High Efficient Ultra-Thin Flat Optics Based on Dielectric Metasurfaces

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Authors Ozdemir, Aytekin

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HIGH EFFICIENT ULTRA-THIN FLAT OPTICS BASED ON DIELECTRIC METASURFACES

Aytekin Ozdemir

A Dissertation Submitted to the Faculty of the

COLLEGE OF OPTICAL SCIENCES

In Partial Fulfillment of the Requirements

For the Degree of

DOCTOR OF PHILOSOPHY

In the Graduate College

THE UNIVERSITY OF ARIZONA

2018

STATEMENT BY AUTHOR

This dissertation has been submitted in partial fulfillment of the requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.

Brief quotations from this dissertation are allowable without special permission, provided that an accurate acknowledgement of the source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

SIGNED: Aytekin Ozdemir

ACKNOWLEDGEMENTS

Here I would like to express my sincere gratitude to my PhD advisors Dr.

Hamza Kurt and Dr. Yuzuru Takashima. I am grateful for Dr. Kurt’s guidance and inspiration, which helps me to find valuable research topics and make great progress in my interested area. The expertise and the skills that he imparted to me will have a profound impact on my future career development. I appreciate Dr.

Takashima’s helps, guidance and mentorship anytime with no hesitation. He provided the conditions for me to succeed in my PhD at OSC and without his and

Dr. Kurt’s collaborative and inspiring approach none of this would be possible.

I would like to thank Dr. Jim Schwiegerling for being my committee member, who gave me detailed suggestions. His contributions in the field of optics and excellent books in SPIE keep illuminating the path of young researchers like me.

I am also grateful to each member in the Dr. Kurt’s group, Zeki Hayran, Nazmi

Yilmaz, F. Taha Bagci, Ibrahim Halil Giden, Utku Gorkem Yasa who provided great support, collaboration and discussions at each step toward my PhD degree. I also want to take this opportunity to express my gratitude to the great academic advising staff at OSC and Graduate College at UofA, Mr. Mark Rodriguez, Mrs.

Lindsay Loebig, Mrs. Elise Bowler for their kind assistance and continuous support even from a very long distance.

I would like to thank my MSc advisor at OSC, Dr. Franko Kueppers, who first accepted me to his group and guided me to the correct research field in PhD 5

program when I was having hard times. I really appreciate Prof. Mark Neifeld for allowing me to work on his volume holography-based computational imaging research and improving my research skills.

I would like to thank my former co-worker and life-time great friend Dr. Yavuz

Ozturk who was always ready to help even in editing my PhD thesis. A hearty thanks to my fellow students, Dr. Cihan Tunc, Muhammed Sen, Dr. Esen Salcin,

Anael Guilmo, Dr. Alejandra Santigo, Charles Greenlee, Dr. Sukumar Murali and many others. Thank you for helping me study and pass the comprehensive exam, keeping me motivated in graduate school, giving great advices for job searching and referring me.

Last but not the least, I would like to thank Dr. Selcuk Akturk, who motivated me not to give up the PhD at OSC even at our 1st introduction, and helped me during the tough days of job search.

DEDICATION

To God, the most merciful, the most gracious, who inspired me to the correct path of success, bestowed upon me the patience and the talents that I need.

To my parents Dursun and Nazli Ozdemir who brought me up by struggling with severe hardships, gave me unconditional support, endless love, and enormous motivation throughout my life.

To my sisters Filiz, Feryal, and Fisun and my brother Fatih Mehmet who always prayed for me throughout the good and tough times, always pushed me to do better and believed in my talents, supported me against the challenges of life.

TABLE OF CONTENTS

LIST OF FIGURES ...... 9

ABSTRACT ...... 14

CHAPTER 1: INTRODUCTION ...... 16

1.1 Metasurfaces...... 17

1.2 Motivation and Topics to Cover...... 19

1.3 References ...... 23

APPENDIX A: POLARIZATION INDEPENDENT HIGH TRANSMISSION

LARGE NUMERICAL APERTURE LASER BEAM FOCUSING AND

DEFLECTION BY DIELECTRIC HUYGENS’ METASURFACES ...... 27

A.1. Introduction ...... 28

A.2. Design and Results ...... 32

A.3. Design of 1D beam deflector ...... 39

A.3.1. Design of 1D flat lens ...... 41

A.3.2. Design of 2D flat lens ...... 43

A.4. Conclusion ...... 49

A.5. References ...... 51

APPENDIX B: METASURFACE LENS ARRAY-BASED EFFICIENT MID-

WAVE INFRARED FOCAL PLANE ARRAYS ...... 58

B.1. Introduction ...... 59 8

B.2. Design and Results ...... 66

B.2.1. Design of the building blocks of metasurface lens ...... 66

B.3. Focal plane array via metasurface lens array ...... 68

B.4. Conclusion ...... 76

B.5. References ...... 77

APPENDIX C: TUNABLE WIDE ANGLE BEAM-STEERING VIA

METASURFACES INFILTRATED WITH NEMATIC LIQUID CRYSTALS . 81

C.1. Introduction ...... 82

C.2. Conclusion ...... 91

C.3. References ...... 93

CHAPTER 2: CONCLUSION AND OUTLOOK ...... 98

LIST OF FIGURES

Fig. A-1. (a) Artistic impression of an all-dielectric resonator metasurface beam deflector and lens (b) Side-view of the unit cell of the designed metasurface lens: a Silicon nanodisk embedded in a host substrate of fused Silica (SiO2). Here nanodisks are arranged in a square lattice array. For the design wavelength λ=1064 nm, the unit cell dimension is equal to P=620 nm, nanodisk height is equal to H=170 nm, and the nanodisk radii (R) vary between 130 to 240 nm. The host Silica thickness values are equal to T1= 700 nm, T2=350 nm. The 500 µm thick back layer of fused Silica is not shown in for the sake of clarity...... 33

Fig. A-2. (a) Transmission and (b) Phase modulation of nanodisk arrays versus wavelength and nanodisk radii with nanodisk height of 170 nm and 620 nm unit cell dimension. Electric dipole (ED) and magnetic dipole (MD) resonance overlap occurs at 1064 nm shown by the vertical line, and overlap region is shown by the white ellipse. (c) Transmission and (d) phase shift at a wavelength of 1064 nm for varying radii of nanodisks calculated from numerical simulations...... 36

Fig. A-3. Plots (a) to (h) depict the geometric dispersion of an array of disks with a periodicity of 620 nm at different wavelengths as indicated from 0.9 nm to 1.2 µm. It can be seen that the MD and ED resonance modes cross for a unique value of radius and height for each of the wavelength observed and that there is near unity transmission at the dipole resonance mode crossing...... 38

show the targeted phase profile and phase of each nanodisk, respectively. (c) Phase of the transmitted field Ex when the plane wave passes through the dielectric metasurface beam deflector...... 40

Fig. A-5. Typical focusing performance of the 1D cylindrical metasurface lens. (a) The targeted phase profile (blue solid line) and phase of each nanodisk unit cells (red circles) of the designed lens with a focal length of 3.5 µm are also shown. (b) Electric field intensity profile in the focal plane (z = 3.5 µm, y = 0). (c) Electric field intensity distribution of the transmitted field at wavelength of 1064 nm...... 43

Fig. A-6. (a) Top-view of the designed all-dielectric flat lens (b) Distribution of the electric field intensity in the xz-plane, (c) and (d) are the field intensity distribution along x-direction (at z = f, y = 0) and z-direction, respectively. The FWHM of the spot is 0.657λ, focal length is f = 3.5 µm and Depth of focus is about 1.5 µm...... 45

Fig. A-7. (a) Intensity distributions of the transmitted light in the xz-plane, through the designed metalenses with different focal lengths of 6 µm, 10 µm, 15 µm, respectively, under the normally incident light with a wavelength of 1064 nm. Diameter of metalens for all is 10.85 µm (b) The electric field intensity along the x-axis and (c) the electric field intensity along the z- axis at the corresponding focusing planes with different focal lengths. 47

Fig. A-8. (a) Intensity distributions of the transmitted light in the xz-plane, through the designed metalenses with different NA values of 0.55, 0.74, 0.84, respectively, under the normally incident light with a wavelength of 1064 nm. The designed focal length for all is 7 µm, and the diameter of metalenses for each is 9.3 µm, 15.55 µm, 21.07 µm, respectively. (b) The electric field intensity along the x-axis and (c) the electric field intensity along the z-axis at the corresponding focusing planes with different NA values...... 48 11

Fig. B-1. (a) Schematic structure of metasurface with periodic a-Si circular posts resting on Sapphire substrate arranged in a square lattice (H=1.92 µm, P=1.50 µm), Top view (left), Side view (right). (b) Intensity transmission and (c) phase of the transmission coefficient variation as a function of a- Si post diameter (D) and period (P). (d) Simulated intensity and phase of the transmission coefficient for a fixed period P=1.50 µm at wavelength λ=3.2 µm for metasurfaces with varied diameter...... 64

Fig. B- 2. (a) Sampled phase profile of a single metalens in the metalens array having a pitch length of 24 µm by arranging a-Si posts with unit cell size of 1.5 µm at the lattice sites. (b) Realization of metalens array by a-Si posts. (c) Focused light intensity distribution at the far-field for a wavelength of 3.2 µm with either TE or TM polarized light. (d) Focused light intensity distribution at the far-field for another wavelength of 4 µm, which is different from the design wavelength...... 69

Fig. B-3. (a) Far-field intensity distribution of light focused by different pixels of the optimized metalens array design at a wavelength of 3.2 µm. (b) Far- field intensity distribution of light focused by different pixels of the optimized metalens array design at a wavelength of 4 µm. (c) and (d) show the cross-section of the focused light intensity and 3D view of the focused light intensity for the 3x3 metalens array at the focal plane, respectively...... 71

degraded by very poor transmission and focusing efficiency), Mie-type dielectric metasurface lensed FPAs (green hexagram marker suffering from higher optical crosstalk, lower focusing efficiency and also narrowband operation)...... 73

Fig. B-5. Analysis of the effect of angle of incidence on the transmission characteristics of periodic a-Si circular posts resting on Sapphire substrate arranged in a square lattice for height, periodicity and wavelength values given as H=1.92 µm, P=1.50 µm, λ=3.2 µm, respectively. (a) Intensity transmission (previously excluded resonance dip occurs around 0.9 µm for all incident angles) and (b) phase of the transmission coefficient variation as a function of a-Si post diameter (D) and angle of incidence of the illuminating beam...... 74

Fig. C- 1. (a) Schematic of a tunable beam steering metasurface. The molecular orientations of LCs are given as an inset. (b) A nano cell arranged through hexagonal lattice and top view of metalens. LCs are infiltrated into the nano holes made of glass (SiO2). Nano cell dimension is set to be a=250nm and height is h=1.8µm. The structure length is L=20μm and width is W=3μm (c) Calculated phase profile for varying nano cell diameter at λ=550nm. Corresponding phase shifts of the nano-cells are indicated in the graph when the radius of the nanoholes ranges between 50nm to 110 nm. (d) Calculated phase profile for varying LCs' molecular orientation from (θLC =0°) to (θLC =90°) at green wavelength (λ=550nm). Note that nano-cell diameter equals d=110nm in this case...... 85

(left) {휃푢푝, 휃푑표푤푛} = 0°, 90°, (center) {휃푢푝, 휃푑표푤푛} = 90°, 90° and (right) {휃푢푝, 휃푑표푤푛} = 90°, 0°...... 88

Fig. C- 3. Calculated deflection angles in terms of LCs' orientations at up/down layers are superimposed as a phase map...... 88

Fig. C- 4. (a) Beam steering scenario for three wavelengths while only changing molecular orientation of the LCs on the bottom surface and the upper

surfaces has the molecular orientation of up=0˚. (b) The beam steering

angle is calculated at fixed wavelengths while only changing molecular orientation of the LCs on the upper surface and the bottom surface has

the molecular orientation of down=0˚...... 90

ABSTRACT

Metasurfaces which emerged as two-dimensional counterparts of metamaterials, facilitate the realization of arbitrary phase distributions using large arrays with subwavelength and ultra-thin features. Even if metasurfaces are ultrathin, they still effectively manipulate the phase, amplitude, and polarization of light in transmission or reflection mode. In contrast, conventional optical components are bulky, and they lose their functionality at sub-wavelength scales, which requires conceptually new types of nanoscale optical devices. On the other hand, as the optical systems shrink in size day by day, conventional bulky optical components will have tighter alignment and fabrication tolerances. Since metasurfaces can be fabricated lithographically, alignment can be done during lithographic fabrication, thus eliminating the need for post-fabrication alignments. In this work, various types of metasurface applications are thoroughly investigated for robust wavefront engineering with enhanced characteristics in terms of broad bandwidth, high efficiency and active tunability, while beneficial for application.

Plasmonic metasurfaces are not compatible with the CMOS process flow, and, additionally their high absorption and ohmic loss is problematic in transmission based applications. Dielectric metasurfaces, however, offer a strong magnetic response at optical frequencies, and thus they can offer great opportunities for interacting not only with the electric component of a light field, but also with its magnetic component. They show great potential to enable practical device functionalities at optical frequencies, which motivates us to explore them one step 15

further on wavefront engineering and imaging sensor platforms. Therefore, we proposed an efficient ultra-thin flat metalens at near-infrared regime constituted by silicon nanodisks which can support both electric and magnetic dipolar Mie-type resonances. These two dipole resonances can be overlapped at the same frequency by varying the geometric parameters of silicon nanodisks. Having two resonance mechanisms at the same frequency allows us to achieve full (0-2π) phase shift on the transmitted beam.

To enable the miniaturization of pixel size for achieving high-resolution, planar, compact-size focal plane arrays (FPAs), we also present and explore the metasurface lens array-based FPAs. The investigated dielectric metasurface lens arrays achieved high focusing efficiency with superior optical crosstalk performance. We see a magnificent application prospect for metasurfaces in enhancing the fill factor and reducing the pixel size of FPAs and CCD, CMOS imaging sensors as well.

Moreover, it is of paramount importance to design metasurfaces possessing tunable properties. Thus, we also propose a tunable beam steering device by combining phase manipulating metasurfaces concept and liquid crystals. Tunability feature is implemented by nematic liquid crystals infiltrated into nano holes in SiO2.

Using electrically tunable nematic liquid crystals, dynamic beam steering is achieved. 16

CHAPTER 1: INTRODUCTION

INTRODUCTION

1.1 Metasurfaces

Bulky optical components have reduced functionality in terms of manipulating light propagation and integration with the optoelectronic devices. On the other hand, artificially designed metamaterials and photonic crystals have tremendously contributed to the field of nanophotonics with the sub-wavelength features of the structural parameters [1,2]. Metasurfaces can be assumed as the two-dimensional version of the three-dimensional metamaterials. As a result, ultra-thin flat optics can be generated by deploying such metasurfaces in the design. Amplitude and phase changes on incident light are induced by spatially varying local nano- elements of metasurfaces [3,4]. Metasurfaces have been proposed for focusing [5–

7], deflecting light [8,9], changing polarization [10,11], generating holograms

[12,13], producing vortex beams [14,15], manipulating thermal emission [16], modulating light intensity [17], and optical cloaking [18,19].

There are two commonly used optical elements that can be grouped as refractive and diffractive elements. In refractive optical elements, wavefront of light is modified by curved surfaces such that different phase accumulation occurs along the optical paths traversing at different distances with respect to the optical axis. In order to have the required phase variation, refractive optical elements involve significant thicknesses compared to the wavelength of light. That makes it very challenging to manufacture these elements. Besides, not all phase functions and variations can be easily performed with refractive optical elements due to the fact that there are stringent requirements on the curvature and surface quality of the 18 refractive structures. Diffractive optical elements (DOE) use interference and diffraction phenomena to produce desired light distributions. Two or more phase functions can be implemented on the same surface of DOE to simplify optical systems [20]. DOEs are thin, light-weighted and compact as compared to the refractive ones. However, one of the disadvantages of a DOE is the limited spectral bandwidth. Diffraction efficiency quickly drops when DOE operates at a wavelength different than the designed one. Even if metasurfaces are similar to the conventional diffractive optics from some aspects, they have many additional superior capabilities. First, sub-wavelength nature and the resonant properties of their scatterers allow metasurfaces to impart multi-level phase shifts in entire 0 to

2π range by only varying the lateral geometry of the meta-atoms or antennas. In conventional diffractive optics, such multilevel phase-shifts require elements with different thicknesses, which can only be fabricated via multi-stage lithography methods. In contrast, due to uniform thickness, metasurfaces can be fabricated by using only a single stage lithography process. Therefore, metasurfaces enable flat and ultrathin optical elements and can be integrated into optical systems while keeping ultra-compact size and light weight [3].

One recently emerged optical design approach is based on metasurfaces [21].

Metasurfaces serve as special interfaces to engineer the transmitted and reflected beams anomalously by modifying the boundary conditions [22]. A thin metasurface achieves manipulation of transmitted wave by means of designed phase gradients that covers the interval from 0 to 2π. Abrupt changes of optical responses happen 19 due to the interactions of light with the constitutive nanoscatterers of the metasurfaces.

Metasurfaces can be either plasmonic or dielectric metasurfaces. Metallic metasurfaces usually operate in reflection mode and they suffer from Ohmic losses

[23]. Meanwhile, dielectric based metasurfaces have both transmission and reflection modes. There is no absorption problem related to the Ohmic losses [24–

26]. Besides, visible and NIR spectra can be targeted with dielectric metasurfaces.

Desired properties of dielectric metasurfaces include large numerical apertures, broadband wavelength operation, high transmission, high diffraction efficiency, and large-scale on-chip fabrication. Due to exotic optical phenomena not readily available, metasurfaces show various capabilities to transform the existing applications into ultracompact, planar-profile designs compared to their conventional bulky counterparts. There are various applications of metasurfaces such as communications, sensing, imaging, energy harvesting, optical modulators, switches, and reconfigurable antennas. Remarkably, these studies have a great potential to make a huge impact on the potential markets of portable and wearable devices, communications, national defense, signal processing and so on.

1.2 Motivation and Topics to Cover

The improvements in nanofabrication technology and downscaling of CMOS transistors enabled substantial size reductions for the electronic sensors over the past few decades. In particular, similar size reductions have been realized for 20 especially image sensors and cameras, as we have witnessed cameras transform from bulky and expensive kinds of equipment to widespread technologies integrated into phones, laptops, tablets, etc. Most of the fundamental size constraint of today’s optical systems are not caused by the electronics, but rather the optics themselves lead to the biggest obstacle against further size reductions. For shorter focal lengths, and thus smaller f-numbers, the bulky glass optics necessitate higher curvatures and take up more space due to their greater volumes. This also gives rise to stringent requirements on the curvature and surface quality of the refractive structures. As we look toward the near future and observe that there is a growing demand for miniaturization and reduction of the system complexity, and obviously, the size constraints of current optical systems will limit the capabilities of sensors.

In order to address this challenge, metasurface optics is a promising candidate which can respond to the growing demand for miniaturization of conventional bulky optics. Another important feature of metasurface optics is its straightforward fabrication using the existing CMOS-compatible semiconductor fabrication methods. Furthermore, this platform enables significant reduction in thickness, weight and easier optical alignment and packaging in camera modules. This will definitely enhance the continuous progress of portable and wearable consumer optics/electronics which has high demand for high performance and low cost miniaturized systems. 21

A variety of metasurface-based replacements of conventional optical components have already been demonstrated, but there are still obstacles against the metasurface-based approach that prevent the widespread usage of this technology.

My research is carried out based on the current limitations and emerging potentials of metasurfaces. Metasurfaces with high efficiency, ultrathin structure, polarization-independence, broad bandwidth, and tunability are theoretically designed and numerically investigated, respectively, and each section in this thesis is summarized as follows.

In Appendix A, all-dielectric Huygens’ metasurface structures are proposed to construct high numerical aperture flat lenses and beam deflecting devices. The designed metasurfaces consists of two-dimensional array of all-dielectric nanodisk resonators with spatially varying radii, thereby introducing judiciously designed phase shift to the propagating light. Owing to the overlap of Mie-type magnetic and electric resonances, high transmission was achieved with rigorous design analysis.

The designed flat lenses have numerical aperture value of 0.85 and transmission values around 80%. It also offers easy fabrication and compatibility with available semiconductor technology. Since the proposed system can easily handle complex wavefront manipulation, it has a great promise for other beam shaping applications.

