DEGREE PROJECT IN TECHNOLOGY, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2020

Dual Polarized Geodesic

Freysteinn Viðar Viðarsson

KTH ROYAL INSTITUTE OF TECHNOLOGY ELECTRICAL ENGINEERING AND COMPUTER SCIENCE Authors

Freysteinn Viðar Viðarsson Information and Communication Technology KTH Royal Institute of Technology

Place for Project

Göteborg, Sweden Stockholm, Sweden

Examiner

Oscar Quevedo-Teruel

Supervisor

Astrid Algaba Brazalez (Ericsson) Martin Johansson (Ericsson) Lars Manholm (Ericsson) Oskar Zetterström (KTH) Nelson J. G. Fonseca (ESA)

ii Abstract

Gradient-index (GRIN) lens antennas, such as the Luneburg lens, posses attractive electromagnetic properties. The smooth change in ensures no internal reflections and the focusing of the electromagnetic waves results in a directive antenna. The main challenge of the design of a GRIN lens is acquiring the required refractive index. Two dimensional dielectric can be realized using 3 dimensional homogeneous surfaces eliminating the challenge of discritizating the continuous change in refractive index. These type of lenses are commonly referred to as geodesic lenses.

In this thesis a dual polarized geodesic is presented. The antenna consists of two metal plates that form a parallel plate waveguide (PPW) section which is deformed to mimic the behaviour of a Luneburg lens. The antenna operates in the Ka band and polarizer unit cells are employed to alter the polarization state of the antenna. The polarizers are placed in a circular configuration in the flare of the antenna to maintain a compact design and good scanning range. Eleven waveguide feeds are used with 10° separation resulting in a scanning range of ±50° in the azimuth plane.

The final design is a lens antenna with a center frequency of 28 GHz and 20 % bandwidth. Simulations of the design show reflection coefficients below -15 dB and crosstalk below -17 dB. The total efficiency at 28 GHz is 90 % and above 85 % for the full frequency band.

iii Sammanfattning

Lutningsindex-linsantenner (GRIN), till exempel Luneburg-linsen, har attraktiva elektromagnetiska egenskaper. Den jämna förändringen i brytningsindexet garanterar att inga interna reflektioner inträffar och fokuset av de elektromagnetiska vågorna resulterar i en direkt antenn. Den största utmaningen att utforma en GRIN-lins är att bestämma de brytningsindexen som behövs. Plana linser kan man förverkliga med användning av tredimensionella homogena ytor som eliminerar utmaningen att diskretisera den kontinuerliga förändringen i brytningsindex. Denna typ av lins kallas geodetisk lins.

I detta examensarbete är en dubbelpolariserad geodetisk linsantenn designad. Antennen består av två metallplattor som bildar en parallell platt vågledare som är deformerad för att efterlikna beteendet hos en Luneburg-lins. Antennen fungerar i Ka- bandet och har polarisator enhetsceller för att ändra antennens polarisationstillstånd. Polarisatorerna placeras i en cirkulär konfiguration i antennen för att bibehålla en kompakt design och ett bra skanningsområde. Elva vågledare används med 10° separation vilket resulterar i ett skanningsområde på ±50° i azimutplanet.

Den slutliga designen är en linsantenn med en mittfrekvens på 28 GHz och 20 % bandbredd. Simuleringar av designen visar reflektionskoefficienter under -15 dB och crosstalk under -17 dB. Den totala effektiviteten vid 28 GHz är 90 % och över 85 % för hela frekvensbandet.

iv Acknowledgements

The work of this thesis was done in the spring semester of 2020 at Ericsson Research in Gothenburg.

I would like to thank my supervisor at Ericsson Astrid Algaba Brazalez, Lars Manholm, and Martin Johansson. They made me feel welcome at Ericsson and always had helpful suggestions. Sincere gratitude to my supervisor at KTH, Oskar Zetterström, and my examiner Oscar Quevedo-Teruel for their encouragement, technical support and help with the manufacturing process. Many thanks to Nelson J.G Fonseca from ESA for his invaluable inputs and contagious enthusiasm.

Lastly thanks to my friends and family who are always there for me.

