Roeloffzen, M. Hoekman, E. J. Klein, L. S. Wevers, R. Bernardus Timens,

D. Marchenko, D. Geskus, R. Dekker, A. Alippi, R. Grootjans, A. van Rees, R. M.

Oldenbeuving, J. P. Epping, R. G. Heideman, K. Wörhoff, A. Leinse, D. Geuzebroek, E.

Schreuder, P. W. L. van Dijk, I. Visscher, C. Taddei, Y. Fan, C. Taballione, Y. Liu, D.

Marpaung, L. Zhuang, M. Benelajla, and K.-J. Boller, “Low-loss Si3N4 TriPleX optical waveguides: Technology and applications overview,” IEEE Journal of Selected Topics in

Quantum Electronics 24(4), 4400321 (2018).

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

[6] J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M.-C. Tien, J. S. Barton, A. Leinse, R.

G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Optics Express 19(4), 3163–3174 (2011).

[7] G.-R. Lin, S.-P. Su, C.-L. Wu, Y.-H. Lin, B.-J. Huang, H.-Y. Wang, C.-T. Tsai, C.-I.

Wu and Y.-C. Chi, ”Si-rich SiNx based Kerr switch enables optical data conversion up to

12 Gbit/s,” Scientific Reports 5, 9611 (2015).

[8] I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Physics Reports 518(1-

2), 1–79 (2012).

[9] M. M. Ismail, M. A. Meor Said, M. A. Othman, M. H. Misran, H. A. Sulaiman, and F.

A. Azmin, “Buried vs. ridge optical waveguide modeling for light trapping into optical fiber”, International Journal of Engineering and Innovative Technology 2(1), 273–278

(2012).

[10] D. Herres, “Basics of TEM, TE, and TM propagation,” https://www.testandmeasurementtips.com/basics-of-tem-te-and-tm-propagation

[11] M. A. Foster, K. D. Moll, and A. L. Gaeta, ”Optimal waveguide dimensions for nonlinear interactions,” Optics Express 12(13), 2880–2887 (2004)

[12] R. Jose and Y. Ohishi, “Higher nonlinear indices, Raman gain coefficients, and bandwidths in the TeO2-ZnO-Nb2O5-MoO3 quaternary glass system,” Applied Physics

Letters 90(21), 221104 (2007).

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

[13] N. N. Greenwood and A. Earnshaw, Chemistry of the Elements (Pergamon Press,

1984), p. 911.

[14] H. Kong, J.-B. Yeo, and H.-Y. Lee, “A study on the properties of tellurium-oxide thin films based on the variable sputtering gas ratio,” Journal of the Korean Physical

Society 66(11), 1744–1749 (2015).

[15] M. Yamada, A. Mori, K. Kobayashi, H. Ono, T. Kanamori, K. Oikawa, Y. Nishida, and Y. Ohishi, ”Gain-flattened tellurite-based EDFA with a flat amplification bandwidth of 76nm,” IEEE Photonics Technology Letters 10(9), 1244–1246 (1998).

[16] P. Nandi and G. Jose, “Spectroscopic properties of Er3+ doped phospho-tellurite glasses,” Physica B: Condensed Matter 381(1), 66–72(2006).

[17] S. J. Madden and K. T. Vu, “Very low loss reactively ion etched Tellurium Dioxide planar rib waveguides for linear and non-linear optics”, Optics Express 17(20), 17645–

17651 (2009).

[18] K. T. Vu and S. J. Madden, “High gain erbium doped tellurium oxide waveguide amplifier”, presented at the Conference on Lasers and Electro-Optics Europe, Munich,

Germany, 22–26 May 2011.

[19] D. B. Keck and R. Tynes, “Spectral response of low-loss optical waveguides,”

Applied Optics 11(7), 1502–1506 (1972).

[20] J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R.

G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Planar waveguides with less than 0.1

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

dB/m propagation loss fabricated with wafer bonding,” Optics Express 19(24), 24090–

24101 (2011).

[21] S. C. Mao, S. H. Tao, Y. L. Xu, X. W. Sun, M. B. Yu, G. Q. Lo, and D. L. Kwong,

“Low propagation loss SiN optical waveguide prepared by optimal low-hydrogen module,” Optics Express 16(25), 20809–20816 (2008).

[22] E. A. J. Marcatili and S. E. Miller, “Improved relations describing directional control in electromagnetic wave guidance,” Bell System Technical Journal 48(7), 2161–2188

(1969).

[23] K. Anastasios, P. Nikolaos, and M. Amalia, “Development of a finite element method mode solver application for optical waveguides,” in Proceedings of the 6th

Balkan Conference in Informatics, vol. 1036 (2013).

[24] E. J. Harvey, Design and Fabrication of Silicon on Insulator Optical Waveguide

Devices (M.Sc. Thesis, Rochester Institute of Technology, 2006).

3+ [25] J. D. B. Bradley, Al2O3:Er as a Gain Platform for Integrated Optics (Ph.D. Thesis,

University of Twente, 2009).

[26] K. T. Vu, S. Farahani, and S. J. Madden, “980nm pumped erbium doped tellurium oxide planar rib waveguide laser and amplifier with gain in S, C and L band,” Optics

Express 23(2), 747–755 (2015).

[27] H. C. Frankis, K. Miarabbas Kiani, D. B. Bonneville, C. Zhang, S. Norris, R.

Mateman, A. Leinse, N. D. Bassim, A. P. Knights, and J. D. B. Bradley, “TeO2

M.A.Sc. Thesis – Chenglin Zhang; McMaster University – Engineering Physics.

waveguides integrated on a low-loss Si3N4 platform for application in scalable photonic circuits,” manuscript in preparation.

[28] H. C. Frankis and J. D. B. Bradley, “Reactively sputtered tellurium oxide films for integrated optics”, presented at Photonics North, Ottawa, ON, Canada, 6–8 June 2017.

[29] K. Miarabbas Kiani, A. P. Knights, J. D. B. Bradley, S. Norris, and N. D. Bassim,

“Improved fiber-chip coupling in waveguides by focused ion beam modification,” presented at the 11th Annual FIB SEM Workshop, McMaster University, Hamilton, ON,

Canada, April 2018.