In Appendix B, I design and propose a more efficient broadband polarization- insensitive all-dielectric metasurface microlenses-based FPA operating in the

MWIR. These dielectric metasurface microlenses achieve substantially high focusing efficiency over 0.85 without degrading the optical crosstalk performance. 22

By systematical analysis of these metasurface microlens-arrays using full-wave solutions, I demonstrated that optical crosstalk can be reduced to low levels ≤ 2.8% while keeping the high efficiency. For the device performance, a similar figure-of- merit (FoM) from the previous reports was used, which was defined as the focusing efficiency per optical crosstalk times the f-number and our device achieved FoM of

91 which outperformed all other types MWIR FPAs designed so far, all staying below a maximum FoM of 84. These proposed metasurface microlens arrays demonstrate great potential for increasing the signal to noise ratio and sensitivity thus paving the way for compact-size, high-resolution FPAs.

Finally, in Appendix C, a tunable beam steering device by combining phase manipulating metasurfaces concept and liquid crystals is proposed. Tunability feature is implemented by nematic liquid crystals infiltrated into nano holes in

SiO2. Using electrically tunable nematic liquid crystals, dynamic beam steering is achieved. The structure has high transmission efficiency staying above 83% in the visible spectrum and wide-angle deflection range between +15 and -15 degrees.

The structure analyses were conducted using finite-difference-time-domain

(FDTD). Besides, double metasurfaces are formed in a hexagonal lattice in order to improve the efficiency by satisfying a non-diffractive, subwavelength operation requirement.

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APPENDIX A: POLARIZATION INDEPENDENT HIGH

TRANSMISSION LARGE NUMERICAL APERTURE

LASER BEAM FOCUSING AND DEFLECTION BY

DIELECTRIC HUYGENS’ METASURFACES

A.1. Introduction

Recently, metamaterials and metasurfaces have attracted significant attention in the optics community [1,2]. Metamaterials are artificial materials which are constituted by nanostructures, and optical resonant effects of these nanostructures allow metamaterials to have unique optical properties due to negative dielectric permittivity, ε and magnetic permeability, µ. Metasurfaces are two-dimensional

(2D) counterparts of metamaterials with thicknesses much smaller than the wavelength of the incident light, enabling complete manipulation of the basic properties of light beams, such as phase, amplitude and polarization [3,4].

Compared to metamaterials, metasurfaces do not require complex fabrication methods and can be fabricated with single step lithographical techniques. Thus, they are well suited for mass production and can be integrated onto a photonic chip.

In addition, metamaterials have high loss in the optical regime; this also limits their practical applications at this particular frequency regime [5]. Even if metasurfaces are ultra-thin, they still effectively manipulate the phase, amplitude, and polarization of light in transmission or reflection mode. Many planar analogs of the traditional bulky optical components, such as lenses [6–13], anti-reflection coatings [14], axicons [8,15], polarization converters [16], optical vortex generators

[17], and absorbers [18] have been demonstrated by using metasurfaces.

Electromagnetic phase control is one of the simplest and probably one of the most unique applications of metasurfaces. Full 2phase control is the key for implementing various applications, such as beam steering, structured light 29 generation, or lensing. Remarkably, metasurfaces can conveniently modulate the phase of electromagnetic waves in various ways, such as dynamical phase control, and geometrical phase control. Dynamical phase control relates to the change in the optical path to acquire the required optical path difference. Metasurfaces introduce interfacial phase discontinuities along the optical path as an alternative approach to realize very compact and flat dynamical phase elements. However, dynamical phase metasurfaces are circular polarization insensitive. The other types of metasurfaces, which are called geometrical phase metasurfaces, have also been proposed and demonstrated experimentally [19,20]. Geometrical phase metasurfaces utilize space-variant polarization manipulation of the incident field in order to induce local phase retardation. This type of phase retardation is actually a

Pancharatnam-Berry (PB) phase shift which in some cases is an undesired effect but can be utilized for spin filter and beam shaping applications. By designing two- layer metasurfaces (one of them is polarization or spin-insensitive and the other one is polarization or spin-controlled), geometric phase and dynamic phase metasurface elements can be integrated to implement ultra-compact polarization beam-splitters and spin filters [21,22]. Majority of initial studies on metasurfaces focused on metal-dielectric structures, which have low efficiency due to nonradiative Ohmic losses at optical frequencies especially operating in transmission mode [23,24].

Many plasmonic-based metasurfaces and flat lenses were recently designed using

V-shaped antennas and rotationally asymmetric nanostructures [8,25–27]. Such systems typically had energy efficiency less than 20% due to increased Ohmic losses in optical frequency regions. On the other hand, almost all metals melt at 30 high temperatures and, thus, they are not well suited for high-power laser applications.

Due to the abovementioned drawbacks of metals, significant work has been done in developing dielectric analogs of metasurfaces in visible and near-infrared range, since many dielectric materials have very low absorption loss in these optical frequencies. Most of the previous designs relied on high contrast grating approaches with nano-pillar structures of higher aspect ratio [11]. High refractive index materials like Silicon were studied to show strong Mie-type scattering mechanism [28]. The well-known “Huygens’ principle” states that the new wavefront is determined by the sum of secondary wavelets generated by all points on the previous wavefront. Low-loss dielectric nanoresonators are designed to emulate the behavior of the forward-propagating elementary wavelets known from the Huygens’ principle [3]. In other words, Huygens’ sources can be achieved by using polarizable subwavelength particles that sustain both magnetic and electric dipolar resonances. The arrangement of many of such particles in a plane creates special reflectionless sheets or metasurfaces that are called Huygens’ metasurfaces

[29]. Silicon nanodisk structures were especially demonstrated to support the simultaneous excitations of electric and magnetic dipole resonances [30–34]. By varying the geometric parameters or the aspect ratio of silicon nanodisks, electric and magnetic dipole resonances can be overlapped at the same frequency. This also suppresses the backward scattering since electric and magnetic resonances will cancel each other in backscattering while interfering constructively in forward direction by realizing Kerker’s condition [35]. Thus, these two dipole resonance 31 mechanisms allow us to tailor the phase shift over 0-2 while having a high transmission and almost zero reflection. Also, silicon is a common material used mostly in semiconductor industry, which may benefit from mature semiconductor fabrication technology. Due to CMOS compatibility and the relative ease of fabrication, silicon-based structures continue to be an important element of the recent state-of-the-art nanophotonic device studies [36]. As a result, it is advantageous to use these silicon nanodisk metasurface structures to implement high-power laser beam manipulation with low-reflection losses and polarization- independence property.

In this chapter, we report the design and analysis of an efficient, ultra-thin planar metasurface lens and beam deflecting device which operates at a wavelength of

=1064 nm, by utilizing the recently developed Huygens’ metasurfaces. Designed devices rely on silicon nanodisk structures which can support both Mie-type electric and magnetic dipole resonances to realize phase manipulation and completely suppress reflection losses. By locally changing the radius of the silicon nanodisk elements, quasi-continuous and abrupt phase changes at modulus of 2π were realized. A flat metasurface lens with a high numerical aperture value of 0.85 and with transmissivity as high as 80% and a metasurface beam deflecting device with beam deflecting angle of 6.9표 with transmissivity of 75% have been designed and numerically demonstrated. With robust optimization algorithms, the design proposed here has great potential to be improved as a future study. Our design offers excellent polarization insensitive operation due to high degree of symmetry.

Also, much higher transmission than the previous studies with the same wavelength 32 of operation at 1064 nm was achieved [37]. The proposed design is considered also easy to fabricate with standard single step electron beam lithography based conventional planar semiconductor fabrication methods due to ultrathin thickness and very small aspect ratio of the designed structures comparing to recent studies with longer pillars [7]. Based on these outstanding properties and spectral scalability, these devices can be utilized in applications where operation at distinct known wavelengths is needed such as high power laser beam systems and fluorescence microscopy techniques.

A.2. Design and Results

The proposed Huygens’ metasurfaces are designed using high index silicon nanodisks, which have subwavelength periodicity and are embedded in a host low refractive index silica material. Other comparative design forms such as silicon free-standing in silica substrate may also be considered. Note that the spectral widths of the Mie-type resonances are determined by the proper choice of the dielectric environment. The refractive-index contrast between the nanodisk and surrounding media significantly affects the mode confinement of the electric and magnetic dipole resonances. Furthermore, by geometrical tuning of nanodisk dimensions, the spectral positions of the two resonances can be adjusted [30,32].

The schematic of 2D all-dielectric Huygens’ metasurface lens is shown in Fig. A-

1 (a) as an example. Silicon nanodisk array period (P), nanodisk height (H) and, nanodisk radius (R) are the three basic structural and geometric design parameters 33 that control the transmission amplitude and phase of the Huygens’ metasurfaces as shown in Fig. A-1 (b).

Fig. A-1. (a) Artistic impression of an all-dielectric resonator metasurface beam deflector and lens

(b) Side-view of the unit cell of the designed metasurface lens: a Silicon nanodisk embedded in a host substrate of fused Silica (SiO2). Here nanodisks are arranged in a square lattice array. For the design wavelength λ=1064 nm, the unit cell dimension is equal to P=620 nm, nanodisk height is equal to H=170 nm, and the nanodisk radii (R) vary between 130 to 240 nm. The host Silica thickness values are equal to T1= 700 nm, T2=350 nm. The 500 µm thick back layer of fused Silica is not shown in for the sake of clarity.

The metasurfaces considered here are designed for a wavelength of 1064 nm and optimized for operation in transmission under normal incident transverse-electric

(TE) polarized plane wave. Design is polarization insensitive due to the symmetry of the structural nanodisk elements given that mode of the single nanodisks is not significantly affected by neighboring nanodisks. In the analysis, the refractive index of Silicon (Si) and Silica (SiO2) are 3.56 and 1.45, respectively as they are extracted from Palik’s handbook [38]. Also, the imaginary part of the refractive index of silicon was taken as about 8x10-4 at 1064 nm from the data of Palik [38]. 34

Using finite-difference time-domain (FDTD) method software, FDTD solutions from Lumerical Inc. the transmission and phase modulation of the nanodisk arrays with different geometric parameters are calculated. The nanodisks are assumed to be embedded in a host substrate of fused Silica (SiO2) in the simulations. The periods of the arrays are optimized in order to get a broader overlap region of the electric and magnetic dipole resonances in the spectrum and, thus, a broader transmission region with respect to variation of nanodisk geometric parameters. It is estimated that a lattice period value of 620 nm is the best option to design a high

NA (numerical aperture) flat lens with a numerical aperture value around 0.85 due to the limitation by the Nyquist sampling criterion (sampling period: 훬푠 = 푃 <

휆 ). To prevent aliasing, the Nyquist-Shannon sampling theorem requires that the 2푁퐴 function be bandlimited and that the sampling frequency 푓s be related to the maximum frequency component, as given below:

1 푓푠 = > 2푓푚푎푥, (1) 훬푠

The highest frequency component is related to the instantaneous frequency as below:

|Δφ(푥, 푦)|푚푎푥 푓 = , (2) 푚푎푥 2휋

Solving for the sampling period yields: 35

휋 훬 < , (3) 푠 |Δφ(푥, 푦)|푚푎푥 and for a parabolic lens phase profile, this leads to a sampling period given by:

휆 훬 = 푃 < , (4) 푠 2푁퐴

Since periods of the arrays are fixed both in the x and y directions, and due to rotationally symmetric nanodisk elements, polarization independence is ensured.