Göteborg, September 2020 Freysteinn Viðar Viðarsson

v Contents

1 Introduction 1 1.1 Background ...... 1 1.2 Luneburg Lens ...... 2 1.3 Geodesic Lenses ...... 3 1.4 Prior Art ...... 5 1.5 Industry Demand ...... 7 1.6 Design Specifications ...... 7 1.7 Thesis Outline ...... 8

2 Theory 9 2.1 Geodesic Surfaces ...... 9 2.2 Polarization ...... 12 2.2.1 Linear Polarization ...... 13 2.2.2 Circular Polarization ...... 13 2.3 Co-Polarization and Cross-Polarization ...... 14

3 Lens Design 15 3.1 The ”Water Drop” Lens ...... 15 3.2 Flare ...... 16 3.3 Feeding ...... 17 3.4 Lens Layout and Results ...... 19 3.5 Modifying the Lens Profile ...... 22 3.5.1 The Modified Water Drop Lens ...... 25

4 Polarizer 29 4.1 Polarizer Unit Cell ...... 29 4.2 Floquet Study ...... 31 4.3 Integrating Lens and Polarizer ...... 32

vi CONTENTS

5 Manufacturing and Adjustments 37 5.1 Polarizer ...... 37 5.2 Stepped Horn ...... 38 5.3 Feeding Network ...... 39

6 Results 42 6.1 S-Parameters ...... 42 6.2 Far Field Scanning Results ...... 43 6.3 Losses ...... 44

7 Future Work and Sustainability 48 7.1 Conslusion and Future work ...... 48 7.2 Words on Sustainability ...... 49

vii List of Figures

1.2.1 An illustration of how a Luneburg lens transforms a point source at its periphery to a plane wave on the opposite side of excitation...... 3 1.2.2 Plot showing how the refractive index inside a Luneburg lens varies from the lens center...... 4 1.3.1 An illustration how the folding idea can be implemented as proposed by Kunz [11] ...... 5

2.1.1 (a) Refractive index distribution of the flat Luneburg lens. (b) The profile of the Rinehart-Luneburg lens...... 10 2.1.2 Illustration of a beam bending when travelling between two different mediums where n2 > n1 ...... 12 2.2.1 Propagating EM wave with linear polarization ...... 13 2.2.2Propagating EM wave with circular polarization ...... 14

3.1.1 Surface profile of the water drop lens with an aperture width of 107 mm. Blue dashed line shows the medium profile and the red lines the PPW implementation. Electric field distribution in the lens is included in the inset...... 16

3.2.1 Reflection coefficient of the flare. The flare has a length Lf = 14.5 mm

and height Hf = 12 mm ...... 17 3.3.1 Dimensions from data sheet of a WR28 [32] ...... 18 3.3.2The horn has 3 steps to transit from the height of the waveguide to the height of the lens...... 18 3.3.3Cross-section of stepped horn showing relevant design dimensions. . . 18 3.3.4Reflection coefficients of transition from feed to lens profile. The inset shows how the model was simulated...... 19 3.4.1 (a) Top view of the bottom plate of the lens (b) Cross Section of the lens 20 3.4.2S-parameters when feeding port 6 ...... 21 3.4.3Far field results when feeding port 6 ...... 21

viii LIST OF FIGURES

3.5.1 Strip of the lens profile with PMC boundaries in x-direction ...... 22 3.5.2An illustration of how lens profile is modified. Blue line shows the original profile and the red curve shows the profile after being modified 23 3.5.3Reflection coefficients of the lens strip with varied chamfering on the 1st bend ...... 23 3.5.4Reflection coefficients of the lens strip with varied chamfering on the 2nd bend ...... 24 3.5.5 Reflection coefficients of the original lens strip and the lens strip with chamfer1 = 0.5 mm and chamfer2 = 0.35 mm ...... 24 3.5.6Comparison Between S-parameters of original lens profile and modified (a) Reflection Coefficients (b) Selected Crosstalk ...... 26 3.5.7 S-parameters of modified lens when feeding port 6 ...... 27 3.5.8S-parameters of modified lens when feeding port 1 ...... 27 3.5.9Electric field at 28 GHz on the lens (a) Port 1 being fed - Bottom plate (b) Port 6 being fed - Bottom plate (c) Port 1 being fed - Top plate (d) Port 6 being fed - Bottom plate ...... 28 3.5.10Farfield results of the modified water drop lens...... 28

4.0.1 General view of the polarizer functionality ...... 30 4.1.1 Polarizer unit cell ...... 30 4.1.2 3-Layered polarizer configuration ...... 31 4.2.1 Polarizer in CST with unit cell boundary conditions ...... 32 4.2.2Visualisation of the TE(0,0) and TM(0,0) modes of the Floquet ports . 32 4.3.1 Transmittivity of TM and TE waves with varying rotation on the last polarizer...... 33 4.3.2Reflection coefficients of the integrated aperture ...... 33 4.3.3Selected crosstalk of integrated aperture ...... 34 4.3.4Far field results for port 1 and port 6 at 25.2, 28 and 30.8 GHz . . . . . 35 4.3.5Normalized radiation pattern of the lens with a flare and the lens with polarizers when feeding the center port...... 36

5.1.1 Smooth bend added to polarizer ...... 37 5.2.1 Corner Radius in stepped horn ...... 38 5.2.2Reflection coefficient, stepped horn to lens profile w. corner radius . . 38 5.3.1 (a) Top and bottom plate assembled (b) Top plate (c) Bottom plate . . . 39

ix 5.3.2Top and bottom plate combined showing four ports on the sides and seven on the backside...... 40 5.3.3Reflection coefficients of lens with feeding network ...... 40 5.3.4Crosstalk with feeding network ...... 41

6.1.1 Reflection coefficients of all 11 ports ...... 43 6.1.2 Selected crosstalk of neighbouring ports...... 43 6.1.3 Crosstalk between all ports ...... 44 6.2.1 Total efficiency of all ports of the radiating antenna...... 44 6.2.2Superimposed far field results of all ports at the center frequency and upper and lower frequencies...... 45 6.2.3Surface plot of the co-pol and X-pol radiation pattern at 28 GHz . . . . 46 6.3.1 (a) Results from this work (b) Results from [35] (c) Results from [36] . 47

List of Tables

1.6.1 Design Requirements ...... 8

3.3.1 Optimized parameter for the stepped horn...... 19 3.4.1 Far field performance when feeding port 6 ...... 20 3.5.1 Radiation pattern for port 1 and port 6 of the modified water drop lens 25

4.3.1 Radiation pattern performance for integrated lens. Port 1 and port 6 . . 34

x Chapter 1

Introduction

1.1 Background

In 1912 the RMS Titanic sank 600 km from the shores of Newfoundland, 1500 souls perished that day, but 700 survived thanks to the recent progress in wireless communications. The wireless operator on the Titanic was able to send a distress signal to a nearby vessel that arrived 4 hours later. Guglielmo Marconi was celebrated as the savior of the surviving passengers as he was the first to see the advantages of gearing vessels with wireless telegraph tools [1]. Marconi may have had the foresight to develop radio communication for commercial use, but was the one to propose the theory of electromagnetic radiation in 1864 and it was Heinrich Hertz that transmitted and received the first wireless signal in 1886 confirming Maxwell’s theories[2]. Since the birth of electromagnetic theory, significant advances in the branch of telecommunications have been made, especially in recent decades. Nowadays, 5G is the main focus of wireless communications.

5G stands for the fifth generation of mobile networks, but what came before 5G? The first generation (1G) was an analog transmission and was limited in terms of coverage and sound quality. Additionally, roaming between operators was not supported and calls were not encrypted, so bugging calls was no feat of engineering. Launched in the late ’70s in Japan it gained popularity in Europe and America in the 1980s. In 1991, the second generation (2G) was launched in Finland. The 2G network was digital and increased the quality of calls, reduced static noise, and allowed for text and picture messages. The migration from 2G to the third generation (3G) was a revolution in the

1 CHAPTER 1. INTRODUCTION industry. 3G technology enabled surfing on the web and making video calls possible and allowing for download speeds up to 7 Mbps and a data rate of up to 2 Mbs. The fourth-generation (4G), also been called LTE (Long term evaluation), offered speeds between 100 Mbps and 1 Gbps and latency of 100 ms[3]. We have started the transition to 5G, but what is the difference between 5G and the 4G, which we all have come to know and love? In contrast to popular belief, 5G will also operate in the same frequency band as 4G so the 5G network will use the preexisting 4G cell towers as well as the new 5G towers. However, 5G will also operate in the mm-waveband, the exact frequency bands vary between countries and continents, in Europe for example, the 26-27.5 GHz band is already reserved for 5G. During the development of 5G, we might see frequency bands up to 300 GHz being used. Moving up in frequency will result in a massive increase in bandwidth compared to the 4G network, which is vital since the current frequency bands are getting crowded, and predictions anticipate a drastic increase in mobile users in the coming years [4]. With the transition to 5G there will also be an improvement in data rates as well as a reduction of latency. This improvement will depend on what kind of cellular towers are in one’s vicinity, but a data rate of up to 20 Gbps and a latency of 1 ms are possible [5]. The 5G revolution is thrilling, but there will be obstacles to overcome. One of the larger challenges is the increase in path losses when moving to higher frequencies. Highly directive, low loss and high gain antennas are therefore of interest. Fully metallic lenses meet these criteria perfectly! Lens antennas are large devices in terms of wavelength; they are good for focusing electromagnetic waves and can be designed as fully metallic devices. One lens in particular has been a popular research topic due to its attractive properties is the Luneburg lens.

1.2 Luneburg Lens

A Luneburg lens is a graded-index (GRIN) lens with a rotationally symmetric response. The lens has two focal points, one at its periphery and the other at infinity, meaning if the lens is excited with a point source on its periphery, it produces a plane wave at the opposite side. An illustration of this is shown in Figure 1.2.1. The required refractive index, n, of the lens was derived by Rudolf Luneberg in the mid 20Th century and is given by equation 1.1 [6]. … ( ) ρ 2 n(r) = 2 − (1.1) R

2 CHAPTER 1. INTRODUCTION

Where R is the radius of the lens, and ρ is the radial coordinate, the lens refractive √ index varies from 2 at its center to 1 at its boundary. Since it has a unity refractive index at its boundary, there will be no reflections when placing the lens in free space.

Figure 1.2.1: An illustration of how a Luneburg lens transforms a point source at its periphery to a plane wave on the opposite side of excitation.

The smooth change in refractive index means that there are no internal reflections in the antenna and due to its rotational symmetry means that theoretically it has no scanning losses, combined with the fact that it needs a relatively low refractive index makes it an appealing device. Scanning is also very simple since one only needs to change the position of excitation making the needed feeding network very simple compared to other scanning devices such as an array of patch antennas or a reflector dish.

1.3 Geodesic Lenses

Luneburg lenses can be 2D or 3D devices, the 3D version of the lens allows for scanning in any direction in space while the 2D lens can only scan in a plane. However, 3D lenses traditionally use dielectrics which have drawbacks such as losses at high frequencies and risk of outgassing when used in a high vacuum environment such as space [7]. The

3 CHAPTER 1. INTRODUCTION

1.5

1.4

1.3

1.2 Refractive Index 1.1

1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Normalized Radius [ /R] Figure 1.2.2: Plot showing how the refractive index inside a Luneburg lens varies from the lens center. planar version of the Luneburg lens can be manufactured as a fully metallic device by employing metasurfaces. Those designs are suitable for high-frequency applications since there are no dielectric losses to consider and space applications since there is no risk of outgassing. However, metasurfaces are resonant devices by nature, so there is a risk of those designs being narrowband. It is worth mentioning that there has been work done on metasurfaces of higher symmetries, which notably increases the bandwidth of operation and has been used to design wideband lenses [8][9]. Additionally, metasurfaces are sub-wavelength structures meaning when moving to higher frequencies and entering the mm-wavelengths, high precision is needed for manufacturing risking high manufacturing cost. An alternative method of designing a Luneburg lens is using a profile that mimics the lens behavior, commonly referred to as geodesic lenses. Geodesic lenses offer a solution to the previously mentioned problems.

The Rinehart-Luneburg (R-L) lens is a geodesic lens proposed by Rinehart in the middle of the last century [10]. This lens provides the same functionality as the planar Luneburg lens. However, it can be manufactured using a homogeneous medium, such as air or vacuum, which is ideal for space applications and antenna designs at high frequencies. To achieve the focusing property which characterises the Luneburg lens, the R-L lens uses the third dimension, the dimension orthogonal to the beamforming plane. The lens’s required shape to mimic the refractive index of the Luneburg lens

4 CHAPTER 1. INTRODUCTION is obtainable using optical theory. The main disadvantage of the R-L lens, compared to the flat Luneburg lens, is that the required profile height is roughly 0.6 times the lens’ radius, making it less attractive due to its bulkiness. In the ’50s, Kunz proposed the idea of ”folding” the R-L lens to achieve a more compact solution, researchers from KTH and ESA revisited the idea resulting in a novel lens antenna design [11][12]. In such work, a compact lens design which is achievable by folding the R-L lens while conserving the optical paths. Figure 1.3.1 shows the principle of folding the lens.

Figure 1.3.1: An illustration how the folding idea can be implemented as proposed by Kunz [11]

1.4 Prior Art

In the 1950’s Winston Kock did impressive work on fully metallic lens antennas [13][14]. The operation principle of those antennas were based on the difference of phase velocities of guided waves in a waveguide environment. Those designs were extremely bulky making them impractical therefor lenses were more commonly constructed using dielectric materials such as foams or polyester. In 1953 a 2D configuration of the Luneburg lens was designed and manufactured, in that design the fundamental mode (TE10) was supported in a Parallel plate waveguide (PPW)

5 CHAPTER 1. INTRODUCTION filled with dielectrics. The refractive index was tailored by varying the height of the PPW section [15]. However lens antennas never gained popularity due to their bulkiness at MHz frequencies. Recently there has been an increased interest in lens antennas and many Luneburg lenses, both 2D and 3D configurations, are reported in the literature using dielectrics and metasurface. ([16]-[17]). An increased interest in fully metallic designs has led to further research on higher symmetric unit cells which show interesting electromagnetic properties. Mainly portray low dispersive behavior, those studies have led to designs of wideband fully metallic Luneburg antennas [8][9] [18].

Luneburg lenses with alternative polarization states have also been designed. In [19], a flat circularly polarized Luneburg lens was manufactured using PCB technology. The antenna had 20% bandwidth in the X-band, a scanning range of ± 35° and an efficiency of 32 %. A 3D-printed Luneburg lens was reported in [20] with dual circular polarization. This was achieved by having a circularly polarized feed. The lens had 33 % bandwidth in the Ka-band with a reflection coefficient under -10 dB and an axial ratio of less than 3dB. A flat parallel plate, 3D-printed Luneburg lens with circular polarization, was designed in [21]. The lens is composed of dielectric posts that vary the refractive index but also act as a polarizer. The antenna is excited with two orthogonal polarization states. The posts then slow one polarization state more than the other, creating circular polarization. In [22], a PPW beamformer with circular polarization is designed. Here, an array of fully metallic, periodically loaded waveguides are used as polarizers added to the aperture’s output. Achieving both right hand circular polarization (RHCP) and left hand circular polarization (LHCP) by having two stacked and separate beamforming plates. Each plate guides the wave into a different row of the polarizer, making it possible to get both LHCP and RHCP. The discretization of the waveguide polarizers limits the scanning range which is reported to be ±19°.

On geodesic lenses, the literature is not as extensive as on the traditional Luneburg lens and it is more focused on how to derive geodesic profiles from the refractive index using geometrical optics and ray tracing [6][10][11][23][24]. One recent publication was dedicated to a design of a R-L lens at 60 GHz [25]. The design is fully metallic and had a scanning range of ±55° and a radiation efficiency around 90 %. The lens used in this work is based on comprehensive work from a collaboration between researchers from KTH and ESA. They confirmed that the Rinehart-Luneburg lens could be made more compact than the standard height Rinehart-Luneburg lens by folding the lens, but still

6 CHAPTER 1. INTRODUCTION have the characteristics of a Luneburg lens [26]. In 2017 the first work on what is called the ”water drop” lens was published [27]. The name water drop was chosen since the shape of the lens resembled ripples in water when a water drop hits the surface. That work was verified using a full-wave simulation model and a manufactured prototype, which showed excellent performance over the frequency range 28-36 GHz and a scanning capability of ± 60°. Later on, more extensive literature was published from the same group accurately describing the mathematics how the folding of the lens was achieved and including performance comparison between other lenses, such as metasurface Luneburg lens and Rinehart-Luneburg lenses, showing the potential of the design[28].

1.5 Industry Demand

Although the geodesic Luneburg lens has attractive properties, there are a few demands from the industry the lens does not meet. Firstly, it is the potential of using the lens in an array for both increased directivity and the possibility of scanning in the elevation plane, that is the plane orthogonal to the beamforming plane. With the new shape of the water drop lens, multiple lenses can be stacked on each other, introducing an elegant solution to the problem. Secondly is the lens’s polarization, which has only been vertical. The need for different polarization states can be seen from two perspectives, space application, and wireless telecommunication. For space applications, circular polarization is preferred since it reduces the effect of Faraday rotation. In wireless communication, two orthogonal polarization states are desirable. That way, two signals can be sent on the same carrier frequency that can then be separated using polarization-division multiplexing, making more efficient use of the frequency band. Here we aim for a design that addresses both the need for alternative polarization states and that can be employed in an array configuration.

1.6 Design Specifications

In this thesis, the objective is to design a water drop lens and a polarizer to transform linear vertical polarization to linear ± 45° polarization. The design should have low losses, a wide scanning range, and be suitable to be used in an array configuration. The prime focus is to achieve a good polarization state over the bandwidth with adequate

7 CHAPTER 1. INTRODUCTION efficiency.

Table 1.6.1: Design Requirements

Center Frequency 28 GHz Bandwidth 20 % (25.2 - 30.8 GHz) with S11 below -15 dB Beam width 5° in azimuth (Not so strict) Scan Capability ± 50° Polarization ± 45° (Main focus of this work)

1.7 Thesis Outline

The outline of the thesis is as follows. In chapter 2 theory of transformation optics and polarization of electromagnetic waves. Chapter 3 includes lens, feeding and flare design and evaluation of the lens performance and a modification to the original lens profile. Chapter 4 is dedicated to polarizer design and the polarizer integration with the lens. Chapter 5 introduces adjustments to the designs from manufacturing point of view. In chapter 6 simulation results of the finalized design are presented. Including losses and scan capabilities of the lens. In chapter 7 there is discussion about the work done in this master thesis and future work.

8 Chapter 2

Theory

2.1 Geodesic Surfaces

As previously mentioned R. F. Rinehart proposed an alternative to the flat Luneburg lens where the required refractive index can be mimicked in a metallic PPW region by deforming the PPW region, an illustration of the flat lens and the geodesic lens can be seen in Figure 2.1.1. Rinehart derived the profile by having the arc length of the geodesic length as a function of the lens radius, s(ρ), where ρ is a normalized radius. Then by equating the displacement in the radial and azimuthal direction to the flat lens a set of differential equations can be derived.   ndr = ds,  (2.1) nrdφ = ρdφ

This is readily seen by observing Figure 2.1.1. Note that here two separate variables are used for the radius of the flat Luneburg lens and the geodesic lens, r and ρ. This is to avoid confusion and since in general if all parameters are introduced as variables of t, then r(t) ≠ ρ(t). With equation 2.1 and 1.1 (the refractive index of the Luneburg lens), Rinehart derived the arc length as a function of the normalized radius [23].

ρ + arcsin(ρ) s(ρ) = , ρ ≤ 1 (2.2) 2

Writing the elementary arc length in cylindrical coordinates using ds2 = dρ2 + ρ2dφ2 = dρ2 + dz2, then the arc length can be written as a function of the derative of z(ρ) for

9 CHAPTER 2. THEORY

Figure 2.1.1: (a) Refractive index distribution of the flat Luneburg lens. (b) The profile of the Rinehart-Luneburg lens.

ρ ≤ 1.

  √ ( ) dz 2 ds =  1 +  dρ (2.3) dρ

Using Equation 2.1 and 2.3 gives a differential equation describing the lens profile in cylindrical coordinates.

Ã( ) 2 dz 1 1 = − + √ − 1 (2.4) dρ 2 2 1 − ρ2

10 CHAPTER 2. THEORY

Equation 2.4 can then be solved numerically to get the required profile of the Rinehart- Luneburg lens. Kunz proposed that a more compact aperture could be achieved by applying reflective symmetry to the lens as shown in Figure 1.3.1. From equation 2.4 it is clear that the mentioned operation will not change the elementary arc length since the reflective symmetry operation will only change the sign of the derivative z(ρ). That is to say looking at Figure 1.3.1 those three curves all have the same relation between the arc length and the radial distance. The height of the lens after N number of symmetry operation will be hN = h0/2N where h0 is the normalized height of the reference lens. However the discontinued derivative at the folding locations, as seen in Figure 1.3.1, will cause mismatch so the sharp edges ,that introduce reflections and phase aberrations, must be replaced with a smooth function. In [28] there are comprehensive instruction on the design procedure of a modulated geodesic lens and how to evaluate the phase distribution in the aperture. In such investigations the profile is decomposed into spline functions to ensure smoothness at the folding locations. The method used to design the lens is quite brilliant and does not require a full-wave simulator during the design procedure. The achieved spline profile of the lens is mapped to a flat lens with the analogous refractive index, then using ray tracing based on Snell-Descartes law of refraction (equation 2.5 and Figure 2.1.2) the phase distribution in the aperture is evaluated. This method has to be shown quite accurate by the authors even though the ray tracing does not consider the impedance mismatch caused by the bends of the modulated lens.

n1 sin θ1 = n2 sin θ2 (2.5)

The mapping of the profile to a refractive index map is arguably the challenge here but is achieved using transformation optics. In [29] transformation from refractive index map to an arbitrary surface was investigated. Here the interest is going from a given surface to a refractive index map. This is done by first combining equations 2.1 and 2.3 [28].   √ ( ) dr dz 2 dρ =  1 +  (2.6) r dρ ρ

Equation 2.6 can then be solved numerically using boundary condition r = 1 for ρ = 1 to define a function r(t) for any function z(ρ) describing the profile of the aperture. Then equation 2.1 can be used to evaluate n(t) giving the refractive index of the equivalent

11 CHAPTER 2. THEORY

Figure 2.1.2: Illustration of a light beam bending when travelling between two different mediums where n2 > n1 planar lens. When the equivalent refractive index map has been retrieved the phase errors can be evaluated which is to be minimized as well as the lenses height. Meaning two objective functions are evaluated during the optimization procedure.

2.2 Polarization

The polarization of an antenna is simply defined as the direction of the electric field of the radiating aperture. Polarization state is an important property of EM waves and has to be taken in consideration in antenna design. If the antenna does not match the polarization of the EM wave the antenna will not receive any signal from the propagating wave. There are three different polarization states possible for an EM wave

• Linear

• Circular

• Elliptical

Any electric field can be decomposed into two orthogonal field vectors with information

12 CHAPTER 2. THEORY about the amplitude and phase of each component.

E(z, t) = Ex + Ey = Ex exp (j [kz − ωt + φx]) + Ey exp (j [kz − ωt + φy]) (2.7)

Here k is is the wavenumber in free space, ω is the angular frequency and φx and φy are the phases of the fields respectively.

2.2.1 Linear Polarization

If the radiated field vector from an antenna has only one component or two orthogonal components that are in phase it has a linear polarization. That happens when Ex = 0 or Ey = 0 or if Ex ≠ 0 and Ey ≠ 0 then ∆φ = 0°, 180°

Figure 2.2.1: Propagating EM wave with linear polarization

2.2.2 Circular Polarization

If the radiated field vector from an antenna has two orthogonal components of equal magnitude and are 90° out of phase, that is if Ex = Ey and ∆φ = φx − φy = ±90° the antenna has circular polarization. Depending on which component is lagging we get LHCP or RHCP.

13 CHAPTER 2. THEORY

Figure 2.2.2: Propagating EM wave with circular polarization

2.3 Co-Polarization and Cross-Polarization

Co-polarization (Co-pol) of an antenna is the desired polarization state and the cross- polarization (X-pol) is the polarization state orthogonal to the co-pol. For example if the co-polarization is vertical then the X-pol is horizontal. The level of X-pol is the difference in decibels between the co-pol and X-pol. Most commercial electromagnetic simulation tool have a coordinate system called Ludwig3 which provides the co-pol and X-pol of the far field.

14 Chapter 3

Lens Design

The lens antenna in this thesis is based on the work done in [28] and [30]. The antenna is a rotationally symmetric PPW beamformer that mimics the response of a Luneburg lens. The design is fully metallic, making it suitable for high frequency applications. Additionally, the smooth profile results in a simple manufacturing process.

3.1 The ”Water Drop” Lens

The lens consists of a top and a bottom plate which, when combined, form a PPW region that supports the TEM mode. The diameter of the lens can be chosen from performance requirements where the beam width is to be < 5° in the 25.2 - 30.8 GHz band. The aperture size can be chosen based on the 3dB beamwidth formula [31].

λ ∆θ = 51° (3.1) aperture width With ∆θ = 5° equation 3.1 gives aperture width ≈ 10λ = 107 mm. The lens profile required can be seen in Figure 3.1.1

15 CHAPTER 3. LENS DESIGN

Figure 3.1.1: Surface profile of the water drop lens with an aperture width of 107 mm. Blue dashed line shows the medium profile and the red lines the PPW implementation. Electric field distribution in the lens is included in the inset.

The radius is 53.5 mm, and the height of the lens is roughly 13 mm or about 25 % of the radius, which is a notable reduction from the height of the Rinehart-Luneburg geodesic lens. The PPW region height is chosen as 2 mm. Previous work on a modified geodesic lenses reported a design with that same PPW height with excellent radiation efficiency and good beamforming capabilities [30]. Choosing a smaller PPW region height will give a profile closer to the ideal one and reduce phase aberrations but the drawback is an increase in Ohmic losses.

3.2 Flare

A flare is needed for impedance matching to free space. With no flare, the antenna would radiate similarly to a waveguide (WG) of height 2 mm. That would result in a return loss of about 10 dB. Figure 3.2.1 shows the flare design and simulated return loss of the design. The flare has an exponential tapering as shown in Figure 3.2.1 and reflection coefficients are above 20 dB over the frequency band. The width of the simulated flare is 107 mm, the same as the diameter of the lens.

16 CHAPTER 3. LENS DESIGN

Figure 3.2.1: Reflection coefficient of the flare. The flare has a length Lf = 14.5 mm and height Hf = 12 mm

3.3 Feeding

In order to deliver power to the geodesic lens, a feeding network is required. In the lens design presented in [18] coaxial probe was used to excite the fundamental mode, TE10, in a rectangular waveguide followed by a stepped horn to match to the height of the lens. However, impedance mismatch occurred due to tolerances of the coaxial probe’s height, causing reflections. To avoid such problems we have opted for using a standard WR28 (a = 7.112 mm, b = 3.556) waveguide. Datasheet with relevant dimensions is presented in Figure 3.3.1. Only a stepped horn is therefore needed to match the height of the lens will be needed.

17 CHAPTER 3. LENS DESIGN

Figure 3.3.1: Dimensions from data sheet of a WR28 [32]

Figure 3.3.2: The horn has 3 steps to transit from the height of the waveguide to the height of the lens.

Figure 3.3.3: Cross-section of stepped horn showing relevant design dimensions.

To avoid reflections between the stepped horn and the lens, the stepped horn is designed with the lens. Since designing the stepped horn with the whole lens aperture

18 CHAPTER 3. LENS DESIGN would be computationally heavy only a part of the lens profile is modelled. Here we optimize the stepped horn to a portion of the lens as seen in the inset of Figure 3.3.4. In this model the first two bends of the lens are included but no radial curvature is introduced.

Figure 3.3.4: Reflection coefficients of transition from feed to lens profile. The inset shows how the model was simulated.

Table 3.3.1: Optimized parameter for the stepped horn.

Parameter Value [mm]

h1 3.56

h2 3.30

h3 2.50

h4 2.00

d1 15.0

d2 4.60

d2 4.50

d2 11.20

3.4 Lens Layout and Results

Figure 3.4.1 shows the layout of the lens. The feeding network consists of 11 waveguides placed in 10° intervals allowing for a scanning range of ±50°. Throughout this thesis,

19 CHAPTER 3. LENS DESIGN the xy plane is referred to as the elevation plane and is assigned the Greek letter θ. The yz plane is called the scanning plane and is assigned the Greek letter ϕ . The model is simulated as a perfect electric conductor (PEC) material using CST transient solver.

Figure 3.4.1: (a) Top view of the bottom plate of the lens (b) Cross Section of the lens

We start by feeding only the center port to check the performance of the design, S- paremters can be seen in Figure 3.4.2. The figure only includes information about ports 1-6 since due to symmetry identical results are observed in ports 7-11. The radiation pattern can be seen in Figure 3.4.3 and detailed information can be seen in Table 3.4.1.

Table 3.4.1: Far field performance when feeding port 6

Frequency [GHz] 25.2 28 30.8 Directivity [dBi] 18.9 19.6 20.4 3dB Beam Width [°] 6.6 6.6 5.7 SLL [dB] -15.0 dB -19.5 dB -16.5 dB

As can be observed in Figure 3.4.2 the reflection coefficient, S6,6, is not below -15 dB over the band and same goes for the crosstalk of the two(four) neighbouring ports S5,6

20 CHAPTER 3. LENS DESIGN

Figure 3.4.2: S-parameters when feeding port 6

Figure 3.4.3: Far field results when feeding port 6

and S4,6 (S7,6 and S8,6 ). The values of those S-parameters will lead to high losses, and some further investigation to improve the performance is needed. Ideally, the reflection coefficients should be below -15 dB and the crosstalk below -20 dB.

The beam shape at 25.2 GHz does not look as good as at the other frequencies. It depicts a ”shoulder” where the other beams present a sharper dip and the sidelobes are too high and the main side lobes are far away from the main beam. The cause might be because of strong reflections in the lens. Investigation about reflection in the lens is discussed in next section.

21 CHAPTER 3. LENS DESIGN

3.5 Modifying the Lens Profile

Since the flare and feeding design have a return losses above 20 dB, the reflections most likely occur in the lens, mainly, at the bends. The source of reflection can be identified by taking a small strip of the antenna profile and studying it. The model of a strip of the antenna profile can be seen in Figure 3.5.1. In the x-direction, PMC (perfect magnetic conductor) boundary conditions are applied, so the TEM mode is supported in the strip and on each side are WG ports.

Figure 3.5.1: Strip of the lens profile with PMC boundaries in x-direction

In order to reduce the reflections, some modifications must be made to the profile. If the profile is varied too much, the lens will no longer have the same beamforming characteristics, so the modification must be small enough as not to change the lens performance. To reduce the reflections ”chamfering” of the outer radius at the bends is applied, implementation of the chamfering can be seen in Figure 3.5.2.

We start by chamfering the bends independently and observe the effect it has on the reflection coefficients. The first bend is chamfered, and a comparison between reflection coefficients of differently chamfered strips can be seen in Figure 3.5.3. Similarly, the second bend is chamfered while keeping the first bend as the original profile. Results can be seen in Figure 3.5.4.

22 CHAPTER 3. LENS DESIGN

Figure 3.5.2: An illustration of how lens profile is modified. Blue line shows the original profile and the red curve shows the profile after being modified

Figure 3.5.3: Reflection coefficients of the lens strip with varied chamfering on the 1st bend

23 CHAPTER 3. LENS DESