Metasurface Apertures for Wireless Power Transfer and Computational Imaging

Vinay Ramachandra Gowda

Department of Electrical and Computer Engineering Duke University

Date:

Approved:

David R. Smith, Advisor

William T. Joines

Willie J. Padilla

Aaron D. Franklin

Matthew S. Reynolds

Dissertation submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy in the Department of Electrical and Computer Engineering in the Graduate School of Duke University 2019 Abstract Metasurface Apertures for Wireless Power Transfer and Computational Imaging

Vinay Ramachandra Gowda

Department of Electrical and Computer Engineering Duke University

Date:

Approved:

David R. Smith, Advisor

William T. Joines

Willie J. Padilla

Aaron D. Franklin

Matthew S. Reynolds

An abstract of a dissertation submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy in the Department of Electrical and Computer Engineering in the Graduate School of Duke University 2019 Copyright c 2019 by Vinay Ramachandra Gowda All rights reserved Abstract

Metasurface apertures provide an alternative approach to the very commonly used phased arrays or electronic scanned antennas (ESA) for wireless power transfer (WPT) and imaging applications. Array antennas use radiating elements which are often spaced at half-wavelength and uses active phase-shifter at each module to control the phase. However, in a metasurface antenna, the required phase is obtained from the sampled reference wave which propagates over the aperture providing an advance phase to each radiating elements. Metasurface apertures have very low manufacturing costs, planar form factor making them a suitable candidate for applications involving beamforming and wavefront shaping. The thesis is divided mainly into two parts consisting of designing metasurface apertures for WPT applications and computational imaging purposes. In the first part, the proposed WPT system operating by focusing fields in the Fresnel region is presented with two proof of concept demonstrations. The first demonstration includes patch array antennas as the transmit and receive aperture and a half-wave rectifier to convert the RF to DC. The frequency of operation is 5.8 GHz (C-band) and the design of the patch array antenna is tedious and not suitable for a dynamic aperture which is possible by making use of metasurface apertures. The second demonstration consists of a metasurface aperture which uses a holographic technique to achieve focusing of microwaves at a particular focus distance for the transmit aperture. The receiving aperture is a metamaterial absorber which is connected to a

iv rectifying circuit to harvest the power, thereby completing the WPT system. A LED connected as the load is illuminated which indicates the basic functionality of the WPT system. The RF-DC power transfer eﬃciency is in good agreement between simulations and experiments. The proposed system consisting of metasurfaces for both the transmit (focused aperture) and receive aperture (absorber) operates at 20 GHz (in K-band) has not been demonstrated in the literature and is a suitable candidate for higher frequencies (W-Band). The second part consists of designing metasurface apertures demonstrating monostatic and bi-static microwave imaging systems where the metasurface apertures are frequency-diverse and operating at K-band frequencies (18-26.5 GHz). The metasurface apertures consist of radiating irises distributed over the sub-apertures in a periodic pattern. This frequency-diverse aperture produces distinct radiation patterns as a function of frequency that encode scene information onto a set of measurements; images are subsequently reconstructed using computational imaging approaches. In the monostatic case, the metasurface aperture is used as the transit aperture and 4 open-ended waveguides are used as receive aperture. In the case of bistatic case, both the transmit and receive apertures are metasurface apertures which result in increased mode diversity resulting in improved image reconstructions.

v Contents

Abstract iv

List of Tables ix

List of Figuresx

List of Abbreviations and Symbols xiv

Acknowledgements xvi

1 Introduction1

1.1 Dissertation overview...... 1

1.2 Wireless Power Transfer...... 4

1.2.1 Applications of WPT in Near Field...... 6

1.2.2 Applications of WPT in Far Field...... 7

1.2.3 WPT in the Fresnel Zone (Radiative Near ﬁeld)...... 9

1.3 Computational Imaging...... 11

2 An Analysis of a Fresnel Zone WPT system 16

2.1 Introduction...... 16

2.2 Derivation of Focal spot using Gaussian Optics...... 21

2.3 Practical Implementations...... 28

2.3.1 Aperture Architecture...... 28

2.3.2 Holographic Aperture Design...... 29

2.3.3 Phase and Amplitude Constrained Holograms...... 33

vi 2.3.4 Lorentzian Constrained Holograms...... 40

2.4 Schematic of a Fresnel Zone WPT system...... 43

3 System block design and experiments of a Fresnel zone WPT system 45

3.1 Transmitter - Focused Metasurface Aperture Design and Experiments 45

3.1.1 Dual Layer Metasurface Hologram Design...... 50

3.1.1.1 Uniform Focused Aperture...... 50

3.1.2 Tapered Focused Aperture for Lower Sidelobes...... 55

3.1.3 Uniform Eﬃcient Focused Aperture for Lower Sidelobes and Higher Radiation Eﬃciency...... 61

3.1.3.1 Role of the Inward Traveling Wave...... 65

3.1.3.2 Full-Wave simulation results...... 69

3.1.3.3 Low-loss substrate...... 70

3.1.3.4 Experiments...... 75

3.2 Receiver - Metamaterial absorber and Rectiﬁer Design and Experiments 77

3.2.1 Metamaterial Absorber-inspired Antenna Design...... 78

3.2.2 Rectiﬁer Design at K-Band frequencies...... 82

3.2.3 Experimental Result of the Absorber and Rectiﬁer design... 85

4 Practical Implementation of the Fresnel Zone WPT System 88

4.1 Using Focused Patch Array Antennas...... 88

4.2 Using Focused Metasurface Aperture...... 98

5 Computational Imaging using Printed Cavities 102

5.1 Introduction to Computational Imaging...... 102

5.2 Design and optimization of Radiating Irises...... 107

5.3 Imaging Conﬁgurations - Panel to Probe and Panel to Panel..... 111

5.4 Panel to Panel (Bistatic)...... 114

vii 5.4.1 Aperture Design...... 114

5.4.2 Experimental results...... 118

6 Conclusion 122

7 Appendix 126

7.1 Coverage Area Proof...... 126

7.2 Power Eﬃciency calculations...... 127

Bibliography 129

Biography 139

viii List of Tables

2.1 Overall efficiency of amplitude-only holograms for off-axis focusing and ratio α for different binary holograms...... 37

2.2 Overall efficiency of phase-only holograms for off-axis focusing and ratio α for different phase limited apertures...... 38

2.3 Overall eﬃciency of a metasurface for oﬀ-axis focusing and α for different aperture distributions...... 42

3.1 Spot size comparison between Gaussian Optics, CST and Experiments for tapered and not-tapered apertures...... 59

3.2 Power radiated in Co-Pol and Cross-Pol, reported as percentage of incident Power on the corresponding element...... 67

3.3 Design parameters pertaining to SLLs condition, (3.9), for diﬀerent substrates...... 71

3.4 Simulated eﬃciencies (aperture, focal and total), SLL and r for different focused Apertures...... 72

3.5 Spot Size calculated using Gaussian optics formulation, CST simulations, and experiments...... 76

4.1 WPT Eﬃciency Values for ON-Axis (In comparison to No-focusing) And Oﬀ-Axis Focusing, Respectively...... 96

4.2 Measured Transmitted Threshold Power Values for LED Lighting.. 97

4.3 RF - RF eﬃciency (in %) for the Fresnel Zone WPT system..... 101

5.1 Relationship between iris diameter, Q-factor and radiation eﬃciency (0%iris sparsity)...... 109

5.2 Relationship between number of irises, Q-factor and radiation eﬃ- ciency (5mm iris diameter)...... 111

ix List of Figures

1.1 Electromagnetic ﬁelds from an antenna...... 5

1.2 Inductive WPT Applications in real life...... 7

1.3 Far-Field applications...... 8

2.1 Potential usage scenario for a Fresnel zone wireless power transfer system 21

2.2 Illustration of the eﬀective aperture considered for the analytical calculation of the beam waist for oﬀ-axis focusing...... 22

2.3 Intensity plots of a focused beam from an aperture of dimension D=1 m, at a frequency (f) of 10 GHz, plotted for diﬀerent focal lengths pz0q 25 2.4 Beam waist (in cm) as a function of f and D size, using Eq. 2.7. The shaded regions might be considered acceptable for this study...... 26

2.5 Transfer eﬃciency assuming the Rx (a) placed at the focus, as a function of D{w0 (b) of size w0, where (D{w0=1) as a function of z{z0 .. 27 2.6 Cross range 2D plots for both on- and oﬀ-axis case (a) Phase distribution at the aperture plane (b) Focused spots (zoomed in) at z0... 30

2.7 (a) Analytical and numerical w0 as a function of oﬀset angle θ for z0 = 5m. (b) Power transfer eﬃciency as a function of θ (DRx = 3 cm). 32

2.8 Illustrative coverage plot of w0 as a function of θ, z0 in a room (5m x 5m, top view) (a) Analytical (b) Numerical using simulations..... 33

˝ 2.9 Intensity plot for an amplitude holographic lens (z0 at θ = 15 ). (a) y-z plane with higher orders (b) x-y plane with 0th order at the center. 36

2.10 Intensity plot (dB) in the y-z and x-y planes for a phase holographic ˝ lens (z0 at θ = 15 ) for Apertures (a) D (b) E (c) F (d) G...... 39 2.11 Intensity plot of metasurface aperture (aperture H in Table 2.3). (a) y-z plane with higher orders (b) x-y plane with 0th order at the center. 43

x 2.12 Schematic of a WPT system...... 44

3.1 Illustration of the focused metasurface aperture a) cross-sectional view b) Side view...... 51

3.2 a) Coupling distribution for the aperture with and without taper b) Power radiated for diﬀerent slot dimension (inset: unit cell schematic). 55

3.3 Assembled fabricated sample with copper tape covering the edges (a) on-axis untapered (b) tapered aperture...... 56

2 3.4 Normalized |E| patterns at z0 =10cm for tapered and uptapered designs respectively: analytical (a, d), CST (b, e), experimental (c, f).. 58

3.5 Normalized 1-D electric ﬁeld intensity patterns of untapered and tapered metasurface apertures (a) Cross-range (b) Range...... 59

3.6 Slot arrangement on the aperture a) previous design b) current design 64

3.7 Layer by layer illustration of the Holographic Metasurface aperture used as the transmitter...... 65

3.8 Simulation setup for calculating power radiated by different elements at two distinct locations: φ “ 0˝, φ “ 90˝ (Slot pair used for illustration). 66 3.9 Normalized focal patterns of an aperture from CST simulations with an r “ 4. SLL condition given by Eq. 3.9 (a) not satisfied. (b) satisfied. 70

3.10 2-D Normalized |E|2 Simulated (a) Co-Pol (b) Cross Pol, Experimen- tal (c) Co-Pol (d) Cross Pol. e) 1-D for 10 cm (bold) 20 cm (dash).. 74

3.11 a) Top layer b) Middle layer c) Bottom layer of a focusing metasurface aperture (D “ 10 cm) d) assembled fabricated aperture (D “ 20 cm). 76 3.12 Electric ﬁeld along the propagation direction a) Patch array b) Ab- sorber...... 79

3.13 Unit Cell...... 80

3.14 Unit cell properties as a function of f in GHz a) Absorption, Reﬂection and Transmission plots b) Power across load, Metal and Dielectrics.. 81

3.15 Layer by Layer illustration of the Metamaterial inspired absorber design 82

3.16 Schematic of the rectiﬁer circuit...... 83

3.17 a) S11 of the rectiﬁer circuit in ADS b) VLoad varied a s function of Input power...... 84

xi 3.18 Top and bottom layer of the Metamaterial Absorber...... 85

3.19 CST and experimental S11 of the Metamaterial Absorber...... 86 3.20 Fabricated Rectiﬁer Sample...... 86

4.1 Patch array antennas (a) 8x8 Tx array (b) 4x4 Rx array (DTX =21.7 cm, DRX =16 cm)...... 89 4.2 1-D plot of the simulated (dotted) and measured (solid) normalized electric ﬁeld magnitude plots at the focal plane...... 91

4.3 Half-Wave Rectiﬁer (HWR) (a) schematic (b) microstrip implementation...... 92

4.4 Simulated (dashed) and measured (solid) |S11| (dB) patterns for Tx and Rx antennas, and HWR...... 94

4.5 Simulated normalized |E|2 patterns in a transparent fashion to show the Tx antenna in the background (a) on-axis focus (b) oﬀ-axis focus. 95

4.6 Fresnel zone WPT system (a) experimental set-up for received power measurement (b) LED powered using the oﬀ-axis conﬁguration at z=40 cm...... 96

4.7 Experimental schematic of the proposed Fresnel-zone WPT system. 99

4.8 Experimental setup showing the working WPT setup with the LED turned on...... 101

5.1 Cavity imaging system - Tx (L=20 cm), Rx (L=10 cm).(a) Structure of a single printed cavity (b) Panel-to-panel imager experimental set-up.108

5.2 Measured S11 patterns (a) Diﬀerent Iris diameter (b) Diﬀerent Iris concentrations...... 110

5.3 Illustration of (a) panel-to-probe (b) panel-to-panel imaging setup with a 2-D far-ﬁeld pattern slice (22.5 GHz) in front of the apertures. 113

5.4 S11 and radiation eﬃciency patterns for 20 cm x 20 cm and 10 cm x 10 cm printed cavity...... 116

5.5 Singular values for the panel-to-probe and panel-to-panel imaging con- ﬁgurations...... 118

5.6 Reconstructed image of the 2.5 cm resolution target...... 120

xii 5.7 Reconstructed images of the L-shaped phantom (actual outline of the L-shaped phantom with dashed lines) (a) Simulation (b) Experimental.121

7.1 Aperture plane and focal plane...... 127

xiii List of Abbreviations and Symbols

Symbols

µ0 vacuum permeability

12 0 vacuum permittivity 8.854x10 F {m

r relative permittivity tanδ loss tangent

λ wavelength

Abbreviations

MM Metamaterial

WPT Wireless Power Transfer

Tx Transmitter/Transmit Aperture

Rx Receiver/Receive Aperture

ADS Advanced Designed system

HWR Half-Wave Rectiﬁer

SLL Sidelobe Level

ASM Angular Spectrum Method

SNR Signal to Noise Ratio

SAR Synthetic Aperture Radar

ESA Electronically Scanned Array

NSI Near Field Systems, Inc.

xiv VNA Vector Network Analyzer

CBA Cavity backed aperture cELC Complementary Electric Resonator

ELC Electric Resonator

RF Radio Frequency

PSF Point Spread Function

xv Acknowledgements

It all started with an email. Never in my wildest dreams had I imagined David replying to my email asking about opportunities in the group for purusing my Ph.D. One morning, got an email from David that he would excited to have me and he wanted to interview me for pursuing graduate studies at Duke University. The first question he asked me was,” Are you sure you want to leave Folsom, California and for Durham, North Carolina? ”. He believed me then, offered me a path for my doctoral degree and still believes me for which I am ever grateful. Coming out from David’s group is itself an outstanding honor I will cherish in my life. I would like to deeply thank my great advisor, Dr. David R. Smith, who has guided, supported and most importantly believed in me when the projects were going slow. I would also like to thank the members of my committee, Dr. William T. Joines, Dr. Willie J. Padilla, Dr. Aaron Franklin, and Dr. Matthew Reynolds for their support and mentorship during my time here at Duke University. I would like to thank all the current and past members of the Center for Metama- terials and Integrated Plasmonics for their help with my research over the years and a special thanks to Dr. Mohammadreza F. Imani with whom I have learnt a lot tech- nically and shared a lot (mainly soccer). I would finally like to thank the Department of Homeland Security (contract no. HSHQDC-12-C-00049) and Air Force Office of Scientific Research (FA9550-12-1-0491 and FA9550-18-1-0187) who supported parts of this work.

xvi I would not be where I am today without the love and support of my family and friends. My parents, Ramachandra and Radha who have been and always will be role models and exemplary parents. My sister, Bindu, has always been there at the good and bad times, given me the strength and criticism when I most needed it; I would also like to thank my wife, Hema, for caring and supporting me always.

xvii 1

Introduction

1.1 Dissertation overview

The dissertation is organized as follows. In chapter 1, we discuss briefly about wireless power transfer and computation imaging. In chapter 2, we discuss our research efforts in the analysis of a Fresnel zone system. Wireless power transfer (WPT) has been an active topic of research, with a number of WPT schemes implemented in the near- field (coupling) and far-field (radiation) regimes. Here, we consider a beamed WPT scheme based on a dynamically reconfigurable source aperture transferring power to receiving devices within the Fresnel region. In this context, the dynamic aperture resembles a reconfigurable lens capable of focusing power to a well-defined spot, whose dimension can be related to a point spread function. The necessary amplitude and phase distribution of the field imposed over the aperture can be determined in a holographic sense, by interfering a hypothetical point source located at the receiver location with a plane wave at the aperture location. While conventional technologies, such as phased arrays, can achieve the required control over phase and amplitude, they typically do so at a high cost; alternatively, metasurface apertures can achieve dynamic focusing with potentially lower cost. We present an initial tradeoff analysis

1 of the Fresnel region WPT concept assuming a metasurface aperture, relating the key parameters such as spot size, aperture size, wavelength, and focal distance, as well as reviewing system considerations such as the availability of sources and power transfer efficiency. We find that approximate design formulas derived from the Gaussian optics approximation provide useful estimates of system performance, including transfer efficiency and coverage volume. The accuracy of these formulas is confirmed through numerical studies. In chapter 3, we discuss the efforts in designing, fabricating and experimentally verifying each individual blocks of a WPT system. Firstly, we present the design and experimental demonstration of an efficient holographic metasurface aperture that focuses microwaves in the Fresnel zone. The proposed circular structure consists of two stacked plates with their periphery terminated in a conductive layer. Microwaves are injected into the bottom plate, which forms the feed layer, and are coupled to the top holographic metasurface layer via an annular ring. This coupling results in an inward traveling cylindrical wave in the top layer, which serves as the reference wave for a hologram. The radiating elements consist of a slot pair with their orientations designed to couple efficiently with the cylindrical reference wave while maintaining a linearly polarized focused beam. A general condition on the slot pairs radiated power is proposed to ensure low sidelobe level and is validated with full-wave simulation. An aperture that is 20 cm in diameter, operates at 20 GHz, and forms a diffraction-limited focal spot at a distance of 10 cm is experimentally demonstrated. The proposed near-field focusing metasurface has high antenna efficiency and can find application as a compact source for Fresnel-zone wireless power transfer and remote sensing schemes. Secondly, we discuss the design of the receiving aperture which is a metamaterial absorber which consisting of multiple layers to harvest the RF energy. This is later connected to a rectifier circuit to convert the RF to DC which is later shown by powering an light emitting diode (LED). The RF-DC power

2 transfer efficiency is in good agreement between simulations and experiments. In chapter 4, we discuss the the practical implementation of two Fresnel zone WPT system. In the first system, the configuration consists of transmit and receive microstrip patch array antennas, with the receiving antenna connected to a power- harvesting half-wave rectifier (rectenna). Fresnel region operation enables the fields radiated by the transmitting aperture to be localized both in range and cross-range. in C-band (5.8 GHz) frequency. In the second configuration, the transmit (focused aperture) and receive antennas (metamaterial absorber) are metasurfaces operating at 20 GHz (in K-band). We also demonstrate the successful functioning of both WPT configurations by powering an LED using the on-axis configurations. In chapter 5, imaging systems at microwave frequencies based on planar cavity sub-apertures, or metasurfaces. The cavity imager consists of sets of transmit and receive panels, loaded with radiating irises distributed over the sub-apertures in an aperiodic pattern. This frequency-diverse aperture produces distinct radiation patterns as a function of frequency that encode scene information onto a set of measurements; images are subsequently reconstructed using computational imaging approaches. Similar to previously reported computational imaging systems, the cavity-based imager presents a simple system architecture, minimising the number and expense of components required in traditional microwave imaging systems. The cavity imager builds on previous frequency diverse approaches, such as the recently reported metamaterial and air-filled cavity systems, by utilising frequency diverse panels for both the transmit and receive sub-apertures of the imaging system. Though the panel-to-panel architecture has greater sensitivity to calibration error, this implementation nevertheless increases mode diversity and, in the context of a computational imaging system, results in improved image reconstructions. Chapter 6 and Chapter 7 consists of the list of the contributions resulting in journal, conference papers and intellectual properties followed by an appendix section

3 showing the proofs for concepts mentioned in Chapter 2.

1.2 Wireless Power Transfer

The discussion of wireless power transmission (WPT) as an alternative to transmission line power distribution started in the late 19th century. Both Heinrich Hertz and Nicolai Tesla theorized the possibility of wireless power transmission [1]. William C. Brown contributed much to the modern development of microwave power transmission [2] which for many reasons dominates research and development of wireless transmission today. The physical phenomenon of electromagnetic field propagation produces two types of field regions from the source: Near field and far field. The

near field region (Fresnel diffraction, Fresnel number ăă 1) [3] is the region which is very close to the source. In the near field region, there are two sub regions which correspond to radiative and non- radiative near field regions. The non-radiative region is approximately around 3λ distance from the source which means, the energy stays in this distance without being radiated. In this region, the electric and magnetic fields are not coupled and power or energy can be transformed by electric fields using capacitive coupling or by magnetic fields using inductive coupling [4,5,6]. A big drawback about this method is the requirement of both the transmitter (Tx) and the receiver (Rx) should be very close to each other. There are analytical formulas

which give an idea about the distance from the source which is from 0 to 2D2{λ where D is the largest dimension in the transmitter, λ is the free space wavelength for a particular frequency. To overcome short distance power transfer, resonant structures were used for Tx and Rx which would improve the coupling between them resulting in power transfer for slightly greater distance compared to the inductive coupling or capacitive coupling. This method is known as resonant inductive coupling [6]. It can be noted that in-order to have a strong coupling between the Tx an Rx, they need to be close to each other. Another disadvantage is, when the two resonant circuits

4 are close to each other, the resonant frequency of the system is no longer at the frequency designed which would result in tuning the frequency for maximum power transfer. The second sub region under the near ﬁeld regime is the radiative near

field region when the distance is ă 2D2{λ. In this region, the electric and magnetic fields begin interacting with each other resulting in a focused beam before diverging to form plane waves in the far field (ą 2D2{λ). Depending on the size of the Tx aperture, one can find out the numerical aperture, which help in finding out how small of a spot will can be created, at what distance; which will be discussed in later sections. The region which is ą 2D2{λ is often denoted to as far field region or also known as Fresnel diffraction region (Fresnel number„1). This would be applicable for long distance wireless power transfer like microwave power transmission [7]. Fig. 1.1 below gives pictorial representations of the electromagnetic field region for an antenna.

Figure 1.1: Electromagnetic ﬁelds from an antenna

Considering the electric field equations of a dipole [Eq. 1.1] to understand which quantity of the equation contributes to which part of the field region mentioned above. In order to derive the fields of a conducting element as a dipole, let us

5 consider a dipole of length dl with current flowing in the Z-axis. By solving the magnetic vector potential and converting it into spherical co-ordinates, we can solve for the magnetic field which will lead us to finding the equations for the electric fields [8] as shown below.

Idl 1 1 E “ ´ Z k22cosθ ` e´jkr (1.1) r 4π 0 pjkrq3 pjkrq2 „ 

Idl 1 1 1 E “ ´ Z k2sinθ ` ` e´jkr (1.2) θ 4π 0 pjkrq3 pjkrq2 jkr „ 

Eφ “ 0 (1.3)

where k is the freespace wavenumber, λ is the freespace wavelength, r is the distance from the element to the point of observation, I is the current in the wire, dl is the length of the current element, Z0 is the free space impedance. Considering Eq. 1.2, the terms which vary as 1{pkrq3 and 1{pkrq2 corresponds to the fields in the near field region and 1{pkrq term mainly contributes to the radiation term or the far-field region.