During unit cell analysis, the incident plane wave at 1064 nm is normal to the array plane with polarization along the x direction, and periodic boundary conditions are adopted in each boundary of the unit cell to decrease the amount of computation time.

Fig. A-2 (a) and Fig. A-2 (b) show the calculated contours of the transmissivity and transmission phase of the nanodisk arrays for different illumination wavelength and radii (R). By varying the nanodisk radius, relatively high transmission and full phase coverage (0-2can be achieved at the same time for the nanodisk height of

170 nm (nanodisk embedded in SiO2), respectively. It is clear that this enables arbitrary wavefront control by precisely manipulating the spatial distribution of the radius variation of dielectric nanodisk resonators. A fixed lattice period of 620 nm both provides a broad area with high transmissivity and allows easy fabrication with high tolerance as well as less complex design. The more the lattice period reduces, the more coupling occurs between the adjacent unit cells and high transmission region significantly reduces. 36

Fig. A-2 (c) and Fig. A-2 (d) clearly show the transmission and the phase modulation for different nanodisk radii while the wavelength is fixed at 1064 nm as the operation wavelength. For convenience, here the phase modulation of 130 nm radius is set to be zero, and all negative phases are changed to positive by adding

2 to them. This result serves as look-up data for choosing the proper disk radius for the phase manipulation required. In order to achieve any desired phase profile at each spatial location (푥, 푦), an appropriate nanodisk diameter is chosen to 37 minimize the transmission error 훥푇 = |푒푖휑(푥,푦) − 푇(퐷)푒푖휑(퐷)|, where 푇(퐷)푒푖휑(퐷) is the complex transmission coefficient. The other important point in Fig. A-2 (c) is that transmission goes down especially towards the larger radius values of the nanodisks. Considering the fact that periodic boundary conditions are used in the full-wave simulation and nanodisks have fixed period and height, coupling effect gets more pronounced with the larger nanodisk radii. Having radius as the only degrees of freedom makes the design and fabrication easier but results in a trade- off against transmission. Metasurfaces with high aspect ratio subwavelength building blocks can be considered, but fabrication may be harder due to tapering problem of the vertical side-walls of the fabricated structures, and more advanced fabrication methods are required [7].

Geometric dispersion of the infinite disk array resonances was also analyzed as shown in Fig. A-3 (a) to Fig. A-3 (h). As it is indicated, geometric dispersion of an array of disks at different wavelengths starting from 0.9 to1m significantly depends on the height and the radius of the disks. We see that the ED and MD resonance modes cross for a unique value of height and radius for each incident wavelength and there is near unity transmission at the location of resonance overlap or mode crossing. Lattice period is kept constant at the value of 620 nm during these analyses, which is smaller than the incident wavelength of illumination.

Note that when the fabrication errors are taken into account, the phase and transmission values may departure from the ideal values. Rigorous optimization algorithms and sensitivity analyses need to be performed to further improve the performance and address the fabrication errors [39,40]. However, there is still no sufficient optimization study for especially all-dielectric high NA flat lenses due to time consuming full-wave simulation requirement. It should be also noted that chromatic dispersion here is not a significant problem since design is focused on the manipulation of laser beams, which are intrinsically narrowband.

A.3. Design of 1D beam deflector

We firstly start with the design of a metasurface with beam steering ability, in order to show the fundamental ability of the all-dielectric Huygens’ metasurfaces to manipulate the wavefront of a transmitted beam for various applications. By introducing in-plane phase gradient 푑휑/푑푥 at the interface between two media, new degrees of freedom to control light propagation are attained in metasurfaces.

The desired phase function for the beam deflecting functionality is given by

2휋 휑(푥) = 푘 푥 = 푛 sin(휃 ) 푥 (5) 푥 휆 푖 푡

where 푘푥 is a proportionality factor or wave vector along 푥, λ is the wavelength of the incident beam in free-space, 푛푖 is the refractive index of the material at the incidence side, 휃푡 is the deflection angle. For normal incidence and 푛푖, the deflection angle 휃푡 given by [41] 40

−1 휆 푑휑 휃푡 = sin ( ) (6) 2휋.푛𝑖 푑푥

Fig. A-4. (a) Super cell with 10 nanodisks in a periodic array of the beam deflector. It repeats with a period of 6.1 µm along the x-axis and 620 nm along the y-axis. (b) Phase of the electric field (blue line) as a function of x-coordinate at about z = 3.5 µm. The dashed green line and red triangles show the targeted phase profile and phase of each nanodisk, respectively. (c) Phase of the transmitted field Ex when the plane wave passes through the dielectric metasurface beam deflector.

In our simulations, we design periodic supercells of total length 6.2 µm as shown in Fig. A-4 (a), which consist of 10 silicon nanodisks with periodicity of 푃 =620 nm. The radius of each silicon nanodisk is properly selected so that there is total

2 phase difference throughout the super-cell with width of 6.2 µm. Note that there

2휋 is = 36표 phase difference between two adjacent unit cells. Meanwhile, in the 10

FDTD simulations, periodic boundary conditions are adopted along the y-axis, whereas perfectly matched layer boundary conditions are employed along the x- axis and z-axis in order to reduce the computational resources. The designed deflection angle is about 6.8표, and the simulated deflection angle is 6.9표 relative to the surface normal, which is close as shown in Fig. A-4 (c). The desired phase- 41 difference profile of the metasurface beam deflector based on Eq. (5) and Eq. (6) is indicated by the dashed green line in Fig. A-4 (b). Red triangles are the phases of each corresponding silicon nanodisk for the beam deflector. By the result of the

FDTD simulations, the phase of the deflected electric field is shown by the blue solid line in Fig. A-4 (b) as a function of 푥-coordinate at about z=3.5 µm. Also, the overall transmissivity through the beam deflecting metasurface is about 75% at z=3.5 µm.

A.3.1. Design of 1D flat lens

The second Huygens’ metasurface device to be demonstrated is a 1D focusing lens for the transmitted beam. To form and ideally spherical wavefront for a point-like focus at a certain focal length f, the phase shift distribution 휑(푥) along the interface is given by

2휋 휑(푥) = (푓 − √푓2 + 푥2 ) (7) 휆 where λ is the vacuum wavelength of the incident light. Note that the transmission media after the lens is air. In addition, 푓 here is the predefined focal length. With the help of presented look-up data in Fig. A-2 (d), proper mapping can relate the required phase to the resonator radius at spatial position 푥. In the full-wave numerical FDTD simulations of the 1D lens, perfectly matched layers boundary conditions are adopted along the x-axis and z-axis and periodic boundary conditions are employed along y-axis. In the following designs, the focus and the aperture of 42 the lens are chosen as 푓 = 3.5 휇푚, 퐷 = 10.85 휇푚, respectively. These sizes require less computation resources and the design may be scaled to larger sizes at the same NA value of 0.85.

In the FDTD simulation, the lens includes 17 nanodisks along the x-axis and has a width 퐷 = 10.85 휇푚, measured from the edges of the two outermost nanodisk unit cells. The targeted phase profile of the 1D cylindrical lens from Eq. (7) is shown by blue solid line in Fig. A-5 (a). Theoretically available nanodisk unit cell phases at the corresponding spatial positions are also indicated by the red circles in Fig. A-

5 (a).

As also shown by the numerical results in Fig. A-5 (b), the full-width at half- maximum (FWHM) of the focused line for both TE and TM polarizations are

0.586λ nm for NA=0.85 at focal length of 푓 = 3.5 휇푚. Fig. A-5 (c) shows the focused intensity distribution of the transmitted field under an incident TE polarized illumination at xz-plane. 1D metasurface lens clearly generates a quite good focus at the designed position.

The designed 1D metasurface cylindrical lens has a transmissivity of 76%.

Transmission is defined as the ratio of the intensity of the transmitted light beam to that of the incident light. Note that high contrast metasurface flat lens structure shows a deviation of the focal length between the full-wave simulation analysis and the initial design, if diffraction dominates especially for small NA and small lens sizes (small Fresnel numbers) [42]. Because the designed lens here has high NA, 43 geometric optics dominates and, thus, our focal length is in good agreement with the initial design.

A.3.2. Design of 2D flat lens

The design of 2D flat lens requires additional phase gradient along the y-axis. Thus, the new phase distribution along the interface is given by

2휋 휑(푥, 푦) = (푓 − √푓2 + 푥2 + 푦2 ) (8) 휆 44

Each nanodisk at position (푥, 푦) should impart the required phase given by Eq. (8).

In the FDTD simulations of the 2D metasurface lens, perfectly matched layers boundary conditions are adopted along x, y and z directions. Fig. A-6 (a) illustrates the top-view of the designed 2D metasurface lens, where the aperture size is

10.85 휇푚 x 10.85 휇푚. Fig. A-6 (b) shows the electric field intensity of the transmitted light at the focal plane. The intensity enhancement at the focal plane is achieved by more than 30 times. Due to rotational symmetry of the designed lens, focus spots for the TE and TM polarizations are exactly the same. Thus, all results are given for only TE polarization while omitting TM results. In addition, FWHM of the focused spot is 0.657λ, which is close to diffraction limited value of 0.6λ for both TE and TM polarization as shown in Fig. A-6 (c). Total transmissivity of the designed 2D metasurface lens is 80% for the numerical aperture value of NA=0.85.

Depth of focus of about 1.5 µm is also shown in Fig. A-6 (d). 45

To further confirm and analyze the performance of the designed metalens, three other metalenses with different focal lengths equal to f = 6 μm, f = 10 μm and f =

15 μm have also been designed. The aperture size for each was taken the same as

10.85 μm and, thus, all of the three metalenses are composed of 17x17 silicon nanodisks. In theory, when the focal lengths get longer, the NAs will become smaller and the intensities at the focal points will decrease accordingly. The intensity distributions of the transmitted light through three metalenses under the normal incidence of light are shown in Fig. A-7 (a), and the transmission lights are 46 strongly and closely focused at the designed positions for all of three metalenses, respectively. For a quantitative analysis of the focusing effect of three designed metalenses, the electric field intensities along the x-axis and along the z-axis at the focal plane for the designed metalens are presented in Fig. A-7 (b) and Fig. A-7 (c), respectively. The simulated focal lengths are slightly different from the theoretical prediction, which can be mainly attributed to the diffraction effect of small size, high contrast grating lenses, as mentioned before [42]. At the focal planes, the diameters of the focal spot (FWHM along the x-axis) are at sub-wavelength scales, especially for smaller focal length values as shown in Fig. A-7 (b). The corresponding FWHMs are 1040 nm, 1140 nm and 1720 nm for three designed metalenses with focal length of 6 μm, 10 μm and 15 μm, respectively. As depicted in Fig. A-7 (c), the depths of focus (FWHM along the z-axis) are 4.62 μm, 7.2 μm and 16.6 μm for three designed metalenses with focal lengths of 6 μm, 10 μm and

15 μm, respectively. For the metalens with the shortest focal length, the shortest depth of focus and the largest transmission intensity can be achieved, as expected.

Sidelobes are due the diffraction effect, which is more prominent for smaller diameter lenses with NA values smaller than 0.7. They are suppressed especially for larger NA metalenses, as it will be illustrated by the following results.

The focusing ability of the lens is proportional to the NA which is defined as NA = sin[tan−1(D/2푓)], where D is the width of the lens, and f is the focal length of the lens. 47

Fig. A-7. (a) Intensity distributions of the transmitted light in the xz-plane, through the designed metalenses with different focal lengths of 6 µm, 10 µm, 15 µm, respectively, under the normally incident light with a wavelength of 1064 nm. Diameter of metalens for all is 10.85 µm (b) The electric field intensity along the x-axis and (c) the electric field intensity along the z-axis at the corresponding focusing planes with different focal lengths.

For a specific focal length, as the width of the lens increases, the NA will become larger. As shown in Fig. A-8 (a), with plane wave illumination at normal incidence, there will be better focusing properties for the metalenses with larger NA by increasing the metalens’ width. For a quantitative analysis of the focusing effect of three metalenses (focal length of f = 7 μm), Fig. A-8 (b) and Fig. A-8 (c) show that when NA = 0.84, the focusing intensity increases significantly, and FWHM gets smaller compared to the metalenses with NA = 0.74 and 0.55. As well as the 48 conventional lens, for the metalens with the larger NA, the size of the focal spot will be smaller, and the focusing intensity will also increase.

Various light manipulation techniques based on properly designed metasurfaces are possible including polarization independent beam focusing and steering. The targeted figure of merits such as high transmission, small FWHM at the focal point, large NA and acceptable deflecting angle are succeeded in the current study. 49

Considering the available spectral scalability, these devices can be utilized in applications where operation at distinct known wavelengths is needed such as high power laser beam systems and fluorescence microscopy techniques. Since 1064 nm wavelength is of great importance for high power applications and second harmonic generation applications, proposed design focused on that part of the spectrum in the present study.

The proposed metasurface flat lens can be realized using a silicon-on-insulator

(SOI) wafer with a buried oxide (BOX) of thickness 350 nm and top Si layer thickness of 170 nm. The wafers are spin-coated by a negative-tone electron beam resist and electron beam lithography (EBL) is used to define the desired 2D patterns, providing extraordinary in-plane design freedom and precision control.

After exposure and development, the resulting resist pattern is directly employed as an etch mask in a reactive ion etching of the silicon thin film and residual resist can be removed by using oxygen plasma. A plasma enhanced chemical vapor deposition (PECVD) SiO2 is then deposited covering the etched Si cylinders, to achieve the desired substrate thickness of 700 nm. After patterning the back side oxide of the SOI wafer, a Tetramethylammonium Hydroxide (TMAH) etching should be used to remove the bulk Si below the lens [30].

A.4. Conclusion

In conclusion, all-dielectric Huygens’ metasurfaces capable of serving as polarization insensitive beam deflection element and lens for the transmitted beam 50 using high contrast, subwavelength silicon nanodisks are proposed. By rigorous numerical simulations, optimum design parameter region with high transmission and sufficient phase control was achieved. In addition, flat metasurface lens with high numerical aperture value of 0.85 and with transmissivity as high as 80% and a metasurface beam deflection device with beam deflecting angle of 6.9표 with transmissivity of 75% have been obtained. The design is very compact, thin and offers less alignment problem comparing to bulky conventional lenses composed of many surfaces. Since the proposed system can easily handle complex wavefront manipulation, it has a great promise for other beam shaping applications. By playing with the asymmetry of the unit cells used in the design, the system can also be made polarization sensitive. Drawbacks of plasmonic metasurfaces using complex split-ring resonator design with intrinsic Ohmic loss are overcome by using all-dielectric silicon nanodisks as the basic meta-atoms. The design is scalable to other wavelengths and is also easy to fabricate with standard single step electron beam lithography based conventional planar semiconductor fabrication methods due to very small aspect ratio of the designed structures. Therefore, there is a great application prospect in the field of integrated optics via utilizing metasurfaces in the design.

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APPENDIX B: METASURFACE LENS ARRAY-BASED

EFFICIENT MID-WAVE INFRARED FOCAL PLANE

ARRAYS

B.1. Introduction

Metamaterials are artificial materials which are constructed from subwavelength structures , and optical resonant effects of these subwavelength structures allow metamaterials to show great potential in controlling electromagnetic properties via the electric permittivity and magnetic permeability parameters [1,2]. Recently, metasurfaces, as the surface version or two-dimensional (2D) counterparts of metamaterials have been proposed as an alternative to the bulk three-dimensional metamaterials, due to their simple fabrication, lower losses, and smaller footprint

[3].

Composed of two-dimensional arrays of subwavelength scatterers, metasurfaces show great capability to manipulate the amplitude, polarization, and phase of light in either transmission or reflection mode. Due to the superior control over the propagation of the electromagnetic waves, metasurface-based flat lenses [4–6], holograms [7–9], vortex beam generators [10], and wave plates [11–13] have been recently demonstrated.

Mid-wave infrared (MWIR) focal plane arrays (FPAs) have important use in both civil and defense applications. In order to make compact-size, high-resolution, planar MWIR FPAs, an FPA with a smaller pixel pitch with high fill factor is necessary. However, reducing the pixel pitch size while keeping a large fill factor increases the spatial crosstalk between the adjacent pixels significantly as a strict 60 and important trade-off. In other words, trend of reducing pixel size has some profound effects on pixel performance, in general, and optical performance since the wavelength of input light does not scale with technology and diffraction effects come into play. Furthermore, conventional MWIR FPAs require reduced optical aberrations, and this also results in a necessity of increasing the f-number, which increases the optical crosstalk as well [14]. For eliminating the drawbacks of decreasing pixel size, different methods, such as integration of microlens arrays with MWIR FPAs and mesa-isolation method were used [14]. Mesa-isolation method relies on the physical separation of the pixels, which require an etching process that would damage several pixels. As an example of mesa-isolation method, some previous studies on improving the performance of complementary metal oxide semiconductor (CMOS) image sensor pixels relied on placing light guides within pixels [15]. This enhanced the confinement of light inside each pixel by increasing the optical efficiency, and prevented leakage out of the pixel by reducing optical crosstalk. Design of the investigated light guide mechanisms made use of total internal reflection (TIR) and reflection at metal-dielectric interface, respectively. TIR based light guide design requires both a very high refractive index core material and a core region of high-aspect ratio etched over the central pixel area to increase the optical efficiency and decrease the optical crosstalk, but their fabrication is very challenging. On the other hand, while the light guide designs based on reflection of light at metal-dielectric interface demonstrated successful performance in decreasing optical crosstalk, due to the inherent loss of metals, they had lower optical efficiency. Moreover, fabrication of their constituent high-aspect 61 ratio vertically oriented metal cladding interface is currently not possible via standard CMOS process and, thus, new fabrication methods would be needed. Sub- wavelength photon-trapping (PT) structure-based pixel arrays were also shown as an effective means to improve the quantum efficiency and reduce the diffusion crosstalk [16]. However, PT structure had a slightly higher optical crosstalk compared to non-PT pixel arrays with similar geometry.

On the other hand, microlens arrays are used to increase the optical fill factor of

FPAs and CMOS image sensor pixels. They serve to focus and concentrate the incident light onto the pixel regions instead of allowing it to fall on non- photosensitive areas of the pixel array. Thus, integration of different types of microlens arrays to MWIR FPAs has been reported rigorously in a few studies so far [14,17,18]. Even if spherically refractive type microlens arrays reduced the focused spot size or the Airy disk, they suffered from the emergence of the first- order diffraction spots at the centers of the adjacent pixels and, thus, they were not able to enhance the optical crosstalk [14]. In another work, metallic metasurface lens arrays were shown to achieve an optical crosstalk of less than 1% but their focusing efficiency, which is defined as the ratio of the focused light power to the incident light power was very low (<11%) to make them practical in applications

[17]. The primary reason for the poor efficiency performance of metallic metasurfaces is due to the intrinsic nonradiative Ohmic losses and cross- polarization scheme requirement. Because of these drawbacks of metallic metasurfaces, extensive research efforts have been performed based on all- dielectric version of metasurfaces [19–25]. Previous studies on all-dielectric 62 metasurface-based lens array MWIR FPAs relied on Mie-scattering-based

Huygens’ metasurfaces [18]. Even if these Huygens’ metasurfaces demonstrated higher focusing efficiency and large figure-of-merit performance than their metallic counterparts, they operated successfully only in a very narrow spectral band and had an increased optical crosstalk due to poor sampling of the required lens phase profile.

The fundamental narrowband design limitation of Mie-resonance-based metasurfaces arises from the dipole resonances, which occur around a resonance frequency, and, thus give rise to the limited-bandwidth phase manipulation. As a result, instead of using the dipole resonance overlap at a fixed wavelength, we can use high aspect ratio silicon posts to generate truncated-waveguide modes that can be regarded as non-resonant approach since the working principle is not dependent on a fixed wavelength [6,26]. These structures were also shown to have higher transmission and better phase sampling via the flexibility of lattice periodicity selection even for low f-number metalenses [6]. Furthermore, high contrast dielectric metasurface lens arrays can be fabricated in any shape to meet the requirement by using single step conventional UV binary lithography methods [6]

, and sub-metalenses, in particular, can be matched each other perfectly without deadspace. This also means that theoretical fill factor for metasurface lens arrays is

100%, which is similar to diffractive microlenses. Therefore, the great potential of high contrast dielectric metasurface lens arrays should be analyzed and exploited more deeply for the next-generation, compact-size, and high-SNR FPAs. 63

In this study, we report the design and analysis of a more efficient, broadband, polarization-insensitive all-dielectric metasurface lens array-based FPAs which operate in the MWIR. For implementation, a metasurface platform based on high index contrast silicon posts was proposed. In addition, these high contrast dielectric meta-atoms are capable of achieving much higher transmission values with respect to the variation of the geometrical dimension of the posts, comparing to the metallic metasurfaces and Huygens’ metasurfaces counterparts. Thus, by integrating the metalens arrays designed with these meta-atoms to MWIR FPAs, high focusing efficiency can be achieved even with higher f-number values. In addition to that, by making use of these high aspect ratio posts, multipolar resonances, which allow for broadband operation, were ensured. The weak optical coupling property between the posts enabled a phase transformation independent from the lattice periodicity, thus resulted in a much better phase sampling and reduced optical crosstalk problem. 64

In order to realize the abovementioned improvements on the performance of the

MWIR FPAs, we used a metasurface platform based on high-index contrast dielectric meta-atoms arranged on a subwavelength periodic lattice in a low index background medium. The building blocks of metasurface are composed of an array of amorphous silicon posts of different diameters which are resting on a sapphire substrate as shown in Fig. B-1 (a). By using these all-dielectric meta-atoms, the 65 phase shift profile of the metasurface lens arrays were designed, and the object signal and the noise during the detection of small objects with a low SNR was optimized to enhance the performance of the FPA device. The object signal was increased by maximizing the focused optical energy in the central pixel of the pixel array via metasurface lens array. By increasing the f-number and decreasing the optical crosstalk, background noise and optical energy leakage to the adjacent pixels were minimized. We adapted a similar figure-of-merit (FoM) that was proposed in earlier studies [18]. So, FoM is defined as ratio of the product of the f- number and the focusing efficiency to the optical crosstalk. Focusing efficiency and optical crosstalk performance of high contrast dielectric metasurface lens array- based FPAs were also compared to the earlier methods which are composed of refractive microlens arrays and conventional MWIR FPAs. More than 85% focusing efficiency with a sufficiently reduced optical crosstalk performance (≤

2.8%) was achieved by high contrast dielectric metasurface lens arrays which outperform all previous MWIR FPA schemes. The designed high contrast dielectric metasurface FPAs achieved a FoM of 91, which is superior to all other forms of previously reported FPAs. In the next section, we present the design parameters of MWIR FPA and numerical results.

B.2. Design and Results

B.2.1. Design of the building blocks of metasurface lens

In order to design the constituent elements of the metalens arrays, transmission and resonance characteristics of the Si posts were analyzed. An array of a-Si posts of different diameters are arranged on a square lattice resting on a sapphire substrate as depicted in Fig. B-1 (a). Each of the posts behave as a truncated waveguide with circular cross section supporting low quality factor Fabry-Pérot resonances

[6,26,27]. The circular cross section of the posts results in a polarization- independent metasurface structure. Due to the high refractive index contrast between the posts and their surroundings, the posts have a weak optical coupling between them [6]. The weak optical coupling leads to an important consequence such that the phase coverage mainly depends on the diameter of posts and not on the distance between them. This allows the same local phase shift almost independent of the periodicity of the lattice by which metasurfaces are arranged.

Fig. B-1 (b) and (c) show the simulated transmittance and phase of the transmission coefficient for a periodic square lattice posts as functions of lattice constant and post diameter. The simulated transmittance and the phase of the amplitude transmission coefficient as only a function of the post diameter is also shown in

Fig. B-1 (d). The weak dependence of the transmission of the post array to different lattice constant, which can be clearly seen in Fig. B-1 (b) and (c), are another proof for the weak coupling between the posts. For modelling and simulating these Si posts, full-wave simulations were performed using the Lumerical finite-difference 67 time-domain (FDTD) solver. For the MWIR band (3-to-5 µm) FPA design, wavelength of 3.2 µm, post height of 1.92 µm, lattice constant of 1.5 µm are considered. The simulation assumes periodic boundary conditions along the axial directions and perfectly matched layers (PML) boundary conditions were utilized in the normal directions to Si posts. This reduces the computational resources compared to the simulations of scattering from a single post. The refractive index data of a-Si was utilized from the data of Palik [28], and assumed as 3.435. The refractive index of sapphire was assumed as 1.70. Post height must be chosen such that the entire 0-2π phase range is covered by changing the post width, while keeping high transmission values. The lattice constant should be selected such that the lattice is subwavelength and non-diffracting. It should also satisfy Nyquist sampling criterion for all f-number values of the metalenses. Fig. B-1 (d) shows the plot of one-to-one mapping between transmission phase and post diameters. To keep the transmission high, and to satisfy one-to-one relationship between the phase and post diameters, the diameter values corresponding to the sharp resonance were excluded from the design. Thus, the intensity transmission is kept above 91% while

0 to 2π phase range is covered by changing the post diameters. We also note that in contrast to Huygens’ metasurfaces where only the electric and dipole resonances used, the resonant modes of the posts contain higher-order electric and magnetic multipoles. Although, Huygens’ metasurfaces-based lens arrays studied by using

Si nanodisks before produced promising results in a narrow spectral band, they performed very poor in other wavelength values very close to the design wavelength [18]. In addition, due to undersampling of the required metalens phase 68 profile, they resulted in higher optical crosstalk than the metallic metasurfaces.

Furthermore, the unitcells composed of Si nanodisks transmitted with efficiency values from 65% to a maximum of 90%. Note that all transmission values in our design by using higher aspect-ratio nano-pillars were above 91%, thus this resulted in a higher focusing efficiency than Huygens’ metasurfaces and metallic metasurfaces.

B.3. Focal plane array via metasurface lens array

The required, ideal phase profile of a metalens can be given in Eq. (1). Similar design methodology from the earlier metasurface-based lens studies [18] was used.

2휋 휑(푥, 푦) = (푓 − √푓2 + 푥2 + 푦2 ). (1) 휆

In order to reduce the optical crosstalk while keeping the f-number (푓⁄#) as large as possible (such as 1.5), only the limited range of focal length values that provide a phase shift of minimum π radians between the edge and the center of a metalens in the lens array were utilized in the design. Therefore, our dielectric metasurface- based MWIR FPAs had focal lengths varying from 30 to 90 µm with aperture sizes varying from 20 to 30 µm considering the value of focal length. The required lens phase profile from Eq. (1) was realized by sampling it at the lattice sites by placing a scatterer from the periodic posts that most closely impart the desired phase change in transmission mode (see Fig. B- 2 (a)). 69

Fig. B- 2. (a) Sampled phase profile of a single metalens in the metalens array having a pitch length of 24 µm by arranging a-Si posts with unit cell size of 1.5 µm at the lattice sites. (b) Realization of metalens array by a-Si posts. (c) Focused light intensity distribution at the far-field for a wavelength of 3.2 µm with either TE or TM polarized light. (d) Focused light intensity distribution at the far- field for another wavelength of 4 µm, which is different from the design wavelength.

Next, metasurface lens array was realized with a discretized phase profile (see Fig.

B- 2 (b)), and full-wave simulations were performed. Since, lens array is periodic, periodic boundary conditions were used along the axial directions, and the perfectly matched layers (PML) were used in the normal directions to the lenses. In Fig. B-

2 (c), focused light intensity distribution at the far-field, scattered from the central metalens of the optimized design is shown. The operating wavelength is 3.2 µm.

Comparing to the metallic metasurfaces that require the cross-polarization scheme to realize focusing, high contrast dielectric metasurface can focus both 70 polarizations of light much more efficiently. As seen in Fig. B- 2 (d), when source wavelength was changed to 4 µm, the focusing performance of the high contrast metasurface lens array outperformed the Huygens’ or Mie-scattering-based metasurfaces, which are inherently narrowband. Focused light intensity distribution at the far-field for different adjacent pixels of the optimized metalens array is also depicted in Fig. B-3 (a) and (b) at two different wavelengths of light. Furthermore,

Fig. B-3 (c) and (d) show the cross-section of the focused light intensity and 3D view of the focused light intensity for the 3x3 metalens array at the focal plane, respectively. We should note that there is a sharp decay of intensity profile at each focal point. Besides, the peak intensity values are uniformly distributed at the array plane.

Optical crosstalk of the FPA is related to the point-spread-function (PSF) [14].

Thus, optical crosstalk analysis of the proposed arrays can be realized by calculating the ratio of the corresponding PSF distributions inside the neighbor and the central pixels as defined by Eq. (2) which is given below [18]:

∬ 푃푆퐹(푥,푦)푑푥푑푦 퐴푛푒𝑖𝑔ℎ푏표푢푟 푂푝푡푖푐푎푙 퐶푟표푠푠푡푎푙푘 = 100 × (2) ∬ 푃푆퐹(푥,푦)푑푥푑푦 퐴푐푒푛푡푟푎푙

Fig. B-3. (a) Far-field intensity distribution of light focused by different pixels of the optimized metalens array design at a wavelength of 3.2 µm. (b) Far-field intensity distribution of light focused by different pixels of the optimized metalens array design at a wavelength of 4 µm. (c) and (d) show the cross-section of the focused light intensity and 3D view of the focused light intensity for the 3x3 metalens array at the focal plane, respectively.

Optical crosstalk performances of the earlier designs were also compared to the proposed design here. Note that metallic metasurfaces have the lowest optical crosstalk (≤ 2%) for the f-numbers greater than 1.50. Since, they have the smallest unit cell dimensions and, thus, the best sampling of the required phase profile. Mie- scattering-type, or Huygens’ metasurfaces-based dielectric metalenses have been shown to provide lower optical crosstalk (≤ 3%) than the conventional MWIR FPAs and the refractive microlenses; however, their optical crosstalk performance is worse than the metallic metasurfaces due to larger unit cell dimensions and, thus, 72 poor sampling of the required phase profile. In contrast, the designed high index contrast dielectric metasurfaces gave rise to optical crosstalk value (≤ 2.8%), which is better than Mie-type dielectric, but worse than metallic metasurfaces due to larger unit cell size again. High aspect ratio a-Si posts with smaller unit cell size also require a challenging fabrication process. If we compare focusing efficiency results, high contrast dielectric metasurfaces (≥85%) outperform the Mie-type dielectric metasurfaces (≥80%), and metallic metasurfaces (≤11%), therefore offer better practical implementation for metasurface lens arrays. Improved focusing efficiency can be attributed to the lack of polarization sensitivity and the elimination of the intrinsic absorption loss of the metallic metasurfaces.

Efficient detection of objects with low SNR requires an optical system with sufficient photon collection capability. Therefore, focusing efficiency of the metasurface lens arrays should be designed as high as possible. Furthermore, the required incident photons should not be collected by the wrong adjacent pixels to minimize the optical crosstalk, and thereby improve the SNR. In the design of conventional MWIR FPAs with a relatively lower optical crosstalk, smaller f- numbers are used; however this lead to significant optical aberrations [14].

Considering the effect of all the aforementioned parameters, the overall FoM should be proportional to the f-number and the focusing efficiency while inversely proportional to the optical crosstalk [18]. Thus, a FoM can be defined as the following:

푓/# 퐹표푀 = [ ] × 휉 . (3) 푂푝푡푖푐푎푙 퐶푟표푠푠푡푎푙푘 푒푓푓푖푐푖푒푛푐푦 73

Our dielectric metasurfaces were designed and optimized with a target of achieving the maxima of this FoM given by Eq. (3). Finally, FoM values of different metasurface-based MWIR FPAs are compared quantitatively as in Fig. B-4.

Fig. B-4. FoM comparisons for different types of MWIR-FPA, illustrating the significantly improved performance of the proposed (waveguide-based) metasurface lensed FPAs (cyan pentagram marker) over the conventional FPAs (blue diamond marker degraded by higher optical crosstalk), the refractive microlensed FPAs (red circle marker degraded by diffraction noise), the metallic metasurface lensed FPAs (yellow square marker degraded by very poor transmission and focusing efficiency), Mie-type dielectric metasurface lensed FPAs (green hexagram marker suffering from higher optical crosstalk, lower focusing efficiency and also narrowband operation).

Refractive microlens arrays do not improve optical crosstalk and the f-number due to the emergence of the first order diffraction spots and smaller f-numbers required for reduced crosstalk. Even if metallic metasurfaces have significantly reduced optical crosstalk, MWIR FPAs with metallic metasurfaces have the worst FoM due to their very poor focusing efficiency. As it is shown in Fig. B-4, our proposed high index contrast dielectric metasurfaces have the highest FoM due to the achieved low optical crosstalk values with higher f-numbers, which cannot be possible with 74 refractive microlens array and conventional MWIR FPAs. Remarkably, the increase of f-number also means that the imaging system can be made simple and lightweight. Likewise, significant focusing efficiency improvement comparing to metallic metasurfaces allow our proposed design to be superior as well. Note that, since the emphasis of our study here was on optical aspects, a detailed electrical device model analysis of the specific FPA detector performance may be carried out as the future study by incorporating our metasurface lens arrays. Effects of the geometrical parameters, such as lens array spacing, individual lens size, array size, wavelength etc., should be also further investigated. The proposed metasurface structures can be fabricated at low cost using existing a single step conventional

UV binary lithography. There might be some degraded FoM performance in experimental implementation of MWIR FPAs due to possible fabrication defects.

a) b)

(b) phase of the transmission coefficient variation as a function of a-Si post diameter (D) and angle of incidence of the illuminating beam.

In addition to the reduced optical crosstalk and high focusing efficiency, other factors affecting the imaging characteristics of metalens arrays such as wide-angle tolerance is also investigated. Besides, it is known that conventional microlens array-based FPA allows some tolerance on angle of incidence of chief ray from 0 to 10 degrees to allow optical designer to use quasi-telecentric design. Thus, variation of intensity transmission and transmission phase characteristics of Si meta-cells versus variation of the angle of incidence (AOI) of the illuminating light and post diameter is analyzed, as shown in Fig. B-5. Clearly, transmission phase does not change with the variation of the AOI. However, intensity transmission gradually decreases for the angles from 0 to 10 degrees, and low transmission resonance dip occurs around post diameter of 0.9 m for all incidence angles, which can be excluded from the design. The gradual decrease is mainly due to the total internal reflection (TIR) losses at the sapphire/air interfaces. Note that for the incidence angles from 0-10 degrees, no significant change occurred in the transmission coefficient properties. This obviously gives an idea about how much the focusing performance of each metalens is affected by angle of incidence from

0-10 degrees or larger angles. It is also known that microlenses with higher f- number will have less aberration problem at larger field of view, and our metalenses already demonstrate better performance at larger f-numbers with especially no first- order diffraction orders causing crosstalk. On the other hand, for all types of microlens arrays, FoM will go down for larger chief ray incidence angles or oblique chief rays, since optical crosstalk will increase, optical efficiency will go down for 76 the same f-number design [15]. However, comparing to conventional diffractive and refractive microlens arrays possessing previously mentioned drawbacks, it is obvious that we will get better FoM performance with our metalens arrays. This needs to be probably evaluated more rigorously or quantitatively in a new research study.

B.4. Conclusion

In conclusion, we have proposed and numerically demonstrated broadband, high- efficient and low-crosstalk dielectric metasurface lens arrayed MWIR FPAs by exploiting the unique properties of metasurfaces. Metasurface lens array can be used to concentrate light into the light-sensitive areas of a detector array. Focusing efficiency and optical crosstalk performances of the designs were analyzed by implementing full-wave numerical simulations, and achieved results were compared with the performance of metalens arrays relying on metallic metasurfaces, Huygens’ metasurfaces, refractive microlenses, and conventional

FPAs. We obtained high focusing efficiency (≥85%) while achieving the best FoM value of 91 outperforming the FoM value of all other MWIR FPA types, and keeping the optical crosstalk at a level of 2.8%. More importantly, designed metalenses perform much better than refractive microlens arrays without requiring any mesa-isolation techniques, which are generally required for smaller pixel size

FPAs. These metasurfaces also pave the way for high spatial resolution, smaller pixel size and high SNR FPAs to achieve target detection and recognition of objects. 77

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APPENDIX C: TUNABLE WIDE ANGLE BEAM-STEERING

VIA METASURFACES INFILTRATED WITH NEMATIC

LIQUID CRYSTALS

C.1. Introduction

Intensive researches in the area of metasurfaces have provided a new insight to obtain flat and compact optical systems. In this appendix, highly efficient tunable beam steering effect in transmission mode is achieved at wavelength λ=550nm using nematic liquid crystals (LCs) infiltrated into double sided metasurfaces.

Using the electro-optical feature of LCs, the phase profile of the metasurfaces is controlled and thus, the transmitted beam is deflected within the range from -15˚ to

15˚ steering angles. Transparent dielectric materials are used in the designed structure that provides highly efficient beam-steering; the corresponding transmission efficiency is above 83% in the visible spectrum, which is another superiority of the proposed hybrid tunable structure over present plasmonic/metamaterial approaches. The designed metasurface still preserves its beam deflection property covering the visible spectrum and hence, such hybrid structure can be implemented for broadband electro-optically controllable beam steering applications.

Metasurfaces are ultra-thin planar optical components and yet, they still perform very well at manipulating the phase, amplitude and polarization of the incident light with subwavelength spatial resolution; light focusing metalenses [1–3], holograms

[4,5], beam steering [6], and polarization manipulation devices [7] have been demonstrated by using metasurfaces. One of the most attractive property of metasurfaces is the capability of engineering wavefront phase profile by spatially arranging the nano-scattering elements with a subwavelength periodicity and 83 different dimensions [8,9]. Due to high absorption losses of metallic metasurfaces, high-aspect ratio silicon nano-pillars were considered as the common material choice in the designs at short wave infrared and near infrared regions of the electromagnetic spectrum [2]. To get high transmission and to enable 0-2π phase shift on the transmitted beam at the visible region of the spectrum, titanium- dioxide-based designs have been proposed [1,3]. The two-dimensional nature and subwavelength thickness of metasurfaces make them a great candidate for reconfigurable and tunable optical elements. In order to achieve reconfigurable metasurface properties, different approaches have already been studied; researchers have considered mechanically tunable dielectric metasurfaces based on elastic substrates [10], refractive index tuning via thermo-optic effects [11], phase change materials [12], and electrically driven carrier accumulation [13,14]. Electrically tunable liquid crystals (LC) have also been used to demonstrate tunable focusing lenses [15,16], and tunable all-dielectric metasurfaces [17]. However, most of the metasurface-related studies with LCs were either at infrared spectrum or they were based on tuning the background index of the resonators.

Apart from above approaches, a novel hybrid structure is offered in this study, in which case the tunability feature relies on the electrical control of the combined meta-elements integrated with liquid crystals. The proposed tunable metalens structure is composed of hexagonal lattice SiO2 [18] nanoholes infiltrated with nematic LCs. By the help of electro-optical property of anisotropic LCs, the designed metasurface structure provides tunable beam steering when the applied voltage is altered in high temperature. Nematic LCs possesses two refractive 84 indices; namely, ordinary (no) and extraordinary (ne) refractive indices and the effective index of LCs could be arranged in accordance with their molecular orientations, θLC. By the help of effective refractive index change created using molecular LC orientations, corresponding phase accumulation of output waves can be tuned and thus, the desired phase equation becomes controllable.

The studied LC molecules are phenylacetylene, whose ordinary and extraordinary refractive indices equals no=1.628 and ne=2.105 at 550 nm wavelength [19]. In order to obtain the desired phase shift, we selected the LCs having a high birefringence change (i.e.훥푛 = 푛푒 − 푛표). The studied LCs have positive dielectric anisotropy. Therefore, LCs can be used like phase shifter unit cell for incident light.

The effective index of LCs for transverse magnetic (TM) polarization is given by the following equation [20]:

22 nneo nLC  2 2 2 (1) nneocos(LC ) sin (LC )

The relationship between θLC and the control voltage V is stated as the following:

 0, if VV 0  LC   1 VV (2) 2tan exp( c ), if VV   0  2 V0

Where Vc is the critical voltage and V0 is the constant parameter.

Fig. C- 1. (a) Schematic of a tunable beam steering metasurface. The molecular orientations of LCs are given as an inset. (b) A nano cell arranged through hexagonal lattice and top view of metalens.

LCs are infiltrated into the nano holes made of glass (SiO2). Nano cell dimension is set to be a=250nm and height is h=1.8µm. The structure length is L=20μm and width is W=3μm (c) Calculated phase profile for varying nano cell diameter at λ=550nm. Corresponding phase shifts of the nano-cells are indicated in the graph when the radius of the nanoholes ranges between 50nm to

110 nm. (d) Calculated phase profile for varying LCs' molecular orientation from (θLC =0°) to (θLC =90°) at green wavelength (λ=550nm). Note that nano-cell diameter equals d=110nm in this case.

The studied structure is composed of nanoholes on a glass substrate infiltrated with the nematic LCs. Such type of dielectric metasurfaces with high-aspect ratios can be fabricated via atomic-layer deposition technique [21]. Moreover, LCs' infiltration could simply be achieved integrating the metasurface with microfluidic channels based on soft lithography with polydimethylsiloxane compounds [22].

The radius of LCs' cells is varied appropriately to provide phase change between 0-

2π, see Fig. C- 1. The height of LCs' unit cell is selected as h=1.8µm to capture phase between 0-2π for 550nm wavelength. As shown in Fig. C- 1 (a), the required beam steering is accomplished by applying external voltage to the two metasurfaces 86 on the top and bottom of the glass substrate. The drilled nanoholes of the metasurfaces form hexagonal lattice and corresponding lattice constant is 250nm,

2 which is lower than maximum lattice constant (dmax = = 301푛푚) √3neff,LCmax

(Fig. C- 1 (b)). The LCs' unit cells behave as short waveguides due to their relatively high height which allows the incident wave to propagate directly through the cells with high diffractive efficiency [3]. The incoming light is delivered in a controlled manner at a desired angle in the metasurface with phase gradient dφ∕dx at the interface between two media. The phase profile of metasurface for beam steering is given by:

2 (xx ) sin( ) (3)  where ϕ is the deflection angle, λ is the wavelength of the incident beam in the free space.

In this study, double metasurface layers are placed at the top and bottom of the glass substrate: The phase profile of bottom surface φ(x) is created by Eq. 3; however, the phase profile of the top surface is obtained by 2π-φ(x). Corresponding positions of drilled holes on metasurfaces are formed according to the required phase profiles, see the xz- cross-sectional view of the upper metasurface in Fig. C- 1 (b). As can be seen from Fig. C- 1 (a), an external voltage is applied separately from indium tin oxide (ITO) layers, which generates electric field in in xz- plane. Based on the voltage excitation, the infiltrated nematic LC molecules are oriented in xz- plane so that the effective indices as well as the phase of LCs' unit cells change 87 accordingly, see the inset of Fig. C- 1 (a). It is important to note that such hybrid structures requires low-driven voltage input, which can be considered another superiority of the proposed device [23]. The phase of each LCs' unit cell for varying radius and LCs' rotation angle is calculated via finite difference time domain

(FDTD) analyses. Note that full 3D FDTD simulations are performed using the commercial LUMERICAL software package [24]. Fig. C- 1 (c) and Fig. C- 1 (d) show the phase profile as functions of hole diameter and LC rotation angle, respectively. As can be understood from the figures, increasing the radius as well as the LC rotation angle of the unit cells provides a linear increase in the accumulated phase. Therefore, without changing the dimensions of LCs' unit cells the intended phase accumulation can be controlled by only varying the applied voltage of top and bottom metasurfaces, which is the working principal of the studied tunable beam steering effect.

Fig. C- 2. (a) Visualization of controllable beam steering effect depending on the LCs' molecular orientations at up/down layers. (b) Corresponding phase profile when the LCs' rotation angles are adjusted to be (left) {휃푢푝, 휃푑표푤푛} = {0°, 90°}, (center) {휃푢푝, 휃푑표푤푛} = {90°, 90°} and

(right) {휃푢푝, 휃푑표푤푛} = {90°, 0°}.

Fig. C- 3. Calculated deflection angles in terms of LCs' orientations at up/down layers are superimposed as a phase map. 89

Fig. C- 2 (a) is prepared to visualize tunable beam steering effect of the studied hybrid structure based on different voltage excitations at up/down layers. The phase profile shown in Fig. C- 2 (b), under the plane-wave illuminations the proposed LC infiltrated all-dielectric metasurface is able to steer the transmitted beam with

15˚(+15˚) deflection angle to be up=0˚ and down=90˚ (up=90˚ and down=0˚). On the other hand, while keeping the LCs' rotation angles at the two layers to be the same, the incident beam propagates in vertically along y-direction. Beam steering angle variation of the output beam is investigated in detail depending on the LCs' orientations at top/down layer and the calculations are superimposed as a phase map in Fig. C- 3. The following items could be inferred from the map: when the

LC rotation angles are the same at both layers, then, the output beam propagates directly, i.e. φ=0°. Fixing only the applied voltage at the upper (down) layer but increasing that at the down (upper) layer provides beam steering toward clockwise

(counter-clockwise) direction. In keeping with FDTD results in Fig. C- 2, a steering angle of φ=+15˚ (-15˚) is obtained when the LC rotation angles are arranged to be

up=0˚ and down=90˚ (up=90˚ and down=0˚). 90

Fig. C- 4. (a) Beam steering scenario for three wavelengths while only changing molecular orientation of the LCs on the bottom surface and the upper surfaces has the molecular orientation of

up=0˚. (b) The beam steering angle is calculated at fixed wavelengths while only changing molecular orientation of the LCs on the upper surface and the bottom surface has the molecular orientation of down=0˚.

Fig. C- 4 is prepared to investigate the effect of LCs' dispersive properties on the targeted tunable beam steering effect and to show how broadband the proposed hybrid structure can operate in the visible spectrum. Note that the temperature dependences of LCs' parameters are taken into consideration. For that purpose, the 91 output beam steering angle is calculated at fixed wavelengths for only varying LC orientations either at the upper layer (Fig. C- 4 (a)) or at the bottom layer (Fig. C-

4 (b)) but keeping the other layer's LC angles to be 0˚. The figure confirms that the maximum tunability in beam steering effect (φ=±15˚) is obtained at 550 nm wavelength and a reasonable tuning is still obtained for 450 nm (φ=±11˚ beam steering). Nevertheless, at longer wavelengths near infrared (around 650 nm), the calculated beam steering is φ=±6˚. That observation indicates that broadband beam steering effect via the proposed hybrid structure is feasible especially at green and blue wavelengths.

It is crucial to note that high intrinsic optical and conduction losses may arise if the constituent materials were selected to be either silicon or plasmonic metals. Instead, using transparent dielectric materials provides highly efficient beam-steering; in our case, the corresponding transmission efficiency is above 83% in the visible spectrum, which is another superiority of the proposed hybrid tunable structure over the alternative approaches.

C.2. Conclusion

A double metasurfaces composed of hexagonal lattice nanoholes with nematic LCs' infiltration is proposed for highly efficient and broadband beam steering application. By the help of electro-optical characteristic of LCs, the beam deflection can be controlled from φ=-15° to φ=+15° deflection angles by simply varying the low-voltage excitations of the top and bottom metasurfaces. The proposed hybrid 92 metasurface structure is flat and thin so that it is free from spherical aberrations.

Furthermore, the designed LC infiltrated structure may operate from ultraviolet to terahertz regimes by scaling the corresponding lattice constant and selecting appropriate materials. The proposed system may work in high temperature condition and could be used for high energy laser applications.

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CHAPTER 2: CONCLUSION AND OUTLOOK

CONCLUSION AND OUTLOOK

Metalenses based-on all-dielectric metasurfaces have been highlighting the potential of planar technology and have proven their capability to replace their conventional counterparts. Their straightforward CMOS-compatible fabrication methods, significant reduction in thickness, elimination of post-fabrication alignment and assembly steps and easier packaging in camera modules can be given as their important features proving their potential. Despite significant progress in metalens design and performance, there are still many areas to be explored and improved. Compensation of chromatic dispersion is a challenging task, and demonstration of achromatic transmissive lenses with relatively large NAs and high focusing efficiency (>90%) operating in the visible spectrum would be a great breakthrough for the camera industry.

In addition to isolated metalenses, metalens arrays proposed in this work are of great importance for increasing the fill factor and reducing the pixel pitch size of imaging sensors. As the future step of the demonstrated metalens array study here, comprehensive device simulations should be carried out to analyze their effect on the imaging performance of FPAs, CCD and CMOS imaging sensors. Important device parameters such as MTF, optical crosstalk, optical efficiency should be evaluated for different operation conditions, and metalens array geometries.

Moreover, topology optimized multilayered metasurface lens geometries, which focus light into the same focal spot regardless of the angle of incidence, are topics of high interest for current and future research along with metalenses with voltage controlled magnification, focal length and aberrations. 100

On the other hand, modelling of the complex configurations of metasurfaces is not an easy task due to the strong coupling among elements, large number of subwavelength resonators, and non-periodic arrays. Several numerical techniques can be used as the key tools for designing, optimizing and evaluating the metasurfaces. In this work, FDTD is frequently used as a robust and efficient method for characterizing the periodic, subwavelength structures and small-array metasurfaces over a wide frequency band; however, for optimizing larger metasurface arrays integrated to complicated optical systems, faster and more efficient computational tools are required. There is a new emerging interest for creating interface between ray tracing software packages and full-wave simulations tools so that meta-optics can be optimized along with other optical elements. Thus, with possible technological advances in near future, an enhanced use of these numerical techniques will significantly keep helping to reveal the physics behind the fascinating phenomena and will dramatically accelerate the design and characterization processes for various metasurfaces.

Active or tunable metasurfaces allowing for advanced and dynamic optical manipulations are obviously one of the most interesting directions for current and future research. Although the LC infiltrated metasurface work in Appendix C is a great attempt towards the tunability at visible spectrum, much more efficient and functional materials beyond LCs can be incorporated into the metasurface designs whose optical properties are tunable through electric, magnetic, optical, thermal, chemical and mechanical excitations. 101

To summarize, the functionalities of metasurfaces are influenced by the simultaneous contribution of constitutive materials and subwavelength structures.

Incorporating novel material properties and designing more efficient nanostructures will be the common method to extend the exotic properties of metasurfaces to design better state-of-the-art optical elements.