1.2.1 Applications of WPT in Near Field

Applications of Wireless power transfer in the inductive near field region finds itself in the area of Wireless sensing (GPS sensors, accelerometer sensors), Wireless battery charging, Wireless charging pads etc. Companies like Intel, Samsung have been working on Wireless power research and have come up with products which utilize the concept of Wireless power transfer in the Inductive near field region effectively. As shown in the Fig. 1.2, the phone is wireless charged by the charging dock using the idea of inductive coupling. Inductive charging uses two electromagnetic coils to create a magnetic field between two devices, in this case the coils is present in the

6 (a) Phone with a wireless charging (b) Inside view of the charging pad

Figure 1.2: Inductive WPT Applications in real life charger base and the phone. It works on the same theory that the transformer you plug into the wall to charge your phone the normal way. A magnetic field ”creates” electricity through the difference of potential and vibration. The coil in the phone is connected to the battery charging circuit, and the battery is charged using the energy induced in the magnetic field. But, excess heat is created as well, and that’s part of why wireless charging using inductive coupling isn’t the most efficient way to transfer power from the wall to your battery. Also, this is the reason why it takes longer to charge your phone on a charging pad than it does to plug it into the wall. Since the distance between the Tx and Rx needs to very close to each other for the wireless power charging, it becomes less convenient or equal to the conventional plugging the charger into the wall. Fig. 1.2 (b) shows the implementation of the coils inside a smart phone which is later placed on/close to the other coil which is present inside the charging pad.

1.2.2 Applications of WPT in Far Field

The current research in the wireless power transfer ﬁeld is to develop prototype to charge mobile phone and handled computing devices such as tablets, digital music players without being tethered to the connection to a wall plug. The region concen-

7 trated to achieve this is in radiative near field and far field of the electromagnetic field around an object. Power is transmitted by beams of electromagnetic radiation like the microwaves or laser beams. The proposed application for this type of wireless power transfer is solar power satellites and wireless powered drone aircrafts. In the early 1960’s Brown invented the rectenna which directly converts microwaves to DC current. He demonstrated its ability in 1964 by powering a helicopter from the solely through microwaves. The helicopter shown in Fig. 1.3a was flown for 10 hours at an altitude of 50 feet. Dipole antennas were used for the receive antenna and it contained approximately 4000 semiconductors for the rectenna circuit. Fig. 1.3b shows the experiments by having an moving target using a microwave beam at 2.41 GHz generated by an electronically scanned phased array. A CCD (charge couple device) camera is placed to monitor the location of the moving target.The end to end efficiency was approximately 5 % with the received power to be around 88W. In 1982, Brown (Raytheon) and James F. Trimer (NASA) [9] announced the development of a thin-film plastic rectenna using printed-circuit technology that weighed only one-tenth as much as any previous rectenna.

(a) U.S. Air Force/Raytheon helicopter powered by microwave power transmission (b) MILAX prototype in Japan

Figure 1.3: Far-Field applications

Despite these advances, wireless power transmission has not been adopted for

8 commercial use apart from the applications mentioned earlier which are in the inductive near field region. However, research is continuing because of the many promising applications suited for wireless power transmission. An extensive amount of work is done in the field of wireless powering, inductive powering for short ranges, RFID tags, and low power sensors and far field solar power. This is accomplished by receiving incident wave with an antenna and then rectifying the RF voltage which is in the inductive near field region. The receiving systems especially for applications where power transfer is required for long-range distances is huge and bulky. There are advantages of using far-field energy transfer as it can reach places which are remote, nevertheless the infrastructure required would very huge along with very high input power.

1.2.3 WPT in the Fresnel Zone (Radiative Near ﬁeld)

Apertures that focus microwave energy in the Fresnel zone are of interest for a variety of applications such as medical imaging and therapy[10], remote sensing[11, 12] and wireless power transfer[13, 14]. For example, Fresnel-zone focusing is vital to achieving microwave-induced hyperthermia[15], where electromagnetic ﬁelds are con- ﬁned to cancerous regions without harming nearby tissue. Focusing antennas have also gained traction for wireless charging of biomedical implants[13, 14]. In remote sensing[11, 12] focusing apertures are essential to provide precise sensing information (for example, the temperature of food products in a production facility) without direct contact. Among the many applications of focusing electromagnetic waves, wireless power transfer a century-old concept pioneered by Tesla[1] has been of considerable recent interest. Modern approaches have largely been dominated by schemes involving inductive coupling between resonators[4, 16], which severely restricts power transfer short (near contact) operating distances. Interest in wireless power transfer was revived about a decade ago by the work of [4] where the authors showed that

9 the operating distance can be increased by employing coupled resonators[16, 17]. More recently, it was shown that opportunity exists for wireless power transfer at even larger operating distances by employing Fresnel-zone focusing[18, 19, 20], which is particularly necessary in applications where the required separation between the source and receiver precludes inductive, near-field approaches. Structures like patch antenna arrays, retro-directive arrays, and corrugated waveguides have been pursued as a means for focusing electromagnetic fields in the Fresnel zone for power transfer applications[21, 22, 23, 24, 25]. However, such structures usually result in complicated feed networks in the case of patch arrays, and unfavorable configurations for realizing an aperture required for dynamic beamforming in the case of corrugated structures. Forming a local hotspot by shaping the waveforms in a large cavity[26] and using a MIMO configuration [27] have also been proposed. In the far field region, the fields have a plane wave nature and it is hard to focus the beam to certain point of interest. The research work presented in this work focuses operation in the radiative near- field region which is beyond the reactive near field region. Efficient metasurface aperture for both the transmit and receive aperture is designed designed to realize a Fresnel zone Wireless Power system. In chapter 2, an initial trade off analysis of the Fresnel region WPT concept considering a metasurface aperture, relating the key parameters such as spot size, aperture size, wavelength and focal distance is presented. The fields imposed on the aperture is determined by a holographic approach by interfering a hypothetical point source with a plane wave at the aperture location. Appropriate design formulas derived from the Gaussian optics approximation provides estimates of spot size, coverage volume which is confirmed through numerical studies. In chapter 3, the design of the holographic transmit aperture to focus in the Fresnel zone is discussed by considering a radial line slot array antenna topology. Chapter 4 discusses the design of the metamaterial based absorber antenna and the

10 rectifier circuit designed to harvest the RF power received from the receive antenna. Experimental results are also presented. Chapter 5 discusses the implementation of a WPT system by using two different architectures. The first architecture consists of Patch array antennas as the Tx and Rx apertures operating at 5.8 GHz. The effect of using focused aperture is shown by comparing the results of a focused patch array antenna to a not-focused (beamed) patch array antenna. The second architecture consists of using focused metasurface apertures as the transmit aperture and a metamaterial inspired absorber as the receiver operating at 20 GHz. The experimental verification of this proposed system is considered in the future works. Chapter 6 presents the future works with preliminary simulation results along with my list of contributions.

1.3 Computational Imaging

Computational imaging approaches lead to the abstraction of the aperture concept, thus allowing many more imaging paradigms to be considered than are available with conventional approaches. In a computational imaging scheme, a much greater emphasis is placed on the forward model, which describes the ﬁelds radiated from the aperture and their scattering from targets in the scene. The more detailed and accurate the forward model, the more the physical hardware constraints associated with the aperture can be relaxed, thus allowing greater design freedom and potentially the use of less expensive materials and components. While computational imaging techniques can be applied in coherent and in incoherent imaging, the coherent modality is of particular interest because lens trains and other optical or quasi-optical components can be avoided. Only a single surface comprising the aperture is required for a coherent imaging system, thus making the coherent system relatively easy to model and analyze. Coherent apertures are natural for radio frequency (RF) waves, including microwaves and millimeter waves, which are preferentially used in security

11 screening applications due to their ability to penetrate clothing and other noncon- ducting materials. A wide selection of phase-stable sources, detectors, and other components operating in the RF spectrum is readily available, often at relatively low cost, such that coherent RF imaging systems can be readily constructed and deployed. Two common approaches to the formation of a coherent aperture include a single antenna (or pair of transmit/receive antennas) physically scanned over an area, and the use of a dense array of sources and receivers positioned over an area. In the former approach, often termed synthetic aperture, the radiation pattern from the antenna can be modeled as a dipole or similarly simple analytic expression, with the set of distinct measurements indexed by the set of locations of the antenna [28, 29]. In the latter approach, the collection of antennas distributed over the aperture can be modeled as a set of dipole radiators, with the phase and amplitude of each element assumed to be variable. The array factor mathematics for phased arrays and electronically scanned arrays (ESAs) are well known in the context of beam forming and can also provide useful forward models for computational imaging schemes [30, 31, 32, 33]. The commonality between the synthetic aperture and phased array architectures is the simplicity of the description of the radiating antenna. The radiation pattern, which enters into the system transfer function, can then be determined from relatively simple analytic functions and their sums. So long as the fundamental radiating element can be described simply, the radiation properties of much larger and more complex apertures can be simulated. Recently, a new class of aperture has been introduced in the context of microwave and millimeter wave imaging that consists of a parallel-plate waveguide structure, into the top plate of which are patterned resonant, metamaterial irises through which radiation can be emitted. Because the resonance frequencies of the metamaterial irises are distributed randomly over the operating band, the composite aperture produces a set of complex radiation patternsor measurement modesthat change as

12 a function of the driving waveguide frequency, such that image formation can be accomplished using a simple frequency sweep [34, 35]. Experimental demonstrations of this frequency diverse aperture at microwave frequencies have included a microstrip aperture [34], which produced low-resolution images of point-like targets in one angle and in range as well as a parallelplate aperture [34], which produced images over the entire 3D volume of scene space (range and cross range). In both cases, one or more metamaterial apertures were used to illuminate a scene, with a low-gain probe used to capture the backscattered fields. In [34, 35, 36], a frequency-diverse metamaterial imager operating over K-band frequencies (18-26.5 GHz) was demonstrated. The imager consisted of a set of metamaterial panels, each a planar waveguide with a dense array of sub-wavelength, complementary electric (cELC) resonators patterned into the upper conductor. The frequency response of each cELC has a Lorentzian form peaked at the operating wavelength, with a width set by the element quality (Q-) factor. The resonance frequency for each cELC was randomly selected from the K-band by tuning specific aspects of the cELC geometry. As the frequency of the feeding waveguide mode is swept, only certain sets of metamaterial radiators with resonance frequencies equal to the sweep frequency couple to the guided-mode and radiate into free space. The frequency- diverse aperture thus produces a set of complex radiation patterns (or modes) that illuminate the scene, with the number of modes within the frequency bandwidth determined roughly by the element Q-factor. The frequency-diverse metamaterial aperture consists of thousands of cELC unit cells. Due to their sub-wavelength geometry, the cELC elements required high precision printed circuit board (PCB) pro- cesses to achieve the necessary feature sizes. Even with high precision PCB printers, the fabrication tolerance is insufficient to ensure exactly equivalent radiation characteristics between fabricated panels, so that the field patterns must be characterized extensively for each of the fabricated panels. In addition, due to the dispersive nature

13 of the metamaterial elements, large conduction and dielectric losses occur on resonance where the radiation is maximized. The resistive and dielectric losses limit the achievable Q-factor for the system, which is the most important parameter indicating the effective number of independent modes. Given that the losses in the frequency- diverse metamaterial aperture occur in the planar waveguide section, a modification of the aperture was suggested in [37], in which an air-filled cavity was substituted for the planar waveguide. The air-filled cavity has a multi-wavelength thickness such that it supports multiple resonances at a given excitation frequency. An array of non-resonant radiating irises (or holes) patterned into the upper conducting plate forms the sub-aperture, as in the metamaterial panel. The higher system Q-factor associated with the air-filled cavity considerably improves radiation efficiency. In addition, introduction of a spherical indentation, into the otherwise rectangular cavity, mixes the modes and introduces considerable spatial variation into the fields driving the radiating elements. The modes of the final structure are thus chaotic, dispersing rapidly with frequency and exhibit significantly improved mode diversity in comparison with the metamaterial panels. While the chaotic aperture is advan- tageous in terms of mode diversity and effective Q-factor, the cavity modes are not easily predictable and require full-wave numerical simulations to analyze; given the inherently chaotic nature of the modes, small variations in manufacture may produce significant variations in the radiated field patterns. In addition, due to its required multi-wavelength thickness, the chaotic cavity has a relatively thicker profile than might be desirable. Given the advantages of the higher Q-factor cavity versus the simple planar waveguide as the feed, the cavity concept has continued to evolve. Recently, a simpler, PCB version of the cavity was suggested and shown also to improve mode diversity [38]. The printed cavity was made thin enough such that only one mode at any given frequency could be excited; that is, the printed cavity is a single mode

14 system rather than multimode as in the chaotic cavity. The printed cavity provides an increased system Q-factor while retaining the low proﬁle and other desirable characteristics of the planar waveguide.

15 2

An Analysis of a Fresnel Zone WPT system

2.1 Introduction

Excerpts of the following discussion can be found in the manuscript An analysis of beamed wireless power transfer in the Fresnel zone using a dynamic, metasurface aperture by Smith et al. (2017) published in Journal of Applied Physics. Despite the dramatic growth of wireless technology in the communications domain, the use of wireless technology to provide power to devices remains in its infancy, due to both technical as well as market related concerns. Wireless power transfer (WPT) can allow power to be delivered without requiring a wiring infrastructure - a useful feature especially for remote, difficult to access devices, as well as embedded devices and sensors. The challenge for WPT, however, is in achieving a high-efficiency system at reasonable transfer distances. The dominant approach to date to WPT has made use of the magnetic near-fields, in which power is transferred between source and receiver coils that are coupled through non-radiating magnetic fields at very low frequencies of operation (kilohertz through megahertz, for example)[4, 16, 39]. Be- cause near-field magnetic WPT systems are safe in terms of human exposure and can

16 be highly efficient at short distances, they have led to numerous commercialization efforts[40]. However, because the near-field coupling falls off rapidly with distance between source and receiver (as the sixth power of the inverse distance)[41], near-field

WPT schemes require the receiving device to be in close proximity (ă 3λ0)[42, 43] to the power source. While this proximity constraint is less problematic for some applications, such as vehicle charging, it remains an inconvenience in other contexts, and can rule out entire application areas such as powering remote sensors at long ranges. At the other extreme, power transfer can be accomplished using short wavelength radio frequency (RF) power radiated from a source aperture to a receive antenna or aperture[43, 44]. The advantage of such a WPT system is that power can be

transferred over very long distances (from ă 3λ0 to the limit of the Fresnel zone)[43] to targets at arbitrary positions, in hard to access regions or embedded in other materials. The disadvantage for far-field systems is that the beam width from an aperture is limited by diffraction, with the result being that only a minute fraction of power supplied by the source is captured by the receive aperture. In far-field scenarios, for which the distance between source and receive apertures is greater than

2 d “ 2D {λ0 (where D is the aperture dimension)[45], the ratio of the power captured by the receiver to the supplied power is governed by the Friis equation. To achieve even modest efficiency levels for WPT schemes in the far-field regime, enormous apertures would be required. In addition, if the target to be powered is in motion, such as might be the case for an unmanned aerial vehicle (UAV) or autonomous automobile, then the source aperture would need to either be mechanically scanned or electronically reconfigurable. If the distance between source and receiver is within the Fresnel zone (also termed

2 the radiating near-ﬁeld, d ă 2D {λ0), and a line of sight is available, then a high eﬃciency WPT system can be realized by using a large aperture that acts as a lens,

17 concentrating electromagnetic energy at a focal point where the receiving aperture is positioned[21, 46, 22]. In this scenario, a method of dynamically creating and moving a focal spot is needed. Recent intense research and development in the area of metasurface apertures guided wave structures that radiate energy through an array of patterned irises has shown a path to extremely low-cost, mass-producible reconfigurable apertures that could be configured for the WPT application[47, 48]. The metasurface antenna is a passive device, in the sense that active phase shifters and amplifiers are not required to achieve the desired element tuning. Thus, for many implementations there is minimal power dissipation in beam steering, in contrast to typical phased array or electronically scanned antenna systems. Through the control over the phase or amplitude of each radiating element, holographic patterns can be created on the metasurface that mimic the functionality of Fresnel lenses or other diffractive optical elements. The metasurface aperture thus effectively can function as a low-cost, dynamically reconfigurable lens that consumes minimal power. A Fresnel zone WPT system based on a metasurface aperture can potentially achieve very high efficiency at minimal cost. There are a variety of factors that must be considered for achieving a viable Fresnel zone WPT platform. In particular, the wavelength of operation represents a critical design choice. Ideally, short wavelength radiation is desirable, since very small focal spot sizes can be formed with moderate sized apertures. However, the cost of microwave sources increases dramatically at shorter wavelengths, forming a crucial tradeoff decision for the system. Currently, fairly large, dynamically reconfigurable metasurface apertures have been demonstrated at X (8-12 GHz)[49] and K (18-26.5 GHz)[50] bands, and are very likely achievable at W (75-110 GHz) band in the near term. WPT systems operating within any of these bands are within the realm of possibility depending on the particular application. Power harvesting elements at these wavelengths, such as rectennas, have been demonstrated, but high

18 conversion efficiency (ą 50%)[51] circuits may require additional development. As- suming optimal conversion efficiency, we can obtain estimates of the useful range of a Fresnel zone WPT system as a function of aperture size and frequency of operation, based solely on the ideal field patterns expected to fill the aperture. The actual metasurface antenna implementation of a dynamic aperture will have limitations that arise due to the finite size of the metamaterial elements (leading to a subwavelength sampling of the aperture), as well as their inherent dispersive characteristics. Using a well-established model for these elements that describes both their dispersive and radiative properties, it is possible to determine the actual focal spot size and shape, including aberrations introduced by any phase or amplitude limitations inherent to the elements. Phase or amplitude patterns on the metasurface aperture that steer the focal spot throughout the volume of coverage can be determined using holographic techniques, so the effective power transfer efficiency can be studied as a function of the receiver location and orientation. There are many potential usage opportunities for WPT schemes operating in the near-zone. Since the location of Fresnel zone (and realizable focus spot size) depends only on the size of the transmit aperture and the wavelength of operation, many different scenarios can be considered. One possible scenario is presented in Fig. 2.1, which shows an aperture being used to beam power wirelessly to electronic devices within the confines of a room. The advantage of such a scheme is that devices such as cell phones, laptops, computer peripherals, gaming controllers or consoles, watches, radios, small appliances can be positioned anywhere within the line of sight of the source to receive power, requiring no cables or charging stations. For such a scheme to function, each device must be discoverable and locatable by some separate wireless system, which could be built into the protocols of a near-zone system. That is, each device must signal its presence in the room, and communicate its location and orientation with respect to the transmit aperture. In addition, if

19 the device is being powered, it must indicate to the transmit aperture that power is being delivered, such that the system shuts down if the direct path is blocked for any reason (e.g., if a person passes between the aperture and device). This safety interlock system would be essential to accommodate human safety requirements. Since our goal here is to consider the general viability of near-zone power transfer from a power transfer efficiency perspective, we do not consider further the issues of safety and other related protocols that would ultimately become a system engineering topic. For the purposes of the analysis presented here, we consider powering devices within a room of dimensions of 5 m x 5 m x 2.5 m, requiring an aperture large enough that all points within the room are also within the Fresnel region of the transmit aperture. As shown in Fig. 2.1, a single transmit aperture (P1) focuses RF power to several electronic devices within the room, such as R1 and R2. The devices are placed at arbitrary locations in the room, at different focal depths with respect to the transmit aperture, as would be expected in real use scenarios. The transmit aperture must thus be capable of powering targets at different depths and angles, as well as potentially powering multiple receivers from a single aperture. This functionality implies a dynamic aperture capable of creating a tight focus and adjustable focal length.

20 Figure 2.1: Potential usage scenario for a Fresnel zone wireless power transfer system

2.2 Derivation of Focal spot using Gaussian Optics

The efficiency of a WPT system in either the Fresnel or the Fraunhofer regime depends predominantly on the effective aperture sizes of the source and receiver, as well as the free space wavelength. Given our choice of Fresnel region operation the far-field propagation model is not valid. Instead, in the Fresnel region, the aperture behaves like a lens, able to concentrate the transmitted energy to a volume defined by its point spread function (PSF). As a starting point, we assume the aperture behaves as a Fresnel lens, and apply Gaussian optics to characterize the expected field patterns. We consider the line of sight case where a source beam will travel without encountering obstructions. The spatial electric field distribution corresponding to a Gaussian beam can be described analytically using the expression[3, 52] Assuming that the fields are focused from a lens of diameter D and focal length

21 z0, the minimum beam waist can be calculated as shown in the derivation below.

Figure 2.2: Illustration of the eﬀective aperture considered for the analytical calculation of the beam waist for oﬀ-axis focusing

Since we are creating an ideal hologram over the aperture for every focal position in the range of coverage, there are no aberrations introduced to the focus. The widening of the beam waist must arise entirely from the loss of aperture, which we can estimate from the geometry. Consider the situation depicted in Fig. 2.1. The thicker solid line represents the actual aperture. However, we can conceptually replace this aperture, which makes an angle θ with respect to the position of the focal spot, by a second aperture, represented by the thinner line, for which the focal spot is now on-axis. The characteristics of the focal spot must be the same for either aperture, since we assume the hologram is ideal for both cases. Given the position of the focal spot, we have the following relationships:

z z x ´ D{2 cosθ “ 0 , tanα “ 0 , tanβ “ 0 (2.1) 2 2 ? x0 ` z0 x0 ` D{2 z0 a a22 2 2 and R “ x0 ` z0, We seek the length of the eﬀective aperture. Designating the lengths l1 andal2 for the two sections (on either side) of the eﬀective aperture, we can apply the law of sines as follows:

sinα sinpα ´ θq “ l1 D{2 (2.2) sinp π ´ βq sinp π ` β ´ θq 2 “ 2 l2 D{2

which yields

D sinα l “ 1 2 sinpα ` θq (2.3) D cosβ l “ 2 2 cospβ ´ θq

Thus, Deff “ l1 ` l2. While this formula for the eﬀective aperture is not particularly illuminating, we can rearrange the formula to ﬁnd, after some algebra,

R3 Deff “ Dz0 2 2 (2.4) 4 D x0 «R ` 4 ﬀ or

1 D Dcosθ (2.5) eff “ 1 D 2 2 «1 ` 4 p R q sin θﬀ

Eq. 2.5 shows that away from the aperture, where RąąD, the aperture reduction goes simply as the cosine of the angle between the aperture axis and the focal position. Closer to the aperture, however, the aperture reduction occurs more quickly. For the off-axis Gaussian beam waist, then, we should use the effective aperture. Note that for the effective aperture, the focal length is equal to R, so that

23 4 λ0z0 1 D 2 2 w0 “ 2 1 ` p q sin θ (2.6) π Dcos θ« 4 R ﬀ

If we can neglect the term in bracketsa good approximation for the cases under considerationwe obtain a simple formula for the beam waist valid for oﬀ-axis focusing:

4 λ z w “ 0 0 (2.7) 0 π Dcos2θ

Eqn 2.7 shows that the fields of a focused beam tend to be tightly confined laterally around the focus, but extend along the propagation direction by a distance corresponding to the Rayleigh length. Thus, for short focal lengths relative to the aperture dimension, the fields tend to be confined in all dimensions; however, for larger focal lengths, the Rayleigh length tends to be larger and the fields spread out along the propagation direction. Plots of the intensity of the focused beam for several values of are shown in Fig. 2.3. For these illustrative plots, the aperture size is chosen as D= 1 m, and the frequency as f=10 GHz. The solid white curves in Fig. 2.3 are plots of the beam waist w(z).

24 Figure 2.3: Intensity plots of a focused beam from an aperture of dimension D=1 m, at a frequency (f) of 10 GHz, plotted for diﬀerent focal lengths pz0q

Since the minimum beam waist increases with focal length, a straightforward design consideration for the system is that the transfer eﬃciency must be optimized at the farthest desired point from the aperture. For this study, we assume the smallest receive aperture to have dimension of DRx = 3.0 cm, so that a simple

DRX measure of transfer eﬃciency can be taken as ηfocus “ . This simplistic model w0 likely represents a best-case limit of eﬃciency. Using Eq. 2.7, we can perform an initial study of the beam waist versus aperture dimension and frequency as a means of assessing the initial constraints of a WPT system. Such a study is presented in Fig. 2.4, which provides the minimum beam waist at a focal length of 5 m for several values of aperture size and operating frequency. Using Eq. 2.7, we can perform an initial study of the beam waist versus aperture dimension and frequency as a means of assessing the initial constraints of a WPT

25 system. Such a study is presented in Fig. 2.4, which provides the minimum beam waist at a focal length of 5 m for several values of aperture size and operating frequency. Inspection of Fig. 2.4 shows that, as expected, larger aperture and higher frequency provide the smallest beam waists. Given the receive aperture size

considered here (DRx = 3.0 cm), there are a variety of combinations of transmit aperture size and frequency that should optimize efficiency. Assuming a transmit aperture footprint of no larger than 1 m2, Fig. 2.4 shows that frequencies of 60 GHz or higher should provide reasonable transfer efficiency over the volume considered. The eventual choice of frequency will likely be determined by the availability, cost and power conversion efficiency of the RF power source and the rectifier or energy harvester at the receiver. At present, for example, low cost solid-state sources are emerging into the market for bands at 60 GHz and 77 GHz, due to the demand in automotive radar and other large market applications.

Figure 2.4: Beam waist (in cm) as a function of f and D size, using Eq. 2.7. The shaded regions might be considered acceptable for this study.

The possibility of achieving even smaller beam waists at much higher frequencies, such as THz, infrared or even visible, can also be considered. However, highly eﬃcient rectennas (rectifying antennas) can be challenging to design at these frequencies[53]; sources are expensive and not readily available; and the power density in such highly

26 collimated systems can exceed human safety limits. The beam waist and Rayleigh length are the critical parameters for the description of a Gaussian beam, and can be used to generate general scaling arguments for various quantities of interest. For example, assuming all power incident on the receive aperture is recovered, the relative size of the receive aperture to the beam waist should be the only relevant quantity in terms of describing eﬃciency. Fig. 2.5(a) shows how eﬃciency scales with the

ratio of η “ DRx{w0 . As expected, the transfer efficiency reaches a relatively high value (ą 80%) when this ratio is unity, and approaches 100% as the aperture area increases beyond unity. This curve is invariant with respect to focal length, frequency or other parameters. Likewise, the transfer efficiency drops off away from the focus as a function of distance along the propagation axis, as shown in Fig.

2.5(b). If the efficiency is plotted against the unit less parameter z{zR , then a universal curve results. A couple of items should be noted here. We have adopted a fairly simple definition of transfer efficiency that will be applied throughout this analysis. It is relevant, however, to consider in a little more detail what might be the upper limit on possible free-space power transfer efficiency within the Gaussian beam approximation, which should be agnostic to the manner in which the beam is created and absorbed.

Figure 2.5: Transfer eﬃciency assuming the Rx (a) placed at the focus, as a function of D{w0 (b) of size w0, where (D{w0=1) as a function of z{z0

27 2.3 Practical Implementations

2.3.1 Aperture Architecture

In any feasible implementation of a near-zone WPT scheme, the source aperture is likely to take the form of a flat panel that can be wall- or ceiling-mounted and fairly unobtrusive. Wall or ceiling mounting offers the important advantage of line-of-sight propagation to most points in a room. For conventional lenses, even in the most favorable of circumstances, some level of aberrations would be introduced into the beam due to the inherent limitations of planar optics. While the characteristics of the dynamically reconfigurable sources considered here are different from static lenses, additional imperfections in spot size and other metrics can be expected, since the aperture will necessarily be sampled discretely with components that may have limitations in their phase or amplitude control range. One means of forming a dynamic aperture is a phased array or electronically scanned antenna[54, 55]. A phased array consists of an array of radiating elements, each element containing a phase shifter and possibly an amplifier. The radiating elements are positioned at distances of roughly half the free space wavelength apart. If full control over phase and amplitude is available, then it follows from Fourier optics that an electronically scanned antenna has the capability to produce any far- field pattern. However, from the standpoint of a high efficiency WPT system, phased arrays or electronically scanned antennas are not an optimal solution since each of the radiating modules requires external bias power (beyond the wireless power to be transmitted). Power consumption in array control systems can be substantial, easily exceeding the power being transferred to small devices. An alternative architecture for dynamic focusing is that of the metasurface aperture [47, 50, 56, 57], which isin contrast to electronically scanned antennas and phased arraysa largely passive device that achieves reconfigurability via dynamic tuning of

28 metamaterial resonators. The details of the metasurface architecture are beyond the scope of the present study, but we assume some of the metasurface aperture constraints in the consideration of more realistic implementations.

2.3.2 Holographic Aperture Design

As a next level of approximation, we consider the formation of focal spots using an aperture over which any field distribution can be obtained. In this section, we assume that the aperture can be sampled as finely as desired, so that the limitations associated with a flat and finite aperture are explored. To determine the fields everywhere in the region of interest, the fields at the aperture can be propagated using the angular spectrum method (ASM)[3]. In this method, a Fourier transform is taken of the fields on the aperture, resulting in a set of coefficients corresponding to an expansion in plane waves. Each of these plane wave components is then propagated a given distance along the propagation direction, where an inverse Fourier transform can be taken to find the field distribution over the plane. In this work, we assume that an arbitrary field distribution (both amplitude and phase) can be created over the aperture plane, to varying approximations, that will produce a focused spot. We determine the required field distributions by designing a hologram[58, 59]the recorded interference pattern between a reference beam and the scattered complex fields from an object located within the Fresnel region. To arrive at the required amplitude and phase distribution of the aperture field, we construct the aperture field by interfering a point source with a uniform plane wave. Taking the center of the aperture as the origin of the coordinate system, a point source located at the position will produce the aperture field

? ik x x 2 y y 2 z2 e p ´ 0q `p ´ 0q ` 0 Epx, y, 0qα (2.8) 2 2 2 px ´ x0q ` py ´ y0q ` z0 a 29 Eq. 2.8 provides the amplitude and phase distribution needed to design a holographic pattern that will produce a point source of diffraction-limited extent. This initial field distribution can then be back-propagated to determine the fields everywhere in the region of interest. As a practical matter, we find that the amplitude variation is not of great importance in reproducing the point source, so we use only the phase distribution in the following analysis. Examples of the phase hologram are shown in Fig. 2.6, as well as the focused spots produced by these apertures. The hologram fringes must be faithfully reproduced to minimize aberrations, which means we must sample the aperture so as to capture the spatial variation. For the

simulations in this section, a sampling of λ0{8 was used.

Figure 2.6: Cross range 2D plots for both on- and oﬀ-axis case (a) Phase distribution at the aperture plane (b) Focused spots (zoomed in) at z0.

Initially, we investigate focusing with an ideal holographic transmit aperture and a receive aperture placed some distance away. Fig. 2.6 (a) shows the phase distribution

30 required on the aperture plane (on-axis and off-axis), with a 2D intensity plot of the focused spots produced by these apertures. For both simulations, z0 =5 m. The offset value chosen for off-axis focusing is for illustrative purposes only. Comparing the on-axis and off-axis focused intensity patterns, it can be seen that the spot for the off-axis elongates in the cross range direction; that is, the beam waist for the off-axis case slightly increases when compared to the on-axis focusing. The increase in beam waist for off-axis beams is expected due to aperture loss. To confirm the behavior, we compute the beam waist at the focus for an ideal holographic aperture of dimension DT x=1 m. The transmit aperture is designed to produce a focus at a distance of z0 =5 m. Since the selection of the frequency band mainly depends on commercially-available sources, an operating frequency of 77 GHz (corresponding to the automotive radar band) is considered for the analysis presented. The beam waist at the focal plane is taken as the diameter at which the intensity has decreased to 1{e2 or 13.5% of its peak value. The beam waist as a function of off-axis angle (offset along y-axis) is shown in Fig. 2.7a for both the simulations and the approximate analytical Gaussian formula of Eq. 2.7. The coordinates of the focal points are selected such that the total distance

2 2 2 of the focal point to the center of the aperture is constant (r “ x0 ` y0 ` z0).

Using a hypothetical receive aperture of dimension DRx = 3a cm, we can assess power transfer efficiency for off-axis beams. As can be seen in Fig. 2.7b, the transfer efficiency decreases as the beam offset angle θ increases, as expected due to spillover losses.

31 Figure 2.7: (a) Analytical and numerical w0 as a function of oﬀset angle θ for z0 = 5m. (b) Power transfer eﬃciency as a function of θ (DRx = 3 cm).

If one assumes a ﬁxed receive aperture of minimum dimension (assumed to be

DRx = 3 cm), then Eq. 2.7, as well as the numerical results, suggest a coverage area map can be formed that includes all regions of interest for which the beam waist will be small enough for a desired level of power transfer eﬃciency. An analytical estimate of this coverage zone can be extracted from Eq. 2.7 by examining contours in the y-z plane of constant beam waist. For a constant beam waist, Eq. 2.7 leads to the following:

2 2 d d y2 ` z ´ c “ c (2.9) ˜ 2 ¸ ˜ 2 ¸

π w0 where dc “ D 4 λ0 Eq. 2.9 shows that contour of constant beam waist is a circle in the y-z plane

centered at z “ dc{2 and with diameter dc . Thus, for a given aperture size and

operating wavelength, a desired coverage range (dc) can be selected and Eq. 2.8 used to determine the beam waist needed. In the example we study here, the relevant parameters D = 1 m, λ0=4 mm and w0=3 cm. suggest a coverage diameter of 6 m.

32 All beam waists within a given contour are smaller than this value, so that the least power transfer eﬃciency occurs at the periphery of the coverage region. Plotting Eq. 2.7 results in a coverage map such as that shown in Fig. 2.8.

Figure 2.8: Illustrative coverage plot of w0 as a function of θ, z0 in a room (5m x 5m, top view) (a) Analytical (b) Numerical using simulations.

Since we expect the angular behavior predicted by Eq. 2.7 to be very approximate, we also directly compute the coverage map using the numerical method described above. From this map (Fig. 2.8) we see that the contours of constant beam waist are somewhat more elliptical, yet nevertheless fairly close to the simple coverage map predicted by Eq. 2.9.

2.3.3 Phase and Amplitude Constrained Holograms

For the studies conducted above, we assumed that an arbitrary ﬁeld distribution (in both amplitude and phase) could be imposed across the aperture, resulting in diﬀraction-limited focal spots being generated. Although point-by-point simulta- neous control of the phase and amplitude over an aperture can be achieved to a considerable extent in active electronically scanned antennas, such systems are not

33 yet economically viable for larger-volume, low-cost applications such as the WPT scenario envisaged here. The dynamic metamaterial aperture provides a low-cost, manufacturable alternative platform, but comes with certain limitations. In particular, it is not possible to independently control the phase and amplitude of a resonator-based metasurface aperture. The resonance of the metamaterial resonator element possesses a Lorentzian relationship between the phase and amplitude, of- fering a constrained control space. Moreover, for a single resonator, the maximum range of the phase is between -90˝ and +90˝, placing an immediate limitation on the field distribution over the aperture[60]. In practice, because the amplitude of a Lorentzian falls off substantially away from the 0˝ point, the useful phase range is likely substantially smaller. The possibility exists of combining both an electric and a magnetic resonator into the same radiating elements, which would allow the full 360˝ phase range to be accessed; however, these Huygens surfaces[61] are considerably more difficult to design and may be more subject to resistive losses and unwanted inter-element coupling. We will consider Lorentzian constrained holograms later. In this section, we first investigate the potential performance of the holographic aperture for WPT in the presence of phase limitations. Because the dependence of the image produced by a hologram is typically only weakly dependent on the magnitude, we first consider either amplitude-only or phase-only holograms as a basis for comparison. We form the desired hologram in the same manner as in Section 2.3.2 above, conceptually interfering a plane wave with the spherical wave from a point source at over the aperture plane, resulting in the specification of the required complex field distribution over the aperture. An amplitude hologram can be realized by enforcing a binary mask over the aperture, achieved by treating each sampling point as either transparent or opaque; that is, each point on the aperture controls the amplitude

34 in a binary fashion, introducing no phase shift. The result of the binary amplitude hologram is shown in Fig. 2.9a, where the hologram has been designed to produce

˝ a focal spot at an angle of 15 from the normal to the aperture at a distance of z0 = 5m in range. Not surprisingly, the aperture produces a zeroth-order diffracted beam and several other diffracted beams, such that energy is lost from the main focus and additional hotspots are created in the region of interest. The locations of these additional beams and associated focal points can be determined using simple diffraction theory, and agree with the patterns found from the simulation. The scenario illustrated in Fig. 2.9 can be considered a worst-case scenario, since no attempt was made to optimize the aperture distribution. The amplitude mask was created from the ideal hologram by setting points within a particular phase range to transparent, and points outside that phase range to opaque. Two simple binary amplitude designs were considered here: In Aperture A, those regions with phase between 0˝ and 90˝ were set to transparent (all other regions opaque), while in Aperture B those regions with phase between 0˝ and 45˝ were set to transparent (all other regions opaque).

35 ˝ Figure 2.9: Intensity plot for an amplitude holographic lens (z0 at θ = 15 ). (a) y-z plane with higher orders (b) x-y plane with 0th order at the center.

The simulations were conducted over a cubic volume of dimension L=6 m containing a transmit aperture of size DT x=1 m, as shown in Fig. 2.9. The focus was

˝ chosen to be at z0 = 5 m, at an angle of 15 from the aperture normal. The fields are determined over the transmit aperture in the manner described above, and set to zero elsewhere on the aperture plane. For the two apertures considered, A and B, the overall transfer efficiency was determined, as summarized in Table 2.1. As above, in this case one contributor to transfer efficiency is the ratio of the intended receive aperture (DRx) to that of the beam waist at focus, or η . In addition, we define the ratio as the total power radiated by the aperture to the total power in the first order (desired) focused beam. Thus, the overall efficiency of power transfer to

the device is η{α. The total power is calculated by integrating the Poynting vector

over the entire surface of the domain (at z0 = 5 m). A value of indicates no presence of higher order modes, while the presence of higher orders results in α ą 1.

36 Table 2.1: Overall efficiency of amplitude-only holograms for off-axis focusing and ratio α for different binary holograms. Aperture Overall Efficiency (%) α A: 0˝ to 90˝ 14.4 2.4 B: 0˝ to 45˝ 8.9 2.8

As shown in Table. 2.1, α is above 1 for both cases considered, and the efficiency is generally low, indicating that significant power is lost to higher order diffracted modes. With additional optimization, it is possible to suppress some or all of the diffractive orders within an amplitude-only hologram, especially if the amplitude is allowed to take a range of values (grayscale) rather than just binary[62, 63]. We do not consider such optimization here. We next consider the formation of phase holograms, starting from the ideal hologram specification and assuming the phase at each sampled point on the aperture can be controlled to some extent. An ideal phase hologram would allow the phase to vary from -180˝ to +180˝ (aperture C), leading to idea transfer efficiency, as shown in Table 2.2. For a phase only hologram, any limitation of the phase range to less than 360˝ will result in an imperfect hologram and degraded focusing performance; moreover, the inevitable phase discontinuities that result can produce scattering into the higher order diffraction modes. To analyze the effect of limiting the phase, we consider again the case of off-axis focusing (an angle of 15˝ from the aperture normal), limiting the phase values across the aperture to lie within a restricted range, as summarized in Table 2.2. The simulation domain for these examples is identical to that used for the amplitude-only hologram. In these simulations, where the phase of the ideal aperture is required to be smaller than the lower limit of the available phase range of the implementation, the phase was set equal to the lower limit. Where the phase of the ideal aperture is required to be larger than the upper limit of the available phase range, the phase was instead set

37 equal to the upper limit. As Table 2.2 shows, constraining the phase range reduces the overall eﬃciency. The ﬁeld patterns for phase-only holograms with various phase

constraints are shown in Fig.2.10. Again, the aperture is designed to focus at z0= 5 m at an off-axis angle of 15˝ from the normal to the aperture. Due to the phase discontinuity introduced on to the aperture, other diffraction orders occur, resulting in loss of power from the main order or focus. The scenarios considered in Fig. 2.10 correspond to the selected apertures summarized in Table 2.2 (except for Aperture C). With the full 360˝ of phase values, no higher diffraction orders were observed.

Table 2.2: Overall efficiency of phase-only holograms for off-axis focusing and ratio α for different phase limited apertures. Aperture Overall Efficiency (%) α C: -180˝ to 180˝ 78.1 1 D: -135˝ to 135˝ 74.3 1.02 F: 90˝ to 90˝ 52.4 1.38 E: -60˝ to 60˝ 28.9 2.40 G: -30˝ to 30˝ 8.3 7.60

38 Figure 2.10: Intensity plot (dB) in the y-z and x-y planes for a phase holographic ˝ lens (z0 at θ = 15 ) for Apertures (a) D (b) E (c) F (d) G. 39 The beam waist of the main beam remains relatively constant for the various phase holograms, so that the drop in efficiency can be associated with the power loss in the other diffracted orders. The increasing value of in Table 2.2 indicates this loss. The ideal phase-only hologram produces no higher diffraction orders, and thus has a value of α=1. In aperture D, phase values between -135˝ to +135˝ are available, with the remaining sampling points, or pixels, set to either the upper or lower bounds of the phase limits considered. Despite aperture D having a significantly restricted phase range, the overall efficiency remains high and higher order modes are not important. Similarly, in aperture E, phase values between -90˝ to +90˝ are available. The value of α=1.38 corresponds to the increased presence of unwanted diffracted beams as expected. Apertures F and G show a significant increase in because of the increase in the power lost to the other orders, mainly the zeroth order (DC component), as shown in Fig.2.10c and Fig.2.10d respectively. The zeroth order becomes stronger as the phase range on the aperture is reduced. Aperture G corresponds to the worst case scenario of the phase limitations considered, resulting in the largest value of α. The holograms shown here are meant to be illustrative, and have not been optimized. Diffraction into unwanted orders can potentially be removed or at least suppressed through various optimization techniques[64] such as iterative algorithms like Gerchberg-Saxton or Hybrid Input-Output[65].

2.3.4 Lorentzian Constrained Holograms

We have so far considered the analysis of amplitude-only and phase-only holograms, but if we consider a practical metasurface antenna, the amplitude will be linked to the phase through the dispersion relation of the Lorentzian resonance. The metasurface antenna can be modeled as a collection of polarizable magnetic dipoles[35], with each dipole possessing a polarizability of the form

40 iF ω2 αm “ 2 2 (2.10) ω ´ ω0 ` iγω

From Eq. 2.10, the phase of a metasurface element is related to its resonance frequency according to

ω2 ´ ω2 tanpθq “ 0 (2.11) γω

where the γ is a loss term, ω0 is the angular resonant frequency, and F is a coupling factor, which we can set equal to unity for the discussion presented here. To form a desired phase distribution using metasurface elements, the resonance frequency of the element can be controlled by a variety of methods. However, by tuning the resonance frequency, the amplitude of the polarizability is also determined having the form

F ω2 |αm| “ (2.12) 2 2 2 2 pω ´ ω0q ` pγωq

For a desired phase pattern overa the aperture required to create a focus, determined by modifying the resonance frequency at each point, an amplitude pattern will necessarily be imposed deﬁned by Eq. 2.12. Inserting Eq. 2.11 into Eq. 2.12 yields a relatively simple expression linking the phase and amplitude at each point:

F ω |α | “ |cosθ| (2.13) m γ

Eq. 2.13 shows that the amplitude is proportional to the absolute value of the cosine of the phase (with 0˝ occurring at resonance), falling to zero at the extreme values (-90˝ or +90˝).

41 To investigate the impact of the Lorentzian constrained aperture, we again con-

sider the same scenario as above, with the aperture designed to focus at z0 = 5 m at an off-axis focusing (an angle of 15˝ from the aperture normal). Here we consider holograms formed by limiting the phase values across the aperture to lie within a restricted range, as summarized in Table 2.3, while the amplitude at each point is determined from Eq. 2.13. The simulation domain for these examples is identical to that used for the amplitude-only and phase-only holograms. As shown in Table 2.3, limiting the phase reduces the overall efficiency and produces other diffraction orders. The scenario considered in Fig. 2.11 corresponds to Aperture H. The beam waists for the apertures considered in Table 2.3 are constant and the loss in overall efficiency is due to the power lost from the first order mode to the other diffracted orders. Aperture H can be considered as the best case for a metasurface antenna (without further optimization), since it extends the full phase range of -90˝ to 90˝. The overall efficiency is around 34.2%. We then consider aperture I, in which the phase range is further restricted, resulting in further reduction in the overall efficiency due to the increase in the α term as shown in Table 2.3.

Table 2.3: Overall efficiency of a metasurface for off-axis focusing and α for different aperture distributions. Aperture Overall Efficiency (%) α H: -90˝ to 90˝ 34.2 1.8 I: -60˝ to 60˝ 18.5 3.2

42 Figure 2.11: Intensity plot of metasurface aperture (aperture H in Table 2.3). (a) y-z plane with higher orders (b) x-y plane with 0th order at the center.

2.4 Schematic of a Fresnel Zone WPT system

The basic schematic of a WPT system is shown in Fig.2.12 which consists of a microwave source which is a vector network analyzer (VNA) feeding a focused transmitting aperture [66]. The receiver in the proposed WPT system consists of a metamaterial absorber and a rectifying circuit to harvest the RF to DC energy. Fig. 2.12 represents a WPT system specific to the Fresnel zone WPT system we are trying to pursue in the proposed research work. Since the proposed system operates in the Fresnel region, the size of the receive aperture is close to the spot size generated by the transmit aperture at a given focal distance. However, a general WPT system also has a source, transmitter, receiver and a rectifier as the basic building blocks. In the future chapters, the design and experiments of the focused aperture, receiver and the rectifier is studied in detail.

43 Figure 2.12: Schematic of a WPT system

44 3

System block design and experiments of a Fresnel zone WPT system

3.1 Transmitter - Focused Metasurface Aperture Design and Exper- iments

Excerpts of the following discussion can be found in the manuscript Focusing Mi- crowaves in the Fresnel Zone With a Cavity-Backed Holographic Metasurface by Gowda et al. (2018) published in IEEE Access. In this chapter, we shall consider the design and implementation of the focused transmit aperture being the ﬁrst building block in the system schematic diagram considered in Fig.2.12. In designing a WPT system in the Fresnel region, the frequency of operation is a critical parameter which inﬂuences the design of a WPT system in the Fresnel region. A WPT system in the Fresnel region has not been presented in the literature operating in the K-band (18 GHz - 26.5 GHz). Operating at higher frequencies results in a smaller focal spot which can be created at larger focal distances. As the frequency is increased the Fresnel region extends to a larger distance, allowing focusing without increasing the physical size of the aperture. As a

45 proof of concept, we consider the K-band frequency regime which enables us to implement a Fresnel WPT system without significant fabrication and implementation cost. A systematic approach to the design of a Fresnel zone wireless power transfer aperture follows naturally from the basic principles of holography[19]. In this framework, a hologram is designed to form a focal spot at a desired location under the excitation of a reference wave. The hologram is formed by implementing a phase distribution that results from the interference of the back propagated focusing field and the field of the reference wave over a planar surface. From the perspective of antenna engineering, such a Fresnel-zone focusing aperture supports a field (or current) distribution that constructively interferes at a spot within the Fresnel zone. Over the years, various approaches have been proposed to realize such focusing apertures that can be dynamically reconfigured. One approach is that of phased arrays or electronically scanned antennas (ESA’s), which consist of arrays of independently tunable antenna elements. The amplitude and phase of each element can be varied to produce virtually arbitrary aperture field distributions, including those required for Fresnel focusing. Passive phased arrays make use of a single microwave source that is subdivided via a feed network to the radiating elements, each of which has a phase-shifter[55, 67]. This sets the phase of each radiating site, much like in the case of a phase hologram. ESA’s consist of arrays of transmit/receive modules, each containing a phase-shifter as well as one or more amplifiers, which enable arbitrary waveforms to be synthesized[54]. Use of such structures provides enough degrees of freedom to generate any desired aperture distribution; however, this comprehensive control comes at the cost of hardware complexity. In the passive case, the feed network can become complicated as the aperture size grows. In either the passive or active case, the cost, high power consumption of phase shifters and amplifiers, and other complications associated with arrays of active components can be barriers for

46 many potential applications[55, 67]. Particularly for narrowband applications, an alternative to phased arrays and ESA’s are quasi-optical lenses such as Fresnel zone plates[68, 69]. These plates are illuminated by a source in the near field of the aperture and are patterned to form a focal spot on the opposite side of the plate (in transmission mode). While the focal spots produced by this approach are promising, the device has a large form factor due to the use of free space propagation that may not be suitable in many scenarios. The architecture proposed in[69] also relied on mechanical motion to provide beam steering. More recently, near-field focusing plates and leaky-wave antennas have been proposed and have experimentally demonstrated the ability to generate focal spots[70, 71, 72, 73, 74, 75]. However, the operating distance of near- field focusing plates is usually limited due to the confined nature of the reactive near field. Most leaky-wave antenna designs generate a focal pattern consisting of a longitudinal electric field, which significantly complicates receiver design and does not have a favorable form factor[76]. In[70], a leaky-wave antenna was designed to generate a circularly polarized focal spot, but its ability to shift the focal point along the range direction was reliant on changing the driving frequency. Dependence on frequency to produce distinct radiation patterns severely complicates the source and detector circuitry. In a similar manner, the authors in[71] present a holographic radially polarized annular leaky wave antenna for near field focusing; however, the annular slots used in[71] do not offer an easy path to a reconfigurable aperture. Furthermore, similar to the device presented in[70], the generated focal spots consist of longitudinal electric fields, which complicates receiver design. Metasurface design concepts provide a simple and efficient avenue for realizing the desired hologram for focusing applications. One particularly attractive version of a metasurface antenna consists of an array of metamaterial resonators excited by a guided mode. Each metamaterial element leaks a portion of the guided wave

47 into free space[56]. The overall radiation pattern is thus the superposition of the contributions from each element. By properly designing the electromagnetic response of each metamaterial element (for example by altering their geometrical properties), waveforms with desired characteristics can be sculpted. Metasurface antennas[47, 77, 48] have low manufacturing costs and planar form-factors, making them suitable candidates for applications related to beam forming and wave front shaping. While arbitrary control over the phase and amplitude of each radiating element is not easily obtained in this metasurface architecture, sufficient control can be achieved to enable focusing using a variety of phase and/or amplitude holographic design approaches[78, 79]. Benefits of metasurfaces are also discussed in Chapter 2. In[19], the general concept of using metasurface holograms for focusing electromagnetic waves and wireless power transfer was investigated in detail. Here, we design and implement a holographic metasurface aperture that can generate focal spots at prescribed locations in the Fresnel zone. The proposed design is a dual-layer cavity, which consists of a holographic metasurface layer and a feed layer as depicted in Fig. 3.1. The reference wave of the hologram is the guided mode of the planar waveguide structure rather than a plane wave excitation, making the entire structure highly compact. A pattern of slots on the metasurface layer of the structure serves as the hologram, allowing microwaves to radiate out of the cavity and form a focus at desired locations. The holographic pattern is formed from the interference of the field from a hypothetical point source (located at the desired focal spot) backpropagated to the aperture plane, with the reference mode of the cavity. The hologram is realized by carefully positioning slots, placed in such a manner that the hologram field distribution is well approximated. When the slots are excited by the guided mode of the cavity, a diffraction-limited focus is produced at the position of the hypothetical point source. The dual-layer structure depicted in Fig. 3.1 is a well-known structure in antenna

48 engineering. It is usually referred to as a radial line slot array (RLSA) and its characteristics and design process are well established in the literature[80, 81, 82]. Single and dual layer designs have been presented, both of which have mainly been used to generate a highly directive far field beam at desired directions. These designs were initially proposed for satellite communication. We utilize the RLSA configuration here because it ensures high aperture efficiency; the RLSA has a converging wave pattern which balances the substrate/radiation losses to create a more uniform aperture distribution[80, 81]. The high efficiency of the RLSA can be contrasted with that of a single parallel plate waveguide, in which the outward-traveling cylindrical wave rapidly decays as a function of radius and excites only a small portion of the aperture. The dual layer structure used here effectively provides a circumferentially uniform feed, creating an incoming cylindrical wave. Furthermore, the rate of leak- age or coupling strength, of each element can be varied as a function of radius to harness further control over the energy radiated by the device[83, 84, 85, 86]. Such a tapering of aperture’s radiation sources can be used to reduce sidelobe levels. In this section, we describe the operation of the proposed dual-layer holographic metasurface and outline its design procedure. Full-wave simulations and experimental results confirming the proposed design and operation are presented. Samples with and without tapered coupling strengths are demonstrated and a reduction in sidelobe level as a result of tapering is presented. We also discuss the tradeoffs governing the size of the aperture and their impacts on the focal spot characteristics. The proposed design creates a focus with a linear polarization, but a focus in both polarizations could be achieved by patterning the hologram with different element orientations a prospect which is beyond will be examined in future works. While we present only passive designs here, we note that the proposed architecture is compact, planar, and can be made reconfigurable by introducing independently- addressable switchable components, such as diodes, into each radiator[50, 87]. The

49 passive holographic aperture, nevertheless, represents a step in the direction of creating a compact source aperture that can produce focused ﬁelds in the Fresnel zone one of the key components of the ultimate wireless power system envisioned in[19].

3.1.1 Dual Layer Metasurface Hologram Design 3.1.1.1 Uniform Focused Aperture

3.1 shows the cross-sectional and side view of the proposed cavity-backed metasurface aperture. The dual layer cavity design consists of a feed layer and a holographic metasurface layer. Microwaves are injected into the bottom plate through a coaxial adaptor and are coupled into the above metasurface layer patterned with carefully arranged radiating slots via an annular ring on the periphery of the cavity. The diameter of the entire structure is D. The annular ring connecting the two layers, as shown in Fig. 3.1 (a), has an inner diameter of DRing and the outer diameter is the edge of the cavity. This leaves a gap of (D - DRing)/2 from the metal wall, allowing the microwaves to be coupled from the feed layer to the holographic metasurface layer. The appropriate size for the annular ring was selected by running a parametric sweep to minimize reﬂection at the desired frequency of 20 GHz (|S11| ă -10 dB). The thickness of the waveguide is selected to be less than so that only a single mode is supported in the cavity-backed structure.

50 Figure 3.1: Illustration of the focused metasurface aperture a) cross-sectional view b) Side view

To design the focusing metasurface hologram, the first step is to select our desired focal spot located in the Fresnel region. To further simplify the problem, we want the fields at the focus to form a linearly polarized electric field along the y-direction. In the next step, we back propagate the fields from a hypothetical point source at the focal spot to the aperture to determine the fields on the hologram plane. The reference wave within the cavity is multiplied by the complex conjugate of the desired field distribution on the aperture to obtain a hologram, which ideally is a surface that adds a phase advance and attenuation to the reference field. Since the metasurface architecture we are employing here (a distribution of simple slots) does not allow for

51 independent control over the phase and amplitude at each point in the aperture, we focus on reproducing the phase distribution of the hologram, which predominantly governs the focusing performance of the hologram. The result of multiplying the point source fields with the reference wave inside the holographic metasurface layer (the inward cylindrical traveling wave) is thus a distribution of phase values that range between 0 and 2π. Our available phase values to realize this phase hologram are due to two factors: the guided mode and the response of each of the elements. Since the phase introduced by the slots is generally constrained to a narrow set of values, in the present design we only make use of the phase associated with the propagation of the guided mode. At locations where the phase difference between the desired focusing hologram and the guided mode is less than a threshold value a radiating slot is placed. Although the phase is utilized to form the hologram, we will later implement a taper on the aperture to create an amplitude window, which mitigates large sidelobe levels. In future works, the use of subwavelength metamaterial elements with dynamically tunable properties[50, 87] can enable further control over the phase and magnitude distribution on the aperture. Elongated slots are used as radiating elements in the metasurface aperture in this section. Such elements guarantee that the radiated fields exhibit the desired linear polarization. Given the subwavelength width of the slots, they can be modeled as magnetic dipoles polarized along their lengthwise axis[36, 88]. As a result, only magnetic fields parallel to the length dimension can excite the slots. Given our goal to form focal spots with a y-polarized field, we only use the x component of the magnetic field of the reference wave (inward traveling cylindrical wave) in our calculations of the hologram. The x component of this field is given by the Hankel function of the first kind (assuming convention)[45]:

1 Hx “ H1 pkρqcospφq (3.1) 52 where , k is the wavenumber within the waveguide, and is the azimuth angle in

the aperture plane (x-y) measured from the x-axis (see Fig. 3.1) and ρ “ x2 ` y2. Considering the center of the aperture as the origin of the coordinate system,a a point source located at will generate ﬁelds on the aperture, which are given by

? ik x x 2 y y 2 z2 e p ´ 0q `p ´ 0q ` 0 Epx, y, 0qα (3.2) 2 2 2 px ´ x0q ` py ´ y0q ` z0 The reference wave is divideda by the fields from the point source on the aperture plane, E, to produce a hologram which, when stimulated by the inward traveling cylindrical wave, will result in a diffraction-limited focused spot at the location . Since our goal is to generate a phase hologram, we only insert slots in the hologram at locations where the phase difference is below a tolerance, as found from

U “ =Hx ´ =Epx, y, 0q (3.3)

In the calculation of the current hologram, phase differences less than the threshold radians are considered acceptable. At positions satisfying this criterion, a slot is introduced along the x-axis. The threshold value was selected by trial and error to properly approximate the desired aperture field distribution. A higher threshold value would result in defocusing due to imperfect constructive interference at the focal point; a lower threshold value would increase the phase accuracy of the hologram but can result in too few slots on the metasurface layer, causing higher sidelobe levels and aliasing. Using the calculated hologram (U) after thresholding, an illustration of the slot locations required to generate an on-axis focal spot is shown in 3.1 (a). Though phase is traditionally more important in hologram design, the amplitude distribution across an antenna aperture is known to have significant effects on beam width and side lobes levels[45]. For a focused aperture, it is important to have all the power focused in the main beam or main lobe. Reduction of the sidelobe levels

53 in aperture design is a well-known problem, which can be overcome by using tapering of the coupling strength of the slots to the reference wave through varying the element geometry. The coupling distribution in a phase-only hologram metasurface aperture design would be flat; all the elements are identical and couple the same percentage of incident power to free space. To reduce the sidelobe levels, we can apply a taper to the coupling distribution, which will directly affect the effective magnetic surface current distribution on the aperture. The coupling distribution we consider here has lower coupling at the edge of the aperture and gradually increases as we approach the center of the aperture. This tapering resembles the well-known triangle tapering in antenna engineering. If the elements near the edge have greater coupling strength, the reference wave will be depleted before reaching the central elements causing aliasing and higher sidelobes. It is also important to make sure the coupling is not too small overall because the guided mode would not decay before it reaches the center of the aperture (causing the guided wave to significantly vary from the model in Eq.3.1 . It is important to emphasize that a more intelligent design can be found if the complete interactions between the slots and the guided wave is incorporated in the design model. This problem, which can be vital to designing electrically large holograms, will be addressed in future works.

54 Figure 3.2: a) Coupling distribution for the aperture with and without taper b) Power radiated for diﬀerent slot dimension (inset: unit cell schematic).

3.1.2 Tapered Focused Aperture for Lower Sidelobes

To fabricate the metasurface focusing apertures, we patterned the desired collection of slots on the top copper layer of a one-sided, copper-clad Roger 3003 substrate using a U3 LPKF laser milling system. Fig.3.3(a) and Fig.3.3(b) shows the assembled design. The metasurface and the feed layers are aligned along their edges. The edges are covered using copper tape, to provide a cavity structure and clamps are employed around the aperture’s edge to ensure that there is no gap between the two layers. While this is suﬃcient for the proof-of-concept structures presented here, future devices can use binding mechanisms to attach the two layers together.

55 Figure 3.3: Assembled fabricated sample with copper tape covering the edges (a) on-axis untapered (b) tapered aperture.

To measure the field radiated from the metasurface aperture we used a planar near-field scanning system (NSI 200 V3 x 3). The near-field scan of the aperture is performed at the focal plane (located at z0=10 cm) using a WR-42 open-ended rectangular waveguide. The field measurement in this manner can be used to generate the fields everywhere in the Fresnel zone and far field of the aperture[42]. For example, to produce fields at a different distance, we first back propagate the measured near field scan to the aperture plane and subsequently forward propagate to all locations in the range. We first examine the field profile at the focal plane (z0=10cm) in the cross-range direction. This field intensity is plotted in Fig. 3.3 for different structures and for three different cases: analytical, simulated, and experimental. In the analytical case, we model the slots as magnetic dipoles whose complex ampli- tudes are determined by the x-component of the guided magnetic field, as described in Section II[36]. The fields from the slots are then propagated and summed to determine the fields in the focusing region. We note that the decay of the guided

56 wave due to the radiation from the slots is not modeled in our current analytical calculations. The mutual coupling between the slots, which is also not accounted for in the current analytical modeling, may have additional small effects on the focal properties. This interaction and the decay of the guided wave due to radiation from the slots will be accounted for in future works by incorporating a self-consistent dipolar formulation[88, 89, 47]. The simulated case represents the fields from the designed aperture using the commercial full-wave solver, CST microwave studio. The experimental plot corresponds to the results obtained using post-processing of near field scanned data (as outlined above). Examining the cross-range plots in Fig. 3.4 (a-f), a focal spot is evident in both the tapered and the untapered designs. Fig. 3.4 (a-c) represent the design without tapering, where it is evident that the experimental results exhibit higher side lobes when compared to the analytical results. To reduce the sidelobe levels the coupling distribution described in Fig. 3.2(a) is applied and the resulting reduced sidelobes are seen in Fig. 3.4 (e-f).

57 2 Figure 3.4: Normalized |E| patterns at z0 =10cm for tapered and uptapered designs respectively: analytical (a, d), CST (b, e), experimental (c, f).

Next, we present the 1-D point spread function analysis of the analytical, simulated, and experimental results to quantify the focusing capabilities of the designed holographic metasurface apertures. The resulting 1-D focal patterns are plotted in Fig. 3.5(a) along the x direction. Close agreement is seen between the experiments and simulations, verifying the proposed design for both the tapered and untapered designs. The sidelobe levels for the tapered design in simulation and experiment are seen in Fig. 3.5(a) (dotted lines) and are considerably lower compared to the untapered design (solid lines). The beam waist for the tapered design is slightly increased compared to the untapered design, which is a known and inevitable consequence for tapered apertures. An increase in the beam waist can be acceptable as the sidelobes have been substantially reduced, resulting in more power being concentrated in the main focus.

58 Table 3.1: Spot size values (cm) using Gaussian optics, analytical, CST and experimental for on-axis focused metasurface aperture for Untapered and tapered designs

Gaussian Optics Analytical CST Experiments Spot Size (Untapered) 2 2.3 2.3 2.2

Spot Size (tapered) 2 2.4 3.1 3.15

Table 3.1 provides a comparison of the spot size values obtained with the diﬀerent methods for both the tapered and untapered design. The 1{e2 points obtained from Fig. 3.5(a) (black horizontal dotted line) corresponds to the spot size of the metasurface aperture. The predicted focal spot obtained from using the Eq. 2.7 for the untapered design using the the aperture dimensions, focal length, and wavelength of operation.

Figure 3.5: Normalized 1-D electric ﬁeld intensity patterns of untapered and tapered metasurface apertures (a) Cross-range (b) Range

59 From the cross-range analysis shown in Fig 3.5(a), it is evident that the desired

focus is obtained at the desired focal plane z0. We now analyze the fields in the range direction (along the optical axis). The experimental graphs are obtained by post processing of near field scanned data as outlined before. The 1-D range plots for the different structures (tapered and not tapered) and for the three different methods are presented in Fig. 3.5(b). The range plots are shown for distances larger than 3

cm (2λ) from the aperture because the fields close to the aperture (ă 2λ) contain evanescent components that are not considered in the analytical model and measured data[43]. We see that the fields generated by the hologram interfere constructively along the range to form the prescribed focus. However, the range plots in Fig. 3.5(b) reveal the fact that the peak intensity in the range does not occur at the intended focal plane (denoted by the black vertical dotted line). Several other authors[90, 91] have noted this expected phenomenon. When a reference wave is diffracted by an aperture of finite dimension the point of maximum intensity is often not located at the intended geometrical focus but is closer to the aperture a phenomenon commonly referred to as focal shift[90, 91]. In order to better understand the effects of the finite aperture size, let us denote s(x, y) as the ideal aperture field or hologram

(produced by the hypothetical source at F(x0, y0, z0) . This ideal aperture ﬁeld distribution is truncated by the ﬁnite size of the metasurface, denoted by t(x,y),

where t(x,y) = 1 for x2 ` y2 ă D{2 and is zero otherwise. The ﬁelds in the spatial frequency domain area given by the convolution Spkx, kyq b T pkx, kyq , where S is the ideal angular spectrum, T is the aperture angular spectrum and b indicates the convolution operation. As a result, only certain spectral components are transmitted and the components truncated by the ﬁnite size of the aperture will result in the shift of the focus towards the aperture. This explanation means a larger aperture would result in a smaller focal shift. To better quantify this problem in the design process, a unitless parameter called the Fresnel number can be considered[43]. The Fresnel

60 2 number of a system with the largest dimension (D) is given by N “ D {λz0. In the current design, the Fresnel number N is equal to 6.66 which is considered relatively low[91]. In future works, the diﬃculties associated with small Fresnel number can be overcome by using a larger aperture or by operating at higher frequencies. It is also worth noting that the tapering slightly deteriorates the focal shift. This is expected from the analysis above; for a tapered aperture, t(x,y) is not 1 uniformly, which results in further ﬁltering of the spatial components.

3.1.3 Uniform Eﬃcient Focused Aperture for Lower Sidelobes and Higher Radiation Eﬃciency

Excerpts of the following discussion can be found in the manuscript Efficient Holo- graphic Focused Metasurface Aperture by Gowda et al. (2019) submitted to IEEE Access. To reduce the sidelobe levels, a tapering distribution was introduced resulting in lower sidelobe levels was studied in the previous section, but the radiation efficiency of the aperture was 54%, which is considerably low required for any wireless system. As a result of tapering, the spot size generated by the focused aperture is also increased. As a result of the increase in the spot size, the size of the receive antenna to increase the size to intercept the incident energy on the receiver. The slot is oriented in the horizontal direction along the component of the magnetic field (reference wave) exciting the slots.In order to keep a high total efficiency and lower side lobes, a different arrangement of slots which would result in single polarization of the fields at the focal plane is studied in this section. The unit cell consists of two slots, which are oriented in a specific arrangement, which would result in linear polarization and results in better usage of the aperture. The simulated total efficiency of the aperture is high („ 87%) and the sidelobe level is below -10 dB which is shown in Table 3.4. Full-wave simulations and experimental results confirming the proposed design and

61 operation is presented in this section. Similar to the previous section, In order to design a focused metasurface hologram, we need to first calculate the fields required to be on the aperture that would result in a focal spot located in the Fresnel region. The hologram is generated by multiplying the reference wave inside the cavity with the complex conjugate of the fields required on the aperture. The proposed structure is designed to form a linearly polarized electric field along the x-direction. In the design presented in the previous sections, the slots were oriented such that the electric field at the focal plane was polarized along the y-direction. Similarly, to realize the polarization of the electric field along the x-direction, the slot arrangement needs to be vertical as shown in Fig. 3.6(b). The major disadvantage of realizing an aperture with the horizontal or vertical arrangement of the slots is, there are parts on the aperture which dont contribute to the radiation pattern because the reference wave would not couple to the radiating elements. This would result in reducing the effective area utilized on the aperture leading to higher sidelobes at the focal plane. A tapering distribution to reduce the sidelobes is implemented, but the radiation efficiency of the aperture reduces drastically resulting in exploring mechanisms where the radiation efficiency and the sidelobe levels can be optimized. Slot pairs arranged in a certain pattern where all the fields from the slots are coupled to a single linear polarization is used as radiating elements in the metasurface aperture considered in this section. The pair of slots is arranged such that they

˝ ˝ are separated by λg{2 which is equivalent to the phase difference of 0 or 180 . Individually, the slots would generate electric fields in both the polarization (x and y) because of the cylindrical orientation of the slots. However, when the pair of slots are considered together as a single radiating element, the vector sum of the electric field generated from each slot produces a linear polarized electric field at the focal plane (x-direction). Eq.3.4 obtained from [92] gives the mathematical description

62 required to obtain the arrangement of the pair of slots on an aperture. This idea was first pioneered in apertures, which were used for satellite communications to reduce the reflections caused inside waveguides leading to lower radiation efficiency and sidelobes. By using an arrangement of slots as shown in Fig. 3.6 (b), the effective area of the aperture is increased when compared to the design presented in [66] using the slot arrangement shown in Fig. 3.6 (a). These radiating elements guarantee the radiated fields to exhibit the desired linear polarization. Elongated slots arranged in a certain pattern where all the fields are coupled to a single polarization are used as radiating elements in the metasurface aperture considered in this section. By using such an arrangement of slots, the effective area of the aperture is increased when compared to the design presented in [92]. For the final radiation to combine to produce linear polarization, the slot excitations of phases need to differ by 0˝ or 180˝. Below equations obtained from [92] is used to obtain the slot arrangement. This idea was first pioneered in apertures, which were used for satellite communications to reduce the reflections caused inside waveguides leading to lower radiation efficiency and sidelobes. Such elements guarantee the radiated fields to exhibit the desired linear polarization.

π φ φ θ “ ´ , θ “ ´ (3.4) 1 2 2 2 2

63 Figure 3.6: Slot arrangement on the aperture a) previous design b) current design

The magnetic ﬁeld of the reference wave which is an inward traveling wave is the calculation of the hologram is given by the Hankel function of the ﬁrst kind (assuming convention):

1 Hguided “ H1 pkρq (3.5)

The complex conjugate of the ﬁelds from the point source on the aperture plane as shown in Eq. 3.2, E*, is multiplied with the reference wave to produce a hologram which, when stimulated by the inward traveling cylindrical wave, will result in a diﬀraction-limited focused spot at the location . Since our goal is to generate a phase hologram, only the phase distribution, as found from

U “ =Hguided ´ =Epx, y, 0q (3.6)

The overall structure is a 3 layer design consisting of the holographic metasurface layer, followed by the middle metal layer (annular ring) and feed layer is illustrated in Fig 3.7.

64 Figure 3.7: Layer by layer illustration of the Holographic Metasurface aperture used as the transmitter .

3.1.3.1 Role of the Inward Traveling Wave

As discussed earlier, the primary reason behind using inward traveling cylindrical wave is its ability to compensate for the loss of the guided wave due to radiation. In some previous works, it was suggested that this condition can only be satisfied in substrates with dielectric constant between 1.5 to 2.5 [92]. Here, we propose to use the coupling strength of the radiating element as a means to modify the amplitude profile without any limitation on the substrate choice or element distribution (which dictates the phase profile). We begin by examining the power radiated by a slot pair in a parallel plate waveguide using CST simulations, as shown in Fig. 3.8. The parallel plate waveguide is excited by a cylindrical source (e.g., a coaxial connector) at the center and perfect matched layers terminate its periphery. This simulation allows us to examine the overall coupling of the slot pair (i.e. decay of the guided wave due to its radiation). The phase of the guided wave (Hφ) is also depicted in

65 Fig. 3.8.

Figure 3.8: Simulation setup for calculating power radiated by diﬀerent elements at two distinct locations: φ “ 0˝, φ “ 90˝ (Slot pair used for illustration). .

First, we confirm the proposition that the power radiated by a slot pair configuration is indeed linearly polarized. To this end, we have calculated the power radiated in both the co-polarization (co-pol) and cross-polarization (cross-pol) as a percentage of the incident power on the element at two different locations on the aperture (φ “ 0˝ and φ “ 90˝) as shown in Fig. 3.8. For this simulation, we have used a substrate with a dielectric constant r “ 2.2 and tan δ “ 0.0009 (similar to the one used later in experimental studies). The incident power Pinc on the slots pair is calculated by multiplying the accepted power by the coaxial connector, Pacc, with the angle subtending the element, ∆φ, as denoted in Fig. 3.8 (for more information,

66 see Appendix B of [93]):

∆φ P “ P . (3.7) inc acc 2π

pol The radiated power in each polarization Prad is computed by CST (pol can be co-pol or cross pol). For comparison, we have done this study using both a single slot and a slot pair, results are shown in Fig. 3.8.

As shown in Table 3.2, when the element is placed at φ “ 0˝, both the single slot and the slot pair radiate similar and suﬃcient power in the co-pol, while they both radiate minimal amount of power in the cross pol. However, when the radiating element is placed at φ “ 90˝, the coupling of the single slot is minimal since it is orthogonal to the exciting magnetic ﬁeld. In contrast, the slot pair generates the desired co-pol radiation with the radiated power close to that observed when the element is at φ “ 0˝. The radiated power into the cross polarization from the slot pair is minimal in this location as well. It is worth noting that for all locations in between these two extreme cases, the power radiated by either elements is between the values reported in Table 3.2.

Table 3.2: Power radiated in Co-Pol and Cross-Pol, reported as percentage of incident Power on the corresponding element.

φ “ 0˝ φ “ 90˝

Co-Pol Cross-Pol Co-Pol Cross-Pol

Single Slot 13.86 0.02 0.76 0.24

Slot Pair 13.95 0.03 11.65 2.3

Next, we examine the possibility to modify the amplitude proﬁle across the hologram and consequently tailor the characteristics of the focus. Among various aspects

67 of the focus, ensuring low SLLs is critical for focusing applications and we set our objective to realize low SLLs. High SLLs occur when the radiated fields closer to the edge are higher than the ones near the center. This happens when the increase in the field density of the inward traveling wave cannot compensate the decay due to radiation from slot pairs. Using the results in Table 3.2 as our guide, we can see the maximum of radiation losses happen when φ “ 0˝. We then define a design parameter ∆p that accounts for the percentage of the inward traveling wave that passes through a slot pair without being radiated. Mathematically, this parameter can be described as: P ´ P pol ∆p “ inc rad . (3.8) Pinc The values reported in Table 3.2 are essentially 1 ´ ∆p for different elements in percentage. As the wave traverses from the outermost ring, located at r, and arrives at the second ring, located at r ´ ∆r, the power incident on the slot pair increases by

r r´∆r due to the inward traveling wave—this is based on the assumption that r is large enough that we can use large argument approximation for the Hankel function describing the reference wave. To realize low SLLs, we need to ensure that the inward traveling wave compensates the power decay due to radiation losses, i.e.

r ∆p ą 1. (3.9) r ´ ∆r

In our design, ∆r is usually on the order of a guided wavelength (λg). It is worth noting that according to Table 3.2, we only need to compute this ratio for the element at φ “ 0˝, where the power radiated is strongest. Furthermore, if we guarantee the condition provided in (3.9) for the outermost elements, it automatically ensures it for all other elements located at inner rings. In this manner, we guarantee the aperture ﬁeld distribution is relatively uniform, ensuring low SLLs. It is also worth

68 emphasizing that (3.9) provides us with a design mechanism: for a given substrate and phase profile, we can manipulate the slot’s lengths to ensure the desired amplitude profile. This proposal is verified in the next section by examining a substrate with a large dielectric constant.

3.1.3.2 Full-Wave simulation results

First, we demonstrate that our proposed condition, (3.9), guarantees low SLLs. We design an aperture using a substrate with dielectric constant of 4. This value is out of the range of 1.5-2.5 suggested by [92]. We design this structure to operate at 20 GHz. Considering the limitations of simulation time, the aperture size (D) was chosen to be a modest 10 cm in diameter. The resonant frequency (« 23 GHz) of the slots was intentionally selected to be shifted from the operating frequency (20 GHz) so that the elements are weakly coupled to the guided mode. Highly resonant elements can perturb the guided wave, which would violate our design assumptions. The slot length and width corresponding to this resonant frequency are 4.2 mm and 0.5 mm, respectively. Using the design procedure outlined in Section II for a phase hologram, this structure is designed and simulated using CST. The resulting focal pattern is shown in Fig. 3.9 (a). It should be emphasized that the apertures examined throughout this manuscript have relatively low Fresnel number which leads to a phenomenon called focal shift where the peak intensity is not at the intended focal plane. This phenomenon is well studied in literature and an explanation is not repeated here [90, 91, 66, 46]. While the focus for the designed aperture is evident in Fig. 3.9, we can see high sidelobes. If we compute the ratio given by (3.9) for this structure it is 0.94, which is below 1 (see Table 3.3 ). This can be explained by noting the fact, as the substrate dielectric constant increases, the spacing between the rings, (∆r « λg), decreases. As a result, the compensation of the guided wave ﬁeld density due to the convergence

69 decreases. To combat this issue, as proposed in the previous section, we need to design elements with lower coupling, i.e. higher ∆p. To do this, the slot length is varied until the desired level of ∆p is achieved and we meet the condition of (3.9). The new slot length is 3.85 mm (which is resonant at around 24 GHz). The exact values for the design ratio is presented in Table 3.3. This slot length is then utilized to implement the holographic aperture. The simulated focal pattern generated by this design using CST is also shown in Fig. 3.9, clearly exhibiting lower SLLs compared to the case where the design condition (3.9) was not satisﬁed. The lower limit in the cross range plots shown are set to 0.1 (corresponding to ´10 dB) to further highlight the low SLLs. The results in Fig. 3.9 clearly verify the importance of the condition given by (3.9) in designing the focusing holographic metasurface.

Figure 3.9: Normalized focal patterns of an aperture from CST simulations with an r “ 4. SLL condition given by Eq. 3.9 (a) not satisﬁed. (b) satisﬁed.

3.1.3.3 Low-loss substrate

In the previous subsection, we used a substrate with high dielectric constant to demonstrate the importance of our proposed design condition in realizing low SLLs. In this subsection, we design the aperture using substrates that are practically avail-

70 able. In doing so, we also illustrate the utility of the proposed slot pair in increasing aperture efficiency. Toward this goal, we fist design an aperture similar to that of [66]. All the parameters, such as focal length, 10 cm, diameter, 10 cm, and operating frequency, 20 GHz, are the same with the key difference being the use of a slot pair instead of a single slot [66]. Using the procedure outlined in Section II, we have designed the aperture and simulated it using CST using a low loss Rogers 5880 substrate. The efficiency of the designed aperture with slot pairs as radiating elements, in comparison to the ones reported in [66], is listed in Table 3.4. In the designs used for Table 3.4 the reflection coefficient (S11) has been kept below ´10 dB by running a parametric sweep of the size of the annular gap [66]. The total efficiency reported in Table 3.4 is calculated by multiplying the aperture efficiency and the focal efficiency. The aperture efficiency obtained from CST simulations which includes the reminiscent impedance mismatch. The focal efficiency is defined as the ratio of the power concentrated at the focal spot (an area of 2.25 x 2.25 cm2 is considered) to the power at the entire focal plane.

Table 3.3: Design parameters pertaining to SLLs condition, (3.9), for diﬀerent substrates.

r “ 2.2 r “ 4.0 r “ 4.0 (case 1) (case 2)

∆p 0.85 0.80 0.87

r r´∆r 1.25 1.176 1.176 r r´∆r ∆p 1.062 0.94 1.023 Slot length (mm) 4.8 4.2 3.85

Examining Table 3.4 it is evident that the proposed design utilizing slot pairs exhibit much higher eﬃciency, while keeping the SLL low. While the tapered design of [66] also has a low SLL, it has a fairly low total eﬃciency in contrast to the

71 Table 3.4: Simulated eﬃciencies (aperture, focal and total), SLL and r for diﬀerent focused Apertures Uniform [66] Tapered [66] Uniform Uniform

(single slot) (single slot) (slot pair) (slot pair)

r 3.0 3.0 3.0 2.2

ηaperture 77.1 54.2 84.5 87.6 (%)

ηfocal (%) 43.2 50.7 53.2 55.1

ηtotal (%) 33.3 27.5 44.9 48.3

SLL (dB) ´6.77 ´15.22 ´12.70 ´12.01 design presented here. This is due to the fact that the tapering in [66] was designed without taking into account the polarization of the converging feed wave, and some radiating elements were selected to have very low radiated power. By taking into account the converging feed wave, we have designed the aperture amplitude profile that guarantees low sidelobe level, while maintaining high overall aperture efficiency. In Table 3.4, we can also identify that the improvement achieved in overall efficiency is accomplished by using slot pairs and a lower loss substrate. Since our ultimate goal is focusing and transfer of power, low losses are crucial. As a result, we redesigned the aperture using a substrate that has lower losses, i.e 1.524 mm thick Rogers 5880 substrate with r “ 2.2 and tan δ “ 0.0009. The radiating slots are selected to be resonant at 23 GHz, which for r “ 2.2, results in slots with length and width of 4.8 mm and 0.5 mm, respectively. Using the procedure outlined in Section II, this aperture was designed and simulated using CST. The simulated total efficiency for this design is also reported in Table 3.4 where we can see that using a lower loss dielectric has further increased the total efficiency. Next, we examine the simulated focal pattern, as shown in Fig. 3.10 (a). A

72 clear focal spot with low SLLs is evident. This is consistent with our predictions from Table 3.3 that such a slot pair satisﬁes our design condition for low SLLs (see. (3.9)). It is also worth emphasizing that, as shown in Fig. 3.10 (a), the designed aperture forms the focal spot with the desired polarization and the radiation into cross polarization is minimal.

73 Figure 3.10: 2-D Normalized |E|2 Simulated (a) Co-Pol (b) Cross Pol, Experimen- tal (c) Co-Pol (d) Cross Pol. e) 1-D for 10 cm (bold) 20 cm (dash).

74 3.1.3.4 Experiments

In this section, two diﬀerent samples of the focused metasurface aperture are fabricated and experimentally examined. To fabricate each sample, the designed hologram was patterned onto the top layer of a double-sided copper-clad Roger 5880 substrate using a U3 LPKF laser milling system. The feed layer was also fabricated in a similar manner. The two waveguides were stacked on top of each other and copper tape was used to realize the periphery walls. The top, middle and the bottom layer of the sample with diameter 10 cm is shown in Fig. 3.11 (a-c) and another sample with diameter 20 cm is shown in Fig 3.11 (d). First, we examine the aperture with D = 10 cm. The measured reﬂection coef-

ficient, |S11|, of the focused aperture was below ´10 dB at the operating frequency. The fields generated at the focal plane are measured by performing a near-field scan of the aperture at a distance of 5 cm. The near field scan data was then propagated to the focal plane using a plane-to-plane propagator [42]. The experimental focal pattern computed in this manner is reported in Fig. 3.10 (c), in comparison to the simulated one in Fig. 3.10 (a)–the two results exhibit close agreement. We have also measured the power radiated into the cross polarization, as shown in Fig. 3.10 (d). Evidently, the aperture focused the power into the desired polarization. The slightly higher radiation into the cross polarization in the experimental results can be attributed to fabrication tolerances. In Fig. 3.10 (e), 1-D cross-range plots of the simulated and experimental focal spots are depicted. Excellent agreement between the two is observed, verifying the proposed design and operation. To highlight the low SLLs, a dashed line marks the

´10 dB level in Fig. 3.10 (e).

75 Figure 3.11: a) Top layer b) Middle layer c) Bottom layer of a focusing metasurface aperture (D “ 10 cm) d) assembled fabricated aperture (D “ 20 cm).

Table 3.5: Spot Size calculated using Gaussian optics formulation, CST simulations, and experiments. Gaussian optics CST Experiments

D “ 10cm 2.15 cm 2.2 cm 2.25 cm

D “ 20cm 1.21 cm 1.35 cm 1.45 cm

Table 3.5 provides a comparison of the spot size values obtained from Gaussian optics [19], CST, and experiments. In our calculation using Gaussian Optics, we used the outer ring diameter as the aperture size (D). The 1{e2 points on the cross- range plot in Fig. 3.10 (e) are used for the calculations of the experimental spot size.

76 Clearly, the experimentally measured values closely resemble the simulated ones, as well as the predicted values from Gaussian optics. In most applications, there are harsh constraints on the size of the receiving aperture. To realize a smaller focal spot while also demonstrating the generality of our proposed design and operation, we have also designed a 20 cm aperture to generate a focal spot at 10 cm. The cross-range plot of the focal spot generated by this aperture is also shown in Fig. 3.10 (e) (indicated by the dotted lines). We clearly see a smaller focal spot, while the SLL has stayed below the ´10 dB value. The focal spot examined in this paper is at a distance of 10 cm. Larger distances are desired in some applications. For such scenarios, we need to utilize larger physical apertures or higher frequencies (larger electrical size). However, full-wave simulations of such large structures with large focal distance may be prohibitively time and memory consuming. The close agreement presented in Fig. 3.10 (e) demonstrates that the proposed design procedure can be readily scaled.

3.2 Receiver - Metamaterial absorber and Rectiﬁer Design and Ex- periments

Excerpts of the following discussion can be found in the manuscript Fresnel Zone Wireless Power Transfer using Metasurfaces by Gowda et al. (2019) close to be submitted in Nature Scientific Reports. In a general wireless power transfer system, a compatible receiving antenna is one of the integral parts in the system as shown in Fig. 2.12 and hence it becomes essential to design an efficient receiving aperture suitable for a WPT system. By knowing the transmitting aperture size, focal distance, and wavelength of operation, the spot size at the focal plane can be calculated. The absorber or receiving antenna is designed to have a physical dimensions slightly bigger than the size of the estimated focal spot to reduce the reflections between the source and the receiver

77 and to enhance the received power. A critical distinction between metamaterial absorbers[94] and metamaterial harvesters[95, 96] is that metamaterial harvesters require not only full absorption but also maximum power delivery to a load to ensure that the absorbed power is dissipated across the load. Most of the previous metamaterial absorber designs show that a lossy dielectric substrate[94] is an indis- pensable part of a metamaterial absorber (MMA) making it the main constituent responsible for dissipating the absorbed power. The size of the MMA resonator and spacing between the resonators are both electrically small, which makes the MMA resonator array fundamentally diﬀerent from a classical rectifying antenna array. In a conventional rectifying antenna array, the dimension of the element is generally comparable to a half free-space wavelength and the spacing between elements should be large enough to avoid the destructive mutual coupling between array elements.It has been shown in the literature that in contrast with a single resonator, an array of resonators with close proximity of each other will enhance the power reception [95].

3.2.1 Metamaterial Absorber-inspired Antenna Design

The receiving antenna to intercept the power radiated from the transmit aperture. Several designs consisting a single patch, patch array, a printed dipole and a focused aperture designed to focus at infinity was considered in simulations. For all the designs considered, the fields components in the range direction resulted in reflections causing standing wave pattern between the transmit and receive aperture leading to

low S21. An array of resonator placed at subwavelength spacing from each other can

enhance the power harvesting when compared to a single resonator [95]. The S21 of the system considering the transmit aperture and the absorber (RX aperture) showed an improvement of „ 50% compared to the other receiving apertures considered

78 earlier. The Fig. 3.12 shows the ﬁeld pattern along the optical axis for the patch array and the absorber. The size of the patch array was designed to match the physical size of the absorber along with a S11 below ´10dB at the resonant frequency. The standing patter for the patch array can be clearly seen as shown in Fig. 3.12(a) compared to the absorber shown in Fig. 3.12(b).

Figure 3.12: Electric ﬁeld along the propagation direction a) Patch array b) Ab- sorber

As a result, by considering an aperture which would intercept more power from the transmit aperture was necessary and hence the idea of metamaterial absorber antenna (RX aperture) was pursued. Recently, using the well-known metamaterial absorber concept [94], a metamaterial absorber as an energy collecting mechanism for electromagnetic energy [95, 96] was explored. The resonator element used is an ELC unit cell as shown in Fig. 3.13. The substrate considered is Rogers TMM

10i which has a high r. Full wave simulation in CST microwave studio with the necessary boundary conditions (depending on the ﬁelds shown in the Fig. 3.13) is carried out to have the resonance of the unit cell at the frequency of operation and high absorption. An array of resonator placed at subwavelength spacing from

79 each other can enhance the power harvesting when compared to a single resonator

[95]. The S21 of the system considering the transmit aperture and the absorber (RX aperture) showed an improvement of „ 50% compared to the other receiving apertures considered earlier.

For a given area, by using a material with higher r and considerably low tan

δ enables us to have more elements in the array compared to a lower r. In addition, having a high r “ 9.8 will also result in an electrically large structure and also matching the impedance of the structure to free space which would result in lesser reﬂections and thereby increase the power incident on the absorber. A study to ﬁnd out the improvement in the power dissipated across the absorber using different dielectrics was conducted in CST and it showed an improvement of 25% if we considered TMM 10i substrate because the number of elements in given a physical area for a higher dielectric material would be high compared to a lower dielectric material.

Figure 3.13: Unit Cell

The absorber which is acting as an energy collector is diﬀerent from the conventional absorber which transferred the incident energy into thermal energy by making

use of a relatively lossy substrate like FR4. A terminal resistor (RL) is connected

from the via to the ground plane which was tuned to get the optimal S11 for the

80 structure. The power dissipated across the load (RL) was found to be 96.7% while the remaining 3.3% was lost in metals and dielectrics combined as shown in Fig 3.14b. The absorption, reﬂection, and transmission calculated from the formula A+R+T =

2 1 is shown in Fig 3.14a. Absorption is given by 1 - |S11| while the refection is given

2 by |S11| and the transmission is 0.

Figure 3.14: Unit cell properties as a function of f in GHz a) Absorption, Reﬂection and Transmission plots b) Power across load, Metal and Dielectrics.

The absorber inspired receiver consisting of sub wavelength resonators is designed in an 8x8 array form as illustrated in Fig.3.15. It should be noted that the vias are not included in the illustration shown in Fig.3.15. The physical dimensions of the absorber are 2.3 cm x 2.3 cm. With the unit cell elements designed to have an array, we now design a combining layer which is a group of power diving and matching circuits based on micro strip transmission lines. All the currents from the via of each unit cell are added to a single 50Ω port which is later connected to a rectiﬁer. The ﬁrst substrate which has the subwavelength metamaterials on the top is TMM 10i having a thickness of 0.762 mm. The substrate for the combining layer is a low loss Rogers

3003 having r = 3 and tan δ of 0.001. The overall radiation eﬃciency including any mismatch loss of the structure in CST is 89% with a directivity of 14.2 dBi.

81 These antenna parameters indicate the performance from a transmit point of view, however by considering the reciprocity theorem, the same antenna can be considered

as a receiving aperture. The S11 of the structure is below -10 dB at the frequency of operation (20 GHz). The overall structure is a ﬁve layer design consisting of the metasurface layer, followed by the TMM 10i substrate, ground layer, combining low loss substrate and ﬁnally the RF combining layer as illustrated in Fig.3.15.

Figure 3.15: Layer by Layer illustration of the Metamaterial inspired absorber design

3.2.2 Rectiﬁer Design at K-Band frequencies

In the block diagram of the WPT system considered in Fig. 2.12, the rectifying circuit forms the ﬁnal component. Most rectenna elements and rectenna arrays are developed for frequencies below 15 GHz. Rectennas operating at millimeter-wave

82 frequencies have the advantages of compact size and higher overall system efficiency for long distance transmission. However, only a few rectenna elements are reported for millimeter-wave operation [53]. The overall performance of a WPT system is normally determined by the efficiencies of the apertures and the rectifier circuit. The configuration described in Fig. 3.16[97] for the rectifier generating higher DC voltage levels for the same input power when compared to the a single diode configuration (Half-wave topology). A general schematic circuit diagram of the circuit consisting of a 10 pF capacitor followed by the matching circuit, the diodes (D1 and D2) and the load (RLoad) is shown in the Fig.3.16. In order to realize an efficient rectifier, having a good matching network becomes increasingly important. A parametric study was conducted to obtain the matching circuit in order to maximize the power delivered to the load and minimize the transmission loss. The input of the rectifier is connected to a 50Ω port which is connected to the 50Ω port on the RX aperture by a through connector.

Figure 3.16: Schematic of the rectiﬁer circuit

The choice of an appropriate diode is crucial at higher frequency and must be done carefully in the design of a high-efficient rectifying circuit. This is because the diode is the main source of losses and its performance impacts significantly the performances of rectennas.Three key parameters of the diode impact the RF-to-DC conversion efficiency.The series resistance (Rs) limits the efficiency through the dissi- 83 pation losses, the zero-bias junction capacitance (Cj0) affects the harmonic currents through the diode and the breakdown voltage (VBR) limits the power handling capability of the rectifier. Keysight ADS software was used to design the schematic and layout for the rectifier using the MACOM MA4E1317 diode [97]. All the diode parameters obtained from the technical document is supplemented into the diode model which is later used in the simulations. The diode was chosen because of its low series resistance resulting in lower dissipation losses. Since the frequency of operation is high, the rectifier design cannot be completely relied only on schematic simulations. ADS momentum is a planar EM solver used for passive circuit modeling. It makes use of frequency-domain technology to accurately simulate complex

EM eﬀects including coupling and parasitics. The results of S11 vs frequency and

VLoad vs input power is shown in Fig. 3.17.

Figure 3.17: a) S11 of the rectiﬁer circuit in ADS b) VLoad varied a s function of Input power

The RF-DC efficiency is defined as the ratio of the power across the load to the input power to the rectifier.

ηRF ´DC “ PLoad{Pin

The load resistor is varied to ﬁnd the optimal voltage which would result in higher RF-DC eﬃciency. The optimized load resistor was 120 ohms and the input power

84 was 20 dBm (100 mW). With the voltage drop across the load being 2.75 V, the

RF-DC eﬃciency can be calculated to be „ 60 %. The highest RF-DC eﬃciency in the literature is around 63% [53].

3.2.3 Experimental Result of the Absorber and Rectiﬁer design

The experimental results of the absorber are compared with CST simulations with the top and the bottom layer of the metamaterial absorber is shown in the ﬁgure below. The size of the absorber is 2.25 cm x 2.25 cm in dimension which corresponds to the focal spot dimensions for a focused aperture of 10 cm in diameter designed to have a focus at 10 cm along the optical axis. A 50Ω co-ax connector is soldered to the bottom layer of the absorber as shown in Fig. 3.18.

Figure 3.18: Top and bottom layer of the Metamaterial Absorber

Fig.3.19 shows the S11 comparison plots between CST and experiments with values below -10 dB (black dotted line). There is a slight shift in the resonant

frequency, however the S11 has low reﬂections at the operating frequency as it below -10 dB.

85 Figure 3.19: CST and experimental S11 of the Metamaterial Absorber

The fabricated design of the rectifier is shown in the figure below. The substrate used for the rectifier design is a low loss Rogers 3003 board whose thickness is 20 mils in order to suppress the surface waves. The surface wave is generated when the energy is concentrated in the substrates causing losses due to radiation.

Figure 3.20: Fabricated Rectiﬁer Sample

The rectiﬁer was connected to a VNA and the power was increased to measure the voltage across the load. The plot of power vs voltage across the load is plotted

86 below and is very close in comparison with the simulated data. The s-parameters

(S11) are also recorded and is below -10 dB at the required frequency and matches very well with the simulated data shown in Fig.3.17(a).

87 4

Practical Implementation of the Fresnel Zone WPT System

In this chapter, a practical implementation of the Fresnel Zone wireless power system is considered by making use of Patch array antenna and Metasurface apertures in two separate sub sections. In section 4.1, a successful demonstration of wireless power transfer is demonstrated. However, such a structure usually results in complicated feed networks and not favorable in realizing an aperture required for dynamic focusing. As discussed in Chapter 2 and Chapter 3, focused metasurface apertures provide an eﬃcient path in realizing a dynamic aperture. In 4.2, a Fresnel zone WPT system is assembled and a successful demonstration of wireless power transfer is demonstrated by turning on a LED.

4.1 Using Focused Patch Array Antennas

Excerpts of the following discussion can be found in the manuscript Wireless power transfer in the radiative near ﬁeld by Gowda et al. (2016) published in IEEE Anten- nas and Wireless Propagation Letters.

88 The Fresnel region WPT implementation studied in this section makes use of two planar microstrip patch arrays, illustrated in Fig. 4.1, with a 8x8 array and a 4x4 array serving as Tx and Rx antennas, respectively. Both antennas were designed using low-loss 1.524 mm thick Rogers 4003 substrate. Investigating Fig. 4.1, it can be seen that different from the Rx antenna composed of edge-fed patches, the Tx antenna consists of inset-fed patches to better accommodate the varying length microstrip transmission lines. We designed the antennas to resonate at 5.8 GHz, a widely used industrial, scientific, and medical (ISM) band. From standard diffraction theory it is possible to obtain an estimate for the achievable focal spot size radius (SS) based on the antenna geometry, focal length, and wavelength of operation.

Figure 4.1: Patch array antennas (a) 8x8 Tx array (b) 4x4 Rx array (DTX =21.7 cm, DRX =16 cm).

Each of the patch elements must be tuned to radiate with a phase such that the collective interference pattern results in the desired focal spot. Computing the phase

89 difference (or time delay) for each of the radiating elements using the geometric length approach, one can achieve constructive field interference at a certain focal point, F(x, y, z), in the Fresnel region. To perform this design, we choose an arbitrary focal point along the optical axis (on-axis), Fon= (0 cm, 0 cm, 40 cm) and calculate the required phase distribution for the individual patch elements within the Tx antenna array shown in Fig. 4.1(a). The length of the microstrip transmission lines feeding the patches are adjusted accordingly to achieve focusing at Fon. When an antenna is designed conventionally, its parameters, such as antenna gain, half-power beam width (HPBW) and radiation efficiency, are defined in the far-field region. Although this work demonstrates Fresnel zone operation, it is still important to analyze these parameters to assess the performance of the Tx array. Full-wave simulations of the Tx antenna were performed in CST Microwave Studio. It was observed that the antenna has a gain of 23.1 dBi with a radiation efficiency of 86% and a HPBW of 7˝. Since the proposed WPT system operates in the Fresnel region, it is important to calculate the spot size or focus width for the focused fields produced by the Tx aperture. This is an important parameter for the design of the Rx antenna which will be discussed in the next section. From CST simulations, the -3 dB points (full width at half-maximum, FWHM) of the electric field produced by the Tx antenna at the focal plane is found to be 13.5 cm, providing a good estimate on the size of the Rx antenna needed to maximize transfer efficiency. The simulated and measured 1-D electric field plots to calculate the FWHM points are shown in Fig. 4.2. For measurement, we used a planar near-field scanning system (NSI 200 V 3 x 3).

90 Figure 4.2: 1-D plot of the simulated (dotted) and measured (solid) normalized electric ﬁeld magnitude plots at the focal plane.

An important aspect of the Rx design procedure is the optimization of the effective aperture size to maximally capture the power emitted from the Tx aperture. Ideally, the aperture size of the receiving antenna should be on the order of the FWHM width of the focused electric field produced by the Tx antenna. From the calculations of spot size in the earlier section, the receiving antenna was designed with dimensions slightly larger to intercept the fields outside the -3 dB region, reducing the spillover loss. We implement the Rx antenna using the 4x4 patch array illustrated in Fig. 4.1(b). The Rx antenna utilizes identical patches and element spacing as the Tx antenna, having the same resonance frequency of 5.8 GHz. The Rx antenna also has uniform amplitude and phase distribution across the aperture, radiating in the broadside direction. As mentioned earlier for the Tx array, although the proposed WPT scheme works in the Fresnel zone, full-wave far-field simulations of the Rx antenna were performed to analyze its radiation characteristics, providing a gain of 17.7 dBi with a radiation efficiency of 88% and a HPBW of 20.7˝.

91 An important component of a WPT system is the rectifier used for harvesting power. Once the transmitted RF signal is received by the Rx antenna, it must be converted to a DC load connected to the output terminal of the antenna. The combination of the rectifier with the antenna array is often termed a rectenna. We used Keysight ADS software to design a HWR circuit relying on the Schottky barrier diode HSMS 8202. We chose this diode due to its small threshold voltage and high rectifying efficiency in the 5.8 GHz band. A schematic circuit diagram of the HWR is shown in Fig. 4.3(a), and a microstrip implementation of the proposed HWR circuit is depicted in Fig. 4.3(b).

Figure 4.3: Half-Wave Rectiﬁer (HWR) (a) schematic (b) microstrip implementation.

We performed a parametric study of the HWR circuit, varying the values of circuit elements in ADS. The study results indicated the optimum discharge time was achieved with C1=10 pF and R1=1 kΩ. The impedance seen at the input of the Rx antenna is Zin = 50Ω while the input impedance of the diode is Zin=2-j40Ω (under 13 dBm input power). To maximize the power delivered to the load, we incorporated into the rectiﬁer board an impedance matching circuit as shown in Fig. 4.3(a). Fig. 4.3(b) depicts a microstrip implementation of the HWR. Starting from the RF connector, it consists of an open-stub used for impedance matching between

92 the diode and the Rx microstrip patch antenna array. The shorted stub within the matching network provides a DC path to the ground. The diode is connected to the end of the main transmission line, followed by an RC load. Not shown in the ﬁgure

is the LED connected to the output terminal of the HWR (replacing R1), serving as a DC load. To fabricate the Tx and Rx patch arrays, as well as the HWR microstrip circuit, we patterned the desired structures into the top copper layer of a double-sided copper- clad Roger 4003 substrate using a U3 LPKF laser milling system. The radiation eﬃciencies of the Tx and Rx array antennas were also measured using the NSI near- ﬁeld scanning system, and reported to be 85% and 87% respectively, providing good

agreement with the simulation results. The reﬂection coeﬃcients (S11) of the Tx and Rx antennas are shown in Fig. 4.4. From Fig. 4.4, we observe the simulated and measured S11 patterns are in good agreement. The slight shift between simulation and measurement can be attributed to over-etching of the printed circuit board

(PCB) during the fabrication process. Fig. 4.4 also shows the S11 of the fabricated HWR (under 13 dBm input power), which is below -10 dB at 5.8 GHz, conﬁrming the accuracy of the matching circuit.

93 Figure 4.4: Simulated (dashed) and measured (solid) |S11| (dB) patterns for Tx and Rx antennas, and HWR.

In a near-zone WPT scenario, the receiver may be positioned off of the optical axis of the Tx aperture. Therefore, it becomes necessary to demonstrate both on- and off- axis field focusing for WPT applications. We designed and fabricated two separate Tx apertures to achieve both on-axis and off-axis focusing (using the geometric length approach discussed earlier). The on- and off-axis focal points were chosen to be

(in units of cm) Fon = (0, 0, 40) and Foff = (8, -8, 40), respectively, and the focal plane field patterns are plotted in Fig. 4.5. In comparison to the on-axis configuration, providing a gain of 23.1 dBi and a radiation efficiency of 86%, the off-axis configuration has a gain of 20.1 dBi and a radiation efficiency of 83%.

94 Figure 4.5: Simulated normalized |E|2 patterns in a transparent fashion to show the Tx antenna in the background (a) on-axis focus (b) oﬀ-axis focus.

We compared the WPT efficiency of our focusing array with that of an unfocused array. For the latter, we fabricated a second 8x8 array, equal in size and element- spacing to our focusing Tx array, but with a uniform phase distribution across all patches. This array provides a gain of 26.3 dBi and emulates a beam-forming aperture that would typically be used to create a beam in the far-field zone. It should be noted here that the advantage of being able to control the radiated fields in range (and therefore achieving a focus at F) comes from the Fresnel zone operation. In the far-field, however, both antennas would work as beam-forming antennas with the ability to perform beam steering but not focusing. The complete experimental setup is shown in Fig. 4.6(a). Our RF source is realized using a vector network analyzer

(VNA) outputting Pout=20 mW (13 dBm). We used an RF ampliﬁer to increase the power fed to the Tx antenna, PT x, to 100 mW (20 dBm). We then positioned the Rx array at the focus point, connected it to a microwave power meter, and recorded the received power, PRx. This procedure was repeated three times: once for the on-axis

95 Tx array, again for the oﬀ-axis Tx array, and ﬁnally using the conventional on-axis

beam-forming array. The calculated WPT eﬃciencies, η “ PRx{PT x, are reported in Table 4.1 for all three cases.

Figure 4.6: Fresnel zone WPT system (a) experimental set-up for received power measurement (b) LED powered using the oﬀ-axis conﬁguration at z=40 cm.

Table 4.1: WPT Efficiency Values for ON-Axis (In comparison to No-focusing) And Off-Axis Focusing, Respectively. On-axis Off-axis Fresnel Focus η Beam-forming η Fresnel focus η

33.2% 19.9% 24.3%

As shown in Table 4.1, the experimental WPT eﬃciency of the conventional beam-forming antenna was measured to be 19.9%. In contrast, when the phases of the arrays elements were designed to form a focus, the eﬃciency scaled to 33.2%. In other words, designing the Tx aperture using the Fresnel focusing technique has

increased the received power from PRx=19.9 mW to PRx=33.2 mW, a factor of 66.8%. Additionally, the transfer eﬃciency at the selected oﬀ-axis point was measured to be

24.3% with the received power recorded as PRx=24.3 mW, still larger than the on-

96 axis beam-forming case. We note that the off-axis efficiency was expected to decrease when compared to the on-axis focused configuration due to aperture reduction. In order to demonstrate the WPT efficiency increase for practical applications, we connected our HWR circuit to the output of the Rx antenna, and an LED (Avago HLMP-1700) to the output terminal of the HWR as shown in Fig. 4.6(b). For this experiment, we measured the transmitted threshold RF power at which the LED turns on for four cases; first, using a direct connection to the VNA, second, using the on-axis focusing configuration, third, using the off-axis focusing configuration, and finally, using the traditional beam-forming structure. The measured threshold power values are shown in Table 4.2. As shown in Table 4.2, the on-axis focusing configuration requires 65.1% less power (40.2 mW) to light the LED in comparison to the traditional beam-forming configuration (66.3 mW). Similarly, the required transmitted threshold power level for the off-axis focusing configuration is 19.7% smaller compared with the beam-forming configuration.

Table 4.2: Measured Transmitted Threshold Power Values for LED Lighting

Direct On-Axis Oﬀ-Axis Beam-forming

7.32 mW 40.2 mW 50.4 mW 66.3 mW

In the experiments conducted in this section, we have demonstrated a WPT scheme operating in the Fresnel zone capable of focusing the radiated ﬁelds at a desired focal point. We have achieved an increase by a factor of up to 66.8% in the received power level as a result of Fresnel focusing.

97 4.2 Using Focused Metasurface Aperture

Excerpts of the following discussion can be found in the manuscript Fresnel Zone Wireless Power Transfer using Metasurfaces by Gowda et al. (2019) close to be submitted to Nature Scientific Reports. With all the required components of a Fresnel zone WPT system designed, we now conduct the experiments to verify the system. The system is setup based on Fig. 2.12 consisting of a transmit aperture, receive aperture and a rectifier circuit. The focused aperture design in Chapter 3 is used as the transmit aperture. The receiving aperture (RX aperture) is placed at the focal distance of the transmit aperture and is connected to the full-wave rectifier circuit whose design and experiments are shown in Chapter 4. In this section we demonstrate the use of a metasurface aperture as the transmitter and show that it is capable of localizing the radiated fields in the Fresnel region required for Fresnel zone WPT system. The passive Fresnel- zone WPT system presented in this report represents a step towards realizing a dynamically tuned wireless power system. The radiating elements on the transmit aperture can be replaced by subwavelength metamaterials which can be controlled by using a diode as demonstrated in [50, 87]. All the individual components which is required to have a Fresnel zone WPT system is design and experimentally verified. The basic schematic of a WPT system is shown in Fig. 4.7.

98 Figure 4.7: Experimental schematic of the proposed Fresnel-zone WPT system

The RF efficiency in a WPT system is important to calculate and is required for calculating the RF to DC efficiency of the WPT system. The RF efficiency can be given by

ηRF “ ηTXηRXηfocus

where ηTX is the transmit aperture efficiency (87%), ηRX is the receive aperture efficiency (85%) and ηf ocus is defined as the ratio of the power at the focal spot to the power at the focal plane (63%). All these values can be obtained from CST simulations and the ηRF is „ 45 %. Fabrication at higher frequencies can be complicated using in-house fabrication equipment’s. To fabricate the Tx aperture, we patterned the desired structures on the top waveguide into the top copper layer of a double-sided copperclad Roger 5880 substrate using a U3 LPKF laser milling system. It was then combined with the bottom waveguide and the side of the structure was covered with copper tapes to provide the cavity effect required. However, the receive antenna and the rectifier

99 are fabricated from a professional board house since it is difficult in house due the multiple layer assembly (receiver) and small components like the diodes (rectifier). The radiation efficiencies of the Tx and Rx array antennas were also measured using the NSI near-field scanning system, and reported to be 85% and 87% respectively. The losses of using the copper tapes does affect the radiation efficiency of the Tx aperture. This can be overcome by making use of a via wall spaced at subwavelength from each other, mimicking what a metal sheet would do. The transmit aperture and the metamaterial inspired absorber is connected to port 1 and port 2 of the vector network analyze. The CBA in Fig 4.7 corresponds

to the transmit aperture. The metamaterial absorber is placed at the location (z0 “ 10cm) where the transmit aperture is designed to focus. Both the transmit and receive aperture are placed on the vertical bars. The S21 of the system is reported after calibrating the cables and the experimental RF eﬃciency is around 23 % and is given by Eq. 4.1. The expected power transfer eﬃciency of the system consisting of the transmit

aperture and receive aperture can be computed using ηRF ´RFSim{Exp “ ηTX ηRX ηfocal, where ηTX is the transmit aperture efficiency, ηRX is the receive aperture efficiency and ηfocal is focal efficiency given by

A focal spot η “ focal A focal plane

All these values are obtained from CST simulations and the ηPTE Expected is „36.04 %. The experimental RF power transfer eﬃciency can be calculated using measured scattering parameters, using;

2 1 ´ |S21| q ηRF ´RFmeas “ 2 2 , (4.1) p1 ´ |S11| qp1 ´ |S22| q

where the transmit aperture is connected to port 1 and receive aperture is con-

100 nected to port 2 of the vector network analyzer (VNA) as shown in the Fig 4.8.

The ηP T EExp is „ 20.2 % at the frequency of operation. The drop in efficiency primarily due to the residual reflection from the absorbing layer; a larger receiving aperture would have exhibited higher efficiency. The efficiency also suffer slightly from fabrication tolerances and unaccounted losses (e.g. connector soldering, etc.).

Figure 4.8: Experimental setup showing the working WPT setup with the LED turned on

A table showing the PTE for simulation, expected and experiments is shown in the Table 4.3 below.

Table 4.3: RF - RF eﬃciency (in %) for the Fresnel Zone WPT system

ηRF ´RFSim ηRF ´RFExp ηRF ´RFmeas

36.04 29.7 20.2

101 5

Computational Imaging using Printed Cavities

5.1 Introduction to Computational Imaging

Excerpts of the following discussion can be found in the manuscripts Multistatic microwave imaging with arrays of planar cavities by O. Yurduseven, V.R. Gowda, J.N. Gollub, D.R. Smith, (2016) published in IET Microwaves, Antennas Propa- gation and Printed aperiodic cavity for computational and microwave imaging by O. Yurduseven, V.R. Gowda, J.N. Gollub, D.R. Smith, (2016) published in IEEE Mi- crowave and Wireless Components Letters and Comprehensive simulation platform for a metamaterial imaging system by Lipworth et. al (2015) published in Applied Optics. Microwaves can penetrate through materials that are opaque at optical wavelengths, yet they are non-ionizing and thus harmless to living tissue at low power levels. Hence, microwave imaging is of considerable interest for security screening, remote sensing, biomedical imaging, and many other applications. A number of microwave imaging systems have been developed and ﬁelded, including synthetic aperture radar (SAR) [28, 98, 99, 100, 101]; holographic imagers [102, 103]; and

102 phased arrays [31, 32, 33]. While these techniques have demonstrated excellent image fidelity, limitations remain, particularly for fast, near real-time imaging. In SAR, an aperture is synthesized by a mechanical raster scan of an antenna over a large area, taking a number of measurements at or near the Nyquist spatial sampling rate (roughly half the operating wavelength). While SAR produces a set of nearly orthogonal scene measurements in the spatial frequency domain (or k-space), the mechanical scan can require long image acquisition times, making SAR approaches challenging to implement for real-time imaging applications. An additional limitation in SAR is the considerable data generated from sampling at the Nyquist rate (diffraction limit); the magnitude of data generated rapidly becomes challenging in terms of storage and transmission for even moderately sized scenes. Holographic approaches in security imaging and biomedical applications have also been demonstrated in the literature. The advantage of holography is that the complex fields (amplitude and phase) scattered from imaged objects can be mathematically reconstructed from amplitude-only measurements, obviating the need for expensive components and more complex circuitry required for phase-sensitive measurements. Despite these advantages, holographic imaging still requires a raster scanned antenna to synthesize an aperture, again limiting the imaging speed. Parallelization of measurements over the aperture is an obvious means of increasing image acquisition speed, and is the basis for phased arrays and electronically scanned antennas (ESAs). Phased arrays provide exquisite control over both the phase and amplitude of the field at every point in the defined aperture, resulting in near arbitrary control over the radiation pattern. Phased arrays and ESAs are optimal in terms of beam-forming, but typically require large numbers of expensive components, including amplifiers and phase shifting circuits, which consume significant power, are bulky, and generally expensive. At the extreme end, ESA’s can require independent transmit and receive modules at every sampled point in the

103 array, each module containing a low noise amplifier, a high power amplifier, phase shifter, and potentially additional active components. These systems can be costly when scaled to the aperture sizes needed in many applications, including resolving human-scale targets for security screening. An alternative method applicable to coherent microwave imaging is to make use of computational imaging techniques to simplify the physical architecture of the system, relying more on processing to make use of more general measurements, and to more intelligently use those measurements to estimate the scene. Computational imaging generalizes the imaging process, so that many more aperture modalities can be implemented to yield high-fidelity images [104]. A new imaging modality that has emerged from the computational imaging framework is the frequency-diverse aperturean aperture designed with radiating elements whose radiative properties vary rapidly as a function of the driving frequency [34]. As a function of frequency, the frequency-diverse aperture produces a set of distinct radiation patterns that illuminate the scene. One or more simple, low-gain horn antennas or probes then captures the field scattered from the scene from each of these complex illumination modes. The scene can then be reconstructed from the set of measurements using computational imaging techniques. If only frequency diversity is used, then there is no need for any mechanical scanning apparatus or active electronic components, leading to a simple architecture that is inexpensive and scalable to very large apertures. In [34, 35, 36], a frequency-diverse metamaterial imager operating over K-band frequencies (18-26.5 GHz) was demonstrated. The imager consisted of a set of metamaterial panels, each a planar waveguide with a dense array of sub-wavelength, complementary electric (cELC) resonators patterned into the upper conductor. The frequency response of each cELC has a Lorentzian form peaked at the operating wavelength, with a width set by the element quality (Q-) factor. The resonance frequency for each cELC was randomly selected from the K-band by tuning specific aspects of

104 the cELC geometry. As the frequency of the feeding waveguide mode is swept, only certain sets of metamaterial radiators with resonance frequencies equal to the sweep frequency couple to the guided-mode and radiate into free space. The frequency- diverse aperture thus produces a set of complex radiation patterns (or modes) that illuminate the scene, with the number of modes within the frequency bandwidth determined roughly by the element Q-factor. The frequency-diverse metamaterial aperture consists of thousands of cELC unit cells. Due to their sub-wavelength geometry, the cELC elements required high precision printed circuit board (PCB) pro- cesses to achieve the necessary feature sizes. Even with high precision PCB printers, the fabrication tolerance is insufficient to ensure exactly equivalent radiation characteristics between fabricated panels, so that the field patterns must be characterized extensively for each of the fabricated panels. In addition, due to the dispersive nature of the metamaterial elements, large conduction and dielectric losses occur on resonance where the radiation is maximized. The resistive and dielectric losses limit the achievable Q-factor for the system, which is the most important parameter indicating the effective number of independent modes. Given that the losses in the frequency- diverse metamaterial aperture occur in the planar waveguide section, a modification of the aperture was suggested in [37], in which an air-filled cavity was substituted for the planar waveguide. The air-filled cavity has a multi-wavelength thickness such that it supports multiple resonances at a given excitation frequency. An array of non-resonant radiating irises (or holes) patterned into the upper conducting plate forms the sub-aperture, as in the metamaterial panel. The higher system Q-factor associated with the air-filled cavity considerably improves radiation efficiency. In addition, introduction of a spherical indentation, into the otherwise rectangular cavity, mixes the modes and introduces considerable spatial variation into the fields driving the radiating elements. The modes of the final structure are thus chaotic, dispersing rapidly with frequency and exhibit significantly improved mode diversity

105 in comparison with the metamaterial panels. While the chaotic aperture is advan- tageous in terms of mode diversity and effective Q-factor, the cavity modes are not easily predictable and require full-wave numerical simulations to analyze; given the inherently chaotic nature of the modes, small variations in manufacture may produce significant variations in the radiated field patterns. In addition, due to its required multi-wavelength thickness, the chaotic cavity has a relatively thicker profile than might be desirable. Given the advantages of the higher Q-factor cavity versus the simple planar waveguide as the feed, the cavity concept has continued to evolve. Recently, a simpler, PCB version of the cavity was suggested and shown also to improve mode diversity [38]. The printed cavity was made thin enough such that only one mode at any given frequency could be excited; that is, the printed cavity is a single mode system rather than multimode as in the chaotic cavity. The printed cavity provides an increased system Q-factor while retaining the low profile and other desirable characteristics of the planar waveguide. The authors in [21] demonstrated imaging based on a configuration of a single panel (for the transmit sub-aperture) and four probes (for the received scattered signal). Continuing to build on the cavity-feed design, we present here a frequency-diverse, multistatic computational imaging system based on single-mode printed planar cavities at microwave frequencies. Multistatic imaging has the benefit of presenting a large aperture without the requirement of raster scans or dense arrays of antennas [105]. Here, the upper conductor of the printed cavities is loaded with an array of circular irises distributed in an aperiodic (Fibonacci) pattern. A similar design to that presented in [38], the printed cavity exhibits better Q-factor and radiation efficiency response in comparison to PCB based metamaterial panels, but is extremely low profile as compared to the air-filled mode-mixing chaotic cavity. The printed cavity does, however, exhibit larger dielectric losses as compared to the air-filled

106 cavity, and hence has a lower overall Q-factor. To increase the available mode diversity, a panel-to-panel imaging configuration is used rather than the panel-to-probe configurations presented in the literature to date. Because the spatial variation of the radiated fields from the cavity panels is so large compared with low-gain horns or probes, panel-to-panel imaging places a greater burden on the system alignment and calibration, but nevertheless improves system resolution and capabilities relative to panel-to-probe systems.

5.2 Design and optimization of Radiating Irises

The printed cavity consists of an array of radiating circular irises distributed in a Fibonacci pattern on the front surface of a double-sided, copper clad printed circuit board (Rogers 4003, r = 3.55 and tanδ = 0.0027). The irises were patterned on the top layer of the PCB using a laser-etching system (ProtoLaser U3 from LPKF). Laser etching is extremely accurate, but care must be taken with respect to the etching parameters as the high power associated with laser beam can result in etching into the substrate, causing a shift in the operational frequency band, especially over the K-band of interest in this paper. The edges of the circuit board are coated with silver paint to form the cavity structure. The thickness of the dielectric substrate is 1.524 mm, smaller than a half-wavelength (guided) for all frequencies over the K-band,

λg/2, in order to suppress the higher-order cavity modes and ensure single-mode operation. The printed cavities are excited using a coaxial feed connected in the center of the ground plane, which launches a cylindrical guided wave into the substrate, described by a second order Hankel function . As the launched wave propagates inside the cavity, it is sampled by the circular irises and undergoes multiple reflections from the cavity walls once reaching the edges. In order to improve the impedance match, a 0.1 mm width annular slot was designed on the top layer as shown in Fig. 5.1a. The radiation efficiency was directly measured via a near-field scan of the printed

107 cavity using a near-ﬁeld scanning system (NSI 200 V-3 x 3). The Q-factor of the printed cavities was determined experimentally by measurement of the signal decay factor from time-domain S11 measurements [106].

Figure 5.1: Cavity imaging system - Tx (L=20 cm), Rx (L=10 cm).(a) Structure of a single printed cavity (b) Panel-to-panel imager experimental set-up.

Because of the higher Q-factor associated with the cavity, the need for resonant irises is eliminated and a much simpler, non-resonant iris design can be introduced. As in [38], we use circular irises as the radiating elements. The coupling of the cavity mode to these irises depends on the iris diameter; consequently, iris diameter is an essential parameter in the design of the sub-aperture, influencing both radiation efficiency and Q-factor of the panel. The radiation efficiency of the transmit and receive panels relates directly to the system signal-to-noise ratio (SNR), while the Q- factor of the panels directly relates to the orthogonality of the measurement modes. Since radiation efficiency is proportional and Q-factor is inversely proportional to the iris diameter, the iris diameter must be chosen to optimize mode diversity for a given

108 system SNR [107]. In order to demonstrate the impact of iris diameter on the mode Q-factor, we fabricated several printed cavities and varied the iris diameter (3 mm, 4 mm and 5 mm). The dimensions of the printed cavity used in the study are 10 cm x 10 cm. Table 5.1 shows the Q-factor and radiation eﬃciency values for the four measured panels. The data in Table 5.1 clearly show the anticipated relationship between the iris diameter, radiation eﬃciency and Q-factor.

Table 5.1: Relationship between iris diameter, Q-factor and radiation eﬃciency (0%iris sparsity) Iris Diameter Quality factor (Q) Radiation Eﬃciency (ηq No Irises 254 - 3 mm 163 31.5 % 4 mm 110 62.6 % 5 mm 71 79.4 %

As can be seen in Table 5.1, increasing the iris diameter increases the radiation efficiency at the expense of reducing the Q-factor. The measured reflection coefficient

(S11) patterns for all the diﬀerent iris diameters in Table 5.1 are shown in Fig. 5.2(a).

As seen in Fig. 5.2(a), S11 remains below the -10 dB level across the K-band (with small oscillations slightly above -10 dB between 20-21 GHz for the printed cavity with 3 mm irises).

109 Figure 5.2: Measured S11 patterns (a) Diﬀerent Iris diameter (b) Diﬀerent Iris concentrations.

Another important parameter for the design of the printed cavity is the number (or sparsity) of the radiating irises etched into the front surface of the cavity. To investigate the impact of sparsity, different prototypes of the printed cavity with varying iris sparsity ratios were fabricated; without irises (solid version with 100 % iris sparsity), 4 irises (97.4 % iris sparsity), 16 irises (89.6% iris sparsity), 64 irises (58.7% iris sparsity), and 155 irises (fully distributed version with 0% iris sparsity). It should be noted here that although this study can be performed on any iris diameter given in Table 5.1, we chose 5 mm iris diameter due to the large radiation efficiency. The measured S11 patterns for different iris concentrations in the cavity are shown in Fig. 5.2(b). It can be seen that increasing the number of irises (and therefore the effective radiating aperture size) improves the S11 response. Table 5.2 demonstrates the measured Q-factor and radiation efficiency values as a function of radiating iris sparsity. All values recorded in the table are experimental and each case was carried out separately. Similar to Table 5.1, it can be seen that increasing the effective radiating sub- aperture size by increasing the number of the radiating irises results in the proposed printed cavity exhibiting higher radiation efficiency at the expense of reducing the Q-

110 Table 5.2: Relationship between number of irises, Q-factor and radiation efficiency (5mm iris diameter). Configuration Iris sparsity Quality factor (Q) Radiation Efficiency (ηq No Irises 100% 254 - 4 Irises 97.4% 225 8.2 % 16 Irises 89.6% 184 26.2% 64 Irises 58.7% 123 62.1% 155 Irises 0% 71 79.4% factor. As the panel-to-panel imaging configuration makes use of frequency-diverse apertures for both transmit and receive, the overall frequency-diversity of the system is increased and therefore it is desirable to maximize the radiation efficiency at the expense of reducing the Q-factor of the individual cavities. In view of this trade-off, fully distributed (0 % iris sparsity) printed cavities with 4 mm irises were chosen for imaging.

5.3 Imaging Conﬁgurations - Panel to Probe and Panel to Panel

The proposed imaging system operates in the K-band frequency regime over a frequency bandwidth of B=8.5 GHz. The K-band was selected as an accessible frequency band that can be utilized for imaging purposes (currently several ﬁelded applications have received IEEE spectrum waivers to do so), and further, it can support the desired resolution limits. Range resolution of the imaging system is directly determined by the operational bandwidth which is 1.76 cm for the K-band. Cross- range resolution is set by the maximum operational frequency and the size of the aperture, and as we discuss below, allows 2.25 cm resolution to be achieved with a moderate sized aperture. In this work, the K-band was sampled with 101 frequency points, with a step size of f=85 MHz. The number of useful sampling frequencies

111 is directly proportional to the Q-factor of a frequency diverse aperture. A higher Q manifests as greater phase diversity between the radiating irises and reduces the correlation between measurement modes. In turn, this allows ﬁner sampling of the frequency bandwidth. However, even if the number of points is not increased, the reduced correlation of the modes produces improved imaging. For direct comparison with previous imaging systems, we limit the measurement points to 101 frequencies. Also, we note that one must balance the trade-oﬀ between increasing the number of measurement modes, to improve imaging, with the computational expense of handling a larger data set. For the small system considered here, this expense is minimal, but for larger systems, it can be substantial and would need to be studied in detail. To date the frequency diverse imaging systems demonstrated in the literature have used panel-to-probe system layouts. In such a system, a signal is transmitted from frequency-diverse apertures and energy scattered from the scene is collected with low-gain and wide bandwidth probe antennas. An illustration of such a system is shown in Fig. 5.3(a).

112 Figure 5.3: Illustration of (a) panel-to-probe (b) panel-to-panel imaging setup with a 2-D far-ﬁeld pattern slice (22.5 GHz) in front of the apertures.

The complexity of the radiation patterns used to encode the imaging scene is chiefly a result of the frequency diversity of the panels. The probe antennas, which lack frequency diversity, have no influence on the measurement modes besides collecting the signal with high efficiency across the operation bandwidth. In comparison, the panel-to-panel configuration, proposed here, uses frequency diverse apertures for both the transmitting and receiving antennas. Fig. 5.3(b) shows the individual panel fields. The coverage in the spatial frequency domain (k-space) is a convolution of the Fourier transformed fields of the individual transmitting and receiving apertures (as a function of frequency). In this approach, the overlapping radiation patterns of the panels projected into the scene have greater diversity and the resulting, combined radiation pattern, varies more rapidly with frequency. Therefore, the panel-to-panel configuration effectively amplifies the frequency diversity of the individual panels and reduces the correlation (information redundancy) between the measurement modes. The scene, can hence, be encoded in less measurement modes and the computa-

113 tional burden of image reconstructing is reduced. In this paper, we will see that the proposed panel-to-panel printed cavity imager reduces the number of measurement modes (and hence the magnitude of generated data processed for imaging) by a factor of half in comparison to the panel-to-probe configuration in [38]. In addition, compared with the multi-wavelength thick air-filled chaotic cavity reported in [37], the PCB printed cavities achieve their imaging results with an extremely low-profile structure. The reduced Q-factor of PCB panels due to the substrate dielectric losses is compensated for by the panel-to-panel architecture, which amplifies the overall Q-factor of the system. Later in section 5.4, we will quantitatively com- pare the system architectures by investigating their SVD spectrum. Singular values are monotonically decreasing and a flatter spectrum corresponds to higher diversity among the modes. The SVD spectrum for the panel-to-panel configuration shows superior mode-diversity versus panel-to-probe configuration.

5.4 Panel to Panel (Bistatic)

5.4.1 Aperture Design

In this section, we consider the overall aperture configuration. One of the fore- most parameters that influence computational imaging reconstruction algorithms is the SNR of the system. As described above, the panel radiation efficiency deter- mines the amount of the signal transmitted to the scene, as well as the amount of reflected signal captured. Thus, increasing the radiation efficiency of the printed cavities within the imaging system maximizes the amplitude of the measured signal and SNR. A second parameter of critical importance to the system is the number of distinct measurements available over the given bandwidth. Since both the transmitting and the receiving apertures support mode-diversity (frequency diverse apertures) in a panel-to-panel architecture, the overall frequency diversity for the system is increased. Given the increased number of measurement modes associated

114 with panel-to-panel imaging, it is thus favorable to increase the radiation efficiency of the cavities at the expense of reducing the individual cavity Q-factors. This design choice is contrary to that made for the air-filled mode-mixing cavity imager, where low-gain open-ended waveguide probe antennas were used as receiving antennas [20]. The parameters for the individual sub-apertures were determined from the trade-off studies presented in the previous section. The iris diameter was selected to be 4 mm to achieve a reasonable Q-factor and radiation efficiency. The next consideration for the system layout is to choose the size of the cavities or panels. The proposed imaging system has a 20 cm x 20 cm printed cavity as transmitting aperture and four 10 cm x 10 cm printed cavities as receiving apertures, replacing the open-ended waveguide probe antennas with the same flange size (10 cm diameter) in panel-to- probe configuration. The aperture size was chosen to enable the proposed system to achieve sufficient cross-range resolution to image the targets demonstrated in this paper. The measured radiation efficiency for the 10 cm x 10 cm receiving printed cavity is 62.6 % while that for the 20 cm x 20 cm transmitting cavity is 52.1%, averaged over the K-band. The measured Q-factor of the 20 cm x 20 cm printed cavity is Q=171, while for a 10 cm x 10 cm Q is 110. Fig. 5.4 shows the measured S11 and radiation efficiency patterns of the printed cavity in K-band frequency range for both the 20 cm x 20 cm and 10 cm x 10 cm sizes.

115 Figure 5.4: S11 and radiation eﬃciency patterns for 20 cm x 20 cm and 10 cm x 10 cm printed cavity.

The printed cavity imager performs reflection based imaging by measuring the transmission coefficient, S21. The signal radiated from the transmitting cavity panel is reflected back from the imaged object and received by the receiving cavity panels. The received complex signal (amplitude and phase) is recorded in a measurement vector, g, as a function of frequencies over the K-band. The imaged scene is discretized into three-dimensional (3D) voxels, represented by reflectivity values, f, to be reconstructed (inverse problem). Discretization is done over a field-of-view determined by the size of the imaging scene enclosing the imaged target with the size of the voxels selected with respect to the smallest wavelength over the K-band. In order to solve the inverse problem, the first Born approximation is used [17] and the measurement vector g, is correlated to the imaged scene using Eq. 5.1.

gMx1 “ HMxN fNx1 (5.1)

In Eq. 5.1, H denotes the measurement matrix, consisting of the ﬁelds radiated

116 from the cavity imager,HαET x.ERx , where ET x and ET x are the fields from the transmitting and receiving cavities projected to the imaging scene, respectively. The proposed cavity imager has M=404 total number of total measurement modes calculated as number of transmitting cavities (1) x number of receiving cavities (4) x frequency sampling points (101). One method to analyze the mode-orthogonality and the effect of frequency diversity in an imaging system is to investigate the singular value spectrum of the measurement matrix, H, obtained through SVD analysis [108]. For this analysis, two imaging configurations were considered: panel-to-panel and panel-to-probe. For the panel-to-probe configuration, the receiving cavity panels demonstrated in Fig. 5.3(b) were replaced by low-gain open-ended waveguide probe antennas as shown in Fig. 5.3(a). In Fig. 5.5, a comparison between the normalized singular value curves of different experimental systems is demonstrated. For the singular values found in Fig. 5.5, the imaging scene was selected to be 1 m x 1 m at a distance of d=1 m from the cavities and the imaging frequency was swept across 101 frequency points over the K-band. From Fig. 5.5, it is evident that the panel-to-panel system produces less correlated measurement modes in comparison to the panel-to-probe system. In other words, given a certain SNR level for imaging, the number of useful modes generated from a set of frequency measurements for the panel-to-panel configuration is higher than the panel-to-probe configuration.

117 Figure 5.5: Singular values for the panel-to-probe and panel-to-panel imaging con- ﬁgurations.

5.4.2 Experimental results

The experimental setup consists of a printed cavity of D=20 cm and four more printed cavities of D=10 cm. The main difference between these cavities is the size; the Fibonacci pattern and the iris size are consistent for both panel sizes. The radiation pattern of these printed cavities can be characterized individually by measuring the fields using a NSI near-field scanning system. Once all the scans are completed, the imager setup is prepared to perform the experiments. However, one can easily introduce alignment errors in the position of the cavities between when they are measured and mounted in the experimental setup. These misalignment errors can be overcome by designing a planar frame with all five printed cavities rigidly attached to the framesuch that they share a global origin at the center of the imager. With this method, all of the positions of the printed cavities remain intact during the near-field scan and during the experiments. Fig. 5.3(b) shows the picture of the

118 panel-to-panel imager setup. The transmit cavity was fed using the first port of a vector network analyzer (VNA, Agilent N5245). The receiving cavities were connected to the second port of the VNA through a Keysight L7106C coaxial switch connected to an Agilent 11713C switch driver. All combinations of the transmit and receive panels are switched through and illuminate the scene with a 30 ms switch dwell time (limited by the mechanical switching speed of the L7106C switch). Imaging of a number of targets, including a resolution target, a smiley face target and an inclined L-shaped phantom, was performed at a distance of 1 m away in range (x-axis) from the cavity imager. The imaging scene was discretized into cubic voxels of 5 mm, which is below the half wavelength diffraction limit in K-band, resulting in N=10,000 voxels. One has to take into account the fact that we are using only M=404 measurement modes (50 % less in comparison to the panel-to-probe configuration demonstrated in [38]) in order to reconstruct an imaging scene of total N=10,000 voxels. It is evident that the imaging scene is significantly under sampled (M ă N). With this in mind, we make use of a compressive image reconstruction method, two-step iterative shrinkage/thresholding (TwIST) with total variation [109, 110]. While the employment of the proposed panel-to-panel system layout enables imaging using such a small number of measurement modes due to the increased mode orthogonality, the system also further benefits from this selection due to the compressive nature of the imaging problem discussed in this paper. In order to demonstrate the capability of the printed cavity imager to perform imaging at the diffraction limit, imaging of a resolution target was carried out. The field-of-view for the imaging scene was 15˝, fully enclosing the resolution target. The resolution target consists of vertical and horizontal stripes with a width of 2.5 cm, selected according to the cross-range (y-z plane) resolution of the imager. The reconstructed images are shown in Fig. 5.6 below demonstrate the ability of imaging at diffraction limit with the cross-range

119 resolution being δcr=2.25 cm and the range resolution being δr= 1.76 cm calculated using Eq. 5.2 and Eq. 5.3.

λ R δ “ center (5.2) cr 2D

c δ “ (5.3) r 2B

In Eq. 5.2 and Eq. 5.3, c is the speed of light, B is the imaging bandwidth B=8.5

GHz, λcenter is the wavelength at center frequency fc=22.5 GHz, D is the overall aperture size of the cavity, R is the distance between the imager and the target or range distance. It should be noted here that for the calculation of the cross-range resolution, δcr, the size of the transmitting and receiving apertures are different. Consequently, an effective aperture was defined, corresponding to the average of the transmitting and receiving aperture sizes.

Figure 5.6: Reconstructed image of the 2.5 cm resolution target.

120 Following the imaging of the resolution target, imaging of an L-shaped phantom and a smiley face target was performed. Due to bigger size of these targets, imaging was done over a larger ﬁeld-of-view, 23˝, fully enclosing the imaged objects. Reconstructed images are shown in Fig. 5.7.

Figure 5.7: Reconstructed images of the L-shaped phantom (actual outline of the L-shaped phantom with dashed lines) (a) Simulation (b) Experimental.

121 6

Conclusion

In chapter 2, a beamed wireless power transfer (WPT) system as an interesting alternative to near-ﬁeld magnetic coupling schemes which mainly operates at very low proximity. The possibility of selectively beaming power to small devices located anywhere within a volume is a desirable advantage. Emerging beam-steering technologies, such as the metasurface aperture analyzed here, have the potential to reach the low price points required for larger-scale adoption in consumer driven markets. Two relevant examples are the mTenna, currently manufactured by Kymeta Corporation (Redmond, WA), which is currently being commercialized as a dynamically recon- ﬁgurable antenna for satellite communications, as well as the MESA radar produced by Echodyne Corporation (Bellevue, WA)both variants of the metasurface aperture. The mTenna makes use of liquid crystal as a means of implementing dynamic tuning, merging display technologies with the metasurface architecture to achieve largescale, reproducible manufacturing at low price points. The MESA makes use of pack- aged, active, semiconductor components integrated into the metasurface structure to achieve dynamic tuning. Both systems have shown that mature, conventional manufacturing solutions are viable to produce the types of holographic apertures

122 that would be needed for the Fresnel zone WPT system analyzed here. The initial studies presented here provide some guidance for initial prospective designs, relating the aperture size and wavelength to system parameters such as transfer efficiency and coverage area. For the studies pursued here, an ideal holographic metasurface aperture with plane wave illumination was considered. A practical system would likely make use of a guided mode rather than a free space wave to create a low- profile device. For such guided wave implementations, higher order diffracted beams can be further rejected because of the natural phase shift of the reference wave over the aperture. In chapter 3, a metasurface holograms are designed and fabricated to focus electromagnetic fields to desired spots with linear polarization. The proposed design and operation were confirmed via simulations and experiments in the K-band frequency range. To highlight the flexibility of this method, two different linearly polarized near-field focusing metasurface apertures were designed, one without tapering and another with tapering to reduce the sidelobe levels. Full-wave simulations, experimental analysis, and analytical predictions for the tapered aperture showed substantially smaller sidelobes when compared with the aperture design without tapering. The demonstrated focusing metasurface holds promise as the building block for wireless power transfer in the Fresnel zone, as suggested in chapter 2. However the design presented does suffer from having lower radiation efficiency and low side lobe levels. As a result, an element that consists of a slot pair that couples to the guided wave is utilized, but with their orientation designed to ensure that the overall radiation is linearly polarized in the focal plane. A general condition that ensures low SLLs is proposed and verified in full-wave simulation. The simulated combined efficiency of the aperture is higher than previous works (48%) and the SLLs is below -10 dB. Ex- perimental results confirming the proposed design and operation are also presented. The next step is to design the receiver which in a WPT system consists of a receiving

123 antenna and a rectifier to convert the RF to DC. The receiving antenna considered is a metamaterial absorber consisting of an array of subwavelength unit cell in a periodic pattern. The absorber is designed such that it harvest the impinged RF energy in contrary to the traditional absorbers and later a rectifier is designed at the operating frequency (20 GHz) to complete all the required block diagrams of for a Fresnel zone WPT system. In chapter 4, a practical implementation of the Fresnel Zone wireless power system is considered by making use of patch array antenna and metasurface apertures in two separate sub sections. In section 4.1, a successful demonstration of wireless power transfer is demonstrated. However, such a structure usually results in complicated feed networks and not favorable in realizing an aperture required for dynamic focusing. As discussed in Chapter 2 and Chapter 3, focused metasurface apertures provide an efficient path in realizing a dynamic aperture. In 4.2 a Fresnel zone WPT system is assembled and a successful demonstration of wireless power transfer is demonstrated by turning on a red colored LED. In chapter 5, a frequency-diverse multistatic imaging system is demonstrated using arrays of planar cavities at microwave frequencies. The proposed imager trans- mits and receives using frequency-diverse printed cavity apertures (panel-to-panel imaging configuration). It exhibits strong mode diversity (compared with panel to probe configuration) and high radiation efficiency, and supports imaging at the diffraction limit. In comparison to conventional imaging modalities, the cavity imager leverages the concept of frequency-diverse computational imaging removing the requirement to use active circuit components and precise mechanical scanning equipment for imaging. These aspects of the cavity imager not only simplify the hardware architecture but also significantly reduce the cost of the system. In order to show the working of the imager, Imaging of a number of objects has been performed and has been demonstrated that the simulation and experimental results are

124 in good agreement.

125 7

Appendix

7.1 Coverage Area Proof

An analytical estimate of the coverage zone can be extracted from Eq. 2.7 by examining contours in the y-z plane of constant beam waist. For a constant beam waist (deﬁned as beam diameter), starting from the equation of beam waist, we have:

4 λ z w “ 0 0 (7.1) 0 π Dcos2θ

We know the deﬁnition of cosθ from Eq.2.1 as

z cosθ “ 0 (7.2) 2 2 x0 ` z0

Substituting Eq.7.2 in Eq.7.1, we get a

2 2 4 λ0py0 ` z0q w0 “ (7.3) π z0D

Re-arranging Eq.7.3, we get an equation of a circle with center at dc/2 in z-axis with diameter of dc = 2(dc/2) 126 2 2 z0dc “ y0 ` z0 (7.4)

Adjusting Eq.7.4, we can ontain an equation for the coverage area which is given by Eq.7.5

2 2 2 dc dc y0 ` z ´ “ (7.5) ˜ 2 ¸ ˜ 2 ¸

π w0 where dc “ D 4 λ0

7.2 Power Eﬃciency calculations

Figure 7.1: Aperture plane and focal plane

Consider a TX as the transmitting aperture and the RX as the receiving aperture. By using basic Poynting vector, we can calculate the power by integrating the Poynting vector over a certain area of consideration.

127 1 S “ |ExH ˚ | “ ω E2 (7.6) 2 0

E2 S “ (7.7) η0

Then the power flow is given by P= S.A and power at the aperture is then given by PTX and the power received at the focal plane is given by PRX . The free space impedance η0 , E is the electric field, H is the magnetic field, w is the angular frequency and 0 is the relative permittivity.

2 |E |dArpx, yq P “ xy (7.8) RX η x y 0 ÿÿ

2 |E |dAtpx, yq P “ xy (7.9) TX η x y 0 ÿÿ

P η “ RX % (7.10) PTX

The area of each discretized pixel in the aperture and focal planes is denoted by

2 dAtpx, yq and dArpx, yq, respectively. The term |Exy| denotes squared value of the magnitude of the electric ﬁeld in each pixel, which is multiplied by the discretized area of the corresponding pixel, resulting in the power density or the power ﬂow.

The eﬃciency is calculated by taking the ratio of PTX and PRX .

128 Bibliography

[1] N. Tesla, “Apparatus for transmitting electrical energy.” (1914). US Patent 1,119,732.

[2] W. C. Brown, “The history of power transmission by radio waves,” IEEE Transactions on microwave theory and techniques 32, 1230–1242 (1984).

[3] M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diﬀraction of light (Elsevier, 2013).

[4] A. Kurs, A. Karalis, R. Moﬀatt, J. D. Joannopoulos, P. Fisher, and M. Soljaˇci´c, “Wireless power transfer via strongly coupled magnetic resonances,” science 317, 83–86 (2007).

[5] A. Rozin and G. Kaplun, “Capcitively coupled bi-directional data and power transmission system,” (1998). US Patent 5,847,447.

[6] A. Karalis, J. D. Joannopoulos, and M. Soljaˇci´c, “Eﬃcient wireless non- radiative mid-range energy transfer,” Annals of Physics 323, 34–48 (2008).

[7] W. C. Brown, “An experimental low power density rectenna,” in “Microwave Symposium Digest, 1991., IEEE MTT-S International,” (IEEE, 1991), pp. 197–200.

[8] C. A. Balanis, “Antenna theory: A review,” Proceedings of the IEEE 80, 7–23 (1992).

[9] W. C. Brown and E. E. Eves, “Beamed microwave power transmission and its application to space,” IEEE transactions on Microwave Theory and Techniques 40, 1239–1250 (1992).

[10] F. Toﬁgh, J. Nourinia, M. Azarmanesh, and K. M. Khazaei, “Near-ﬁeld focused array microstrip planar antenna for medical applications,” IEEE antennas and wireless propagation letters 13, 951–954 (2014).

129 [11] M. Bogosanovic and A. G. Williamson, “Microstrip antenna array with a beam focused in the near-ﬁeld zone for application in noncontact microwave industrial inspection,” IEEE Transactions on Instrumentation and Measurement 56, 2186–2195 (2007).

[12] K. Stephan, J. Mead, D. Pozar, L. Wang, and J. Pearce, “A near ﬁeld focused microstrip array for a radiometric temperature sensor,” IEEE transactions on antennas and propagation 55, 1199–1203 (2007).

[13] J. S. Ho, A. J. Yeh, E. Neofytou, S. Kim, Y. Tanabe, B. Patlolla, R. E. Beygui, and A. S. Poon, “Wireless power transfer to deep-tissue microimplants,” Pro- ceedings of the National Academy of Sciences 111, 7974–7979 (2014).

[14] S. Kim, J. S. Ho, and A. S. Poon, “Midﬁeld wireless powering of subwavelength autonomous devices,” Physical review letters 110, 203905 (2013).

[15] J. Loane and S.-W. Lee, “Gain optimization of a near-ﬁeld focusing array for hyperthermia applications,” IEEE Transactions on Microwave Theory and Techniques 37, 1629–1635 (1989).

[16] A. P. Sample, D. T. Meyer, and J. R. Smith, “Analysis, experimental results, and range adaptation of magnetically coupled resonators for wireless power transfer,” IEEE Transactions on Industrial Electronics 58, 544–554 (2011).

[17] B. Wang, W. Yerazunis, and K. H. Teo, “Wireless power transfer: Metamateri- als and array of coupled resonators,” Proceedings of the IEEE 101, 1359–1368 (2013).

[18] L. Shan and W. Geyi, “Optimal design of focused antenna arrays,” IEEE Transactions on Antennas and Propagation 62, 5565–5571 (2014).

[19] D. R. Smith, V. R. Gowda, O. Yurduseven, S. Larouche, G. Lipworth, Y. Urzhumov, and M. S. Reynolds, “An analysis of beamed wireless power transfer in the fresnel zone using a dynamic, metasurface aperture,” Journal of Applied Physics 121, 014901 (2017).

[20] A. Massa, G. Oliveri, F. Viani, and P. Rocca, “Array designs for long-distance wireless power transmission: State-of-the-art and innovative solutions,” Pro- ceedings of the IEEE 101, 1464–1481 (2013).

[21] V. R. Gowda, O. Yurduseven, G. Lipworth, T. Zupan, M. S. Reynolds, and D. R. Smith, “Wireless power transfer in the radiative near ﬁeld,” IEEE An- tennas and Wireless Propagation Letters 15, 1865–1868 (2016).

130 [22] A. Buﬃ, P. Nepa, and G. Manara, “Design criteria for near-ﬁeld-focused planar arrays,” IEEE Antennas and Propagation Magazine 54, 40–50 (2012).

[23] H.-T. Chou, T.-M. Hung, N.-N. Wang, H.-H. Chou, C. Tung, and P. Nepa, “Design of a near-field focused reflectarray antenna for 2.4 ghz rfid reader applications,” IEEE Transactions on Antennas and Propagation 59, 1013–1018 (2011).

[24] Y. Li and V. Jandhyala, “Design of retrodirective antenna arrays for short- range wireless power transmission,” IEEE Transactions on Antennas and Prop- agation 60, 206–211 (2012).

[25] T. Okuyama, Y. Monnai, and H. Shinoda, “20-ghz focusing antennas based on corrugated waveguide scattering,” IEEE Antennas and Wireless Propagation Letters 12, 1284–1286 (2013).

[26] P. del Hougne, M. Fink, and G. Lerosey, “Shaping microwave ﬁelds using non- linear unsolicited feedback: Application to enhanced energy harvesting,” arXiv preprint arXiv:1706.00450 (2017).

[27] D. Arnitz and M. S. Reynolds, “Mimo wireless power transfer for mobile devices,” IEEE Pervasive Computing 15, 36–44 (2016).

[28] A. Moreira, P. Prats-Iraola, M. Younis, G. Krieger, I. Hajnsek, and K. P. Papathanassiou, “A tutorial on synthetic aperture radar,” IEEE Geoscience and remote sensing magazine 1, 6–43 (2013).

[29] G. L. Charvat and L. C. Kempel, “Synthetic aperture radar imaging using a unique approach to frequency-modulated continuous-wave radar design,” IEEE Antennas and Propagation Magazine 48, 171–177 (2006).

[30] R. J. Mailloux, Phased array antenna handbook (Artech house, 2017).

[31] R. A. Alhalabi and G. M. Rebeiz, “A 77-81-ghz 16-element phased-array receiver with˘50 beam scanning for advanced automotive radars [j],” IEEE Transaction on Microwave Theory and Techniques 62, 2823–2832 (2014).

[32] G. L. Charvat, L. C. Kempel, E. J. Rothwell, C. M. Coleman, and E. L. Mokole, “An ultrawideband (uwb) switched-antenna-array radar imaging system,” in “2010 IEEE International Symposium on Phased Array Systems and Technology,” (IEEE, 2010), pp. 543–550.

131 [33] A. J. Fenn, D. H. Temme, W. P. Delaney, and W. E. Courtney, “The development of phased-array radar technology,” Lincoln Laboratory Journal 12, 321–340 (2000).

[34] J. Hunt, J. Gollub, T. Driscoll, G. Lipworth, A. Mrozack, M. S. Reynolds, D. J. Brady, and D. R. Smith, “Metamaterial microwave holographic imaging system,” JOSA A 31, 2109–2119 (2014).

[35] G. Lipworth, A. Mrozack, J. Hunt, D. L. Marks, T. Driscoll, D. Brady, and D. R. Smith, “Metamaterial apertures for coherent computational imaging on the physical layer,” JOSA A 30, 1603–1612 (2013).

[36] G. Lipworth, A. Rose, O. Yurduseven, V. R. Gowda, M. F. Imani, H. Odabasi, P. Trofatter, J. Gollub, and D. R. Smith, “Comprehensive simulation platform for a metamaterial imaging system,” Applied optics 54, 9343–9353 (2015).

[37] T. Fromenteze, O. Yurduseven, M. F. Imani, J. Gollub, C. Decroze, D. Carse- nat, and D. R. Smith, “Computational imaging using a mode-mixing cavity at microwave frequencies,” Applied Physics Letters 106, 194104 (2015).

[38] O. Yurduseven, V. R. Gowda, J. N. Gollub, and D. R. Smith, “Printed aperiodic cavity for computational and microwave imaging,” IEEE Microwave and Wireless Components Letters 26, 367–369 (2016).

[39] F. Jolani, Y. Yu, and Z. Chen, “A planar magnetically coupled resonant wireless power transfer system using printed spiral coils,” IEEE Antennas and Wireless Propagation Letters 13, 1648–1651 (2014).

[40] S. Lee, J. Huh, C. Park, N.-S. Choi, G.-H. Cho, and C.-T. Rim, “On-line electric vehicle using inductive power transfer system,” in “Energy Conversion Congress and Exposition (ECCE), 2010 IEEE,” (IEEE, 2010), pp. 1598–1601.

[41] G. Lipworth, J. Ensworth, K. Seetharam, D. Huang, J. S. Lee, P. Schmalen- berg, T. Nomura, M. S. Reynolds, D. R. Smith, and Y. Urzhumov, “Magnetic metamaterial superlens for increased range wireless power transfer,” Scientiﬁc reports 4, 3642 (2014).

[42] A. Yaghjian, “An overview of near-ﬁeld antenna measurements,” IEEE Trans- actions on antennas and propagation 34, 30–45 (1986).

[43] D. Slater, Near-ﬁeld antenna measurements (Artech House, 1991).

132 [44] M. Xia and S. Aissa, “On the eﬃciency of far-ﬁeld wireless power transfer,” IEEE transactions on signal processing 63, 2835–2847 (2015).

[45] C. A. Balanis, Advanced engineering electromagnetics (John Wiley & Sons, 1999).

[46] J. Sherman, “Properties of focused apertures in the fresnel region,” IRE Trans- actions on Antennas and Propagation 10, 399–408 (1962).

[47] M. C. Johnson, S. L. Brunton, N. B. Kundtz, and J. N. Kutz, “Sidelobe cancel- ing for reconﬁgurable holographic metamaterial antenna,” IEEE Transactions on Antennas and Propagation 63, 1881–1886 (2015).

[48] D. F. Sievenpiper, J. H. Schaﬀner, H. J. Song, R. Y. Loo, and G. Tangonan, “Two-dimensional beam steering using an electrically tunable impedance surface,” IEEE Transactions on antennas and propagation 51, 2713–2722 (2003).

[49] D. Bouyge, A. Crunteanu, A. Pothier, P. O. Martin, P. Blondy, A. Velez, J. Bonache, J. C. Orlianges, and F. Martin, “Reconﬁgurable 4 pole bandstop ﬁlter based on rf-mems-loaded split ring resonators,” in “Microwave Sympo- sium Digest (MTT), 2010 IEEE MTT-S International,” (IEEE, 2010), pp. 588–591.

[50] T. Sleasman, M. F. Imani, J. N. Gollub, and D. R. Smith, “Dynamic metamaterial aperture for microwave imaging,” Applied Physics Letters 107, 204104 (2015).

[51] S. Ladan, A. B. Guntupalli, and K. Wu, “A high-eﬃciency 24 ghz rectenna development towards millimeter-wave energy harvesting and wireless power transmission,” IEEE Transactions on Circuits and Systems I: Regular Papers 61, 3358–3366 (2014).

[52] J. W. Goodman, Introduction to Fourier optics (Roberts and Company Pub- lishers, 2005).

[53] C. R. Valenta and G. D. Durgin, “Harvesting wireless power: Survey of energy- harvester conversion eﬃciency in far-ﬁeld, wireless power transfer systems,” IEEE Microwave Magazine 15, 108–120 (2014).

[54] F. C. Williams and W. H. Kummer, “Electronically scanned antenna,” (1981). US Patent 4,276,551.

[55] R. C. Hansen, Phased array antennas, vol. 213 (John Wiley & Sons, 2009).

133 [56] C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two- dimensional equivalents of metamaterials,” IEEE Antennas and Propagation Magazine 54, 10–35 (2012).

[57] H.-T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Reports on Progress in Physics 79, 076401 (2016).

[58] D. Gabor et al., “A new microscopic principle,” Nature 161, 777–778 (1948).

[59] P. Hariharan, Optical Holography: Principles, techniques and applications (Cambridge University Press, 1996).

[60] D. R. Smith, W. J. Padilla, D. Vier, S. C. Nemat-Nasser, and S. Schultz, “Com- posite medium with simultaneously negative permeability and permittivity,” Physical review letters 84, 4184 (2000).

[61] C. Pfeiﬀer and A. Grbic, “Metamaterial huygens surfaces: tailoring wave fronts with reﬂectionless sheets,” Physical review letters 110, 197401 (2013).

[62] A. W. Lohmann and D. Paris, “Binary fraunhofer holograms, generated by computer,” Applied Optics 6, 1739–1748 (1967).

[63] E. Zhang, S. Noehte, C. H. Dietrich, and R. M¨anner, “Gradual and random binarization of gray-scale holograms,” Applied optics 34, 5987–5995 (1995).

[64] R. W. Gerchberg, “A practical algorithm for the determination of the phase from image and diﬀraction plane pictures,” Optik 35, 237–246 (1972).

[65] J. R. Fienup, “Phase retrieval algorithms: a comparison,” Applied optics 21, 2758–2769 (1982).

[66] V. R. Gowda, M. F. Imani, , T. Sleasman, O. S. Yurduseven, and D. R. Smith, “Focusing microwaves in the fresnel-zone with a cavity-backed holographic metasurface,” IEEE Access 6, 12815 – 12824 (2018).

[67] R. Siragusa, P. Lemaitre-Auger, and S. Tedjini, “Tunable near-ﬁeld focused circular phase-array antenna for 5.8-ghz rﬁd applications,” IEEE Antennas and Wireless Propagation Letters 10, 33–36 (2011).

[68] H. D. Hristov, Fresnal Zones in Wireless Links, Zone Plate Lenses and Anten- nas (Artech House, Inc., 2000).

134 [69] S. Karimkashi and A. A. Kishk, “Focusing properties of fresnel zone plate lens antennas in the near-ﬁeld region,” IEEE Transactions on Antennas and Propagation 59, 1481–1487 (2011).

[70] D. Blanco, J. L. G´omez-Tornero, E. Rajo-Iglesias, and N. Llombart, “Holo- graphic surface leaky-wave lenses with circularly-polarized focused near- ﬁeldspart ii: Experiments and description of frequency steering of focal length,” IEEE Transactions on Antennas and Propagation 61, 3486–3494 (2013).

[71] D. Blanco, J. L. G´omez-Tornero, E. Rajo-Iglesias, and N. Llombart, “Radi- ally polarized annular-slot leaky-wave antenna for three-dimensional near-ﬁeld microwave focusing,” IEEE Antennas and Wireless Propagation Letters 13, 583–586 (2014).

[72] M. Ettorre, S. C. Pavone, M. Casaletti, and M. Albani, “Experimental valida- tion of bessel beam generation using an inward hankel aperture distribution,” IEEE Transactions on Antennas and Propagation 63, 2539–2544 (2015).

[73] J. D. Heebl, M. Ettorre, and A. Grbic, “Wireless links in the radiative near ﬁeld via bessel beams,” Physical Review Applied 6, 034018 (2016).

[74] I. Iliopoulos, M. Casaletti, R. Sauleau, P. Pouliguen, P. Potier, and M. Ettorre, “3-d shaping of a focused aperture in the near ﬁeld,” IEEE Transactions on Antennas and Propagation 64, 5262–5271 (2016).

[75] M. F. Imani and A. Grbic, “An experimental concentric near-ﬁeld plate,” IEEE Transactions on Microwave Theory and Techniques 58, 3982–3988 (2010).

[76] Y. Monnai and H. Shinoda, “Focus-scanning leaky-wave antenna with electronically pattern-tunable scatterers,” IEEE transactions on antennas and propagation 59, 2070–2077 (2011).

[77] K. M. Palmer, “Metamaterials make for a broadband breakthrough,” IEEE Spectrum 49 (2012).

[78] B. H. Fong, J. S. Colburn, J. J. Ottusch, J. L. Visher, and D. F. Sievenpiper, “Scalar and tensor holographic artiﬁcial impedance surfaces,” IEEE Transac- tions on Antennas and Propagation 58, 3212–3221 (2010).

[79] S. Larouche, Y.-J. Tsai, T. Tyler, N. M. Jokerst, and D. R. Smith, “Infrared metamaterial phase holograms,” Nature materials 11, 450–454 (2012).

135 [80] M. Ando, T. Numata, J.-I. Takada, and N. Goto, “A linearly polarized radial line slot antenna,” IEEE Transactions on antennas and propagation 36, 1675– 1680 (1988).

[81] M. Ando, K. Sakurai, N. Goto, K. Arimura, and Y. Ito, “A radial line slot antenna for 12 ghz satellite tv reception,” IEEE transactions on antennas and propagation 33, 1347–1353 (1985).

[82] M. Imran and A. Tharek, “Radial line slot antenna development for outdoor point to point application at 5.8 ghz band,” in “RF and Microwave Conference, 2004. RFM 2004. Proceedings,” (IEEE, 2004), pp. 103–105.

[83] A. Akiyama, T. Yamamoto, M. Ando, N. Goto, and E. Takeda, “Design of radial line slot antennas for millimeter wave wireless lan,” in “Antennas and Propagation Society International Symposium, 1997. IEEE., 1997 Digest,” , vol. 4 (IEEE, 1997), vol. 4, pp. 2516–2519.

[84] M. Ando, K. Sakurai, and N. Goto, “Characteristics of a radial line slot antenna for 12 ghz band satellite tv reception,” IEEE Transactions on Antennas and Propagation 34, 1269–1272 (1986).

[85] T. Yamamoto, N. T. Chien, M. Ando, N. Goto, M. Hirayama, and T. Ohmi, “Design of radial line slot antennas at 8.3 ghz for large area uniform plasma generation,” Japanese journal of applied physics 38, 2082 (1999).

[86] S. Peng, C. Yuan, and T. Shu, “Analysis of a high power microwave radial line slot antenna,” Review of Scientiﬁc Instruments 84, 074701 (2013).

[87] T. Sleasman, M. Boyarsky, M. F. Imani, J. N. Gollub, and D. R. Smith, “Design considerations for a dynamic metamaterial aperture for computational imaging at microwave frequencies,” JOSA B 33, 1098–1111 (2016).

[88] L. M. Pulido-Mancera, T. Zvolensky, M. F. Imani, P. T. Bowen, M. Valayil, and D. R. Smith, “Discrete dipole approximation applied to highly directive slotted waveguide antennas,” IEEE Antennas and Wireless Propagation Letters 15, 1823–1826 (2016).

[89] P. T. Bowen, T. Driscoll, N. B. Kundtz, and D. R. Smith, “Using a discrete dipole approximation to predict complete scattering of complicated metamaterials,” New Journal of Physics 14, 033038 (2012).

[90] Y. Li and E. Wolf, “Focal shift in focused truncated gaussian beams,” Optics Communications 42, 151–156 (1982).

136 [91] M. Mart´ınez-Corral and V. Climent, “Focal switch: a new eﬀect in low-fresnel- number systems,” Applied optics 35, 24–27 (1996).

[92] P. W. Davis and M. E. Bialkowski, “Linearly polarized radial-line slot-array antennas with improved return-loss performance,” IEEE Antennas and Prop- agation Magazine 41, 52–61 (1999).

[93] M. F. Imani, T. Sleasman, J. N. Gollub, and D. R. Smith, “Analytical modeling of printed metasurface cavities for computational imaging,” Journal of Applied Physics 120, 144903 (2016).

[94] N. I. Landy, S. Sajuyigbe, J. Mock, D. Smith, and W. Padilla, “Perfect metamaterial absorber,” Physical review letters 100, 207402 (2008).

[95] P. Xu, S.-Y. Wang, and W. Geyi, “Design of an eﬀective energy receiving adapter for microwave wireless power transmission application,” AIP Advances 6, 105010 (2016).

[96] M. El Badawe, T. S. Almoneef, and O. M. Ramahi, “A true metasurface antenna,” Scientiﬁc reports 6, 19268 (2016).

[97] K. Hatano, N. Shinohara, T. Mitani, T. Seki, and M. Kawashima, “Develop- ment of improved 24ghz-band class-f load rectennas,” in “Microwave Workshop Series on Innovative Wireless Power Transmission: Technologies, Systems, and Applications (IMWS), 2012 IEEE MTT-S International,” (IEEE, 2012), pp. 163–166.

[98] N. K. Nikolova, “Microwave imaging for breast cancer,” IEEE microwave magazine 12, 78–94 (2011).

[99] Y. Wang and A. E. Fathy, “Advanced system level simulation platform for three-dimensional uwb through-wall imaging sar using time-domain approach,” IEEE Transactions on Geoscience and Remote Sensing 50, 1986–2000 (2011).

[100] S. Demirci, H. Cetinkaya, E. Yigit, C. Ozdemir, and A. A. Vertiy, “A study on millimeter-wave imaging of concealed objects: Application using back- projection algorithm,” Progress In Electromagnetics Research 128, 457–477 (2012).

[101] J. A. Martinez-Lorenzo, F. Quivira, and C. M. Rappaport, “Sar imaging of suicide bombers wearing concealed explosive threats,” Progress In Electromag- netics Research 125, 255–272 (2012).

137 [102] R. K. Amineh, J. McCombe, and N. K. Nikolova, “Microwave holographic imaging using the antenna phaseless radiation pattern,” IEEE Antennas and Wireless Propagation Letters 11, 1529–1532 (2012).

[103] D. M. Sheen, D. L. McMakin, and T. E. Hall, “Three-dimensional millimeter- wave imaging for concealed weapon detection,” IEEE Transactions on microwave theory and techniques 49, 1581–1592 (2001).

[104] D. J. Brady, Optical imaging and spectroscopy (John Wiley & Sons, 2009).

[105] S. S. Ahmed, Electronic microwave imaging with planar multistatic arrays (Lo- gos Verlag Berlin GmbH, 2014).

[106] W. M. Siebert, Circuits, signals, and systems, vol. 2 (MIT press, 1986).

[107] A. D. Yaghjian and S. R. Best, “Impedance, bandwidth, and q of antennas,” IEEE Transactions on Antennas and Propagation 53, 1298–1324 (2005).

[108] Q. Fang, P. M. Meaney, and K. D. Paulsen, “Singular value analysis of the jacobian matrix in microwave image reconstruction,” IEEE Transactions on Antennas and Propagation 54, 2371–2380 (2006).

[109] J. M. Bioucas-Dias and M. A. Figueiredo, “A new twist: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Transactions on Image processing 16, 2992–3004 (2007).

[110] C. F. Cull, D. A. Wikner, J. N. Mait, M. Mattheiss, and D. J. Brady, “Millimeter-wave compressive holography,” Applied optics 49, E67–E82 (2010).

138 Biography

Vinay Ramachandra Gowda attended Visvesvaraya Technological University, Kar- nataka, India and received a Bachelors of Engineering in Electrical and computer enginnering in 2009. He then received his Masters of Science (M.S. - Thesis) degree in Electrical Engineering from the University of Texas, Arlington, TX, USA, in 2011. After working in Intel/Intel labs from June 2011 to June 2014, Vinay returned to the academic sector in September 2014 to pursue a Ph.D. in Electrical and Computer En- gineering at Duke University’s Center for Metamaterials and Integrated Plasmonics group supervised by Professor David R. Smith. Vinay was awarded with Duke ECE Department Fellowship for 2014-2015, 2015- 2016 academic year and a conference travel Fellowship of 1000 USD in 2015. Vinay has over 10+ publications from several peer-reviewed journals mentioned at the end of this section. The proposed Wireless power transfer system was not only well received in the research community, it was also covered by the several tech and science news organizations such as Nature Physics, Duke University, Daily Mail, Intellectual Ventures, GeekWire, Eureka Alert!, Optical Society of America, University of Washington, TechXplore, Inverse among others. A list of journal papers, patents covering both the main contributions and col- laborative work during Vinay’s time as a PhD student: 1) Vinay R. Gowda, Okan Yurduseven, Guy Lipworth, Tomislav Zupan, Matthew S. Reynolds, and David R. Smith. ”Wireless Power Transfer in the Radiative Near

139 Field.” IEEE Antennas and Wireless Propagation Letters 15, 1865-1868, 2016.

2) D.R. Smith, V.R. Gowda, O. Yurduseven, S. Larouche, G. Lipworth, Y. Urzhumov and M.S. Reynolds. ”An analysis of beamed wireless power transfer in the Fresnel zone using a dynamic, metasurface aperture.” Journal of Applied Physics, 121(1), p.014901, 2017.

3) Vinay.R. Gowda,, Mohammadreza. F. Imani, Timothy Sleasman, and David R. Smith.”Focusing Microwaves in the Fresnel-Zone with a Cavity-Backed Holo- graphic Metasurface”, IEEE Access, 6, 12815-12824, 2018.

4) Vinay.R. Gowda,, Mohammadreza. F. Imani, Timothy Sleasman, and David R. Smith.”Eﬃcient Holographic Focusing Metasurface Aperture”, IEEE Access, 2019 (Submitted).

5) Vinay.R. Gowda,, Mohammadreza. F. Imani, Timothy Sleasman, and David R. Smith.”Fresnel Zone Wireless Power Transfer using Metasurface apertures”, Na- ture Scientiﬁc Reports, 2019 (Submitted).

6) Vinay.R. Gowda,, Mohammadreza. F. Imani, Hemaswaroop Mopidevi, Neil Benjamin, John Pease and David R. Smith. ”ENZ Metamaterials for reducing par- asitic capacitance applicable for low frequency wireless power transfer,” Journal not decided, 2019 (WIP).

7) Vinay.R. Gowda,, Mohammadreza. F. Imani, Hemaswaroop Mopidevi, Neil Benjamin, John Pease and David R. Smith. ”ENZ Metamaterials for reducing para- sitic capacitance applicable for low frequency wireless power transfer,” Duke patent application, 2019 (WIP).

8) Hema Mopidevi, N. Benjamin, J. Pease, David Smith, Mohammadreza. F. Imani Vinay.R. Gowda,.”Power Transfer Systems and methods for blocking RF

140 power with a Metamaterial structure”, LAM Research Patent Application, 2019 (Sub- mitted).

9) Okan Yurduseven, Vinay R. Gowda, Jonah N. Gollub, and David R. Smith. ”Printed aperiodic cavity for computational and microwave imaging.” IEEE Mi- crowave and Wireless Components Letters 26, no. 5, 367-369, 2016.

10) Okan Yurduseven, Vinay R. Gowda, Jonah N. Gollub, and David R. Smith.”Multistatic microwave imaging with arrays of planar cavities.” IET Microwaves, Antennas & Propagation 10, no. 11, 1174-1181., 2016.

11) Okan Yurduseven, Vinay R. Gowda, Jonah N. Gollub, and David R. Smith. ”Printed cavities for computational microwave imaging and methods of use.” US Patent, 15769950, 10/25/2018.

12) Tomas Zvolensky, Vinay R. Gowda, Jonah N. Gollub, Daniel L. Marks and David R. Smith. ”W-band Sparse Imaging System Using Frequency Diverse Cavity-Fed Metasurface Antennas.” IEEE Access, 6, 73659-73668, 2018

13) Guy Lipworth, Alec Rose, Okan Yurduseven, Vinay R. Gowda, Moham- madreza F. Imani, Hayrettin Odabasi, Parker Trofatter, Jonah Gollub, and David R. Smith. ”Comprehensive simulation platform for a metamaterial imaging system.” Applied optics 54, no. 31, 9343-9353, 2015.

14) Timothy Sleasman, Mohammadreza F. Imani, Okan Yurduseven, Kenneth P. Trofatter, Vinay Gowda, Daniel L. Marks, Jonah L. Gollub, and David R. Smith. ”Near Field Scan Alignment Procedure for Electrically-Large Apertures.” IEEE Transactions on Antennas and Propagation, 2017. Red devil (Manchester United) and now a Blue devil (Duke University) for life!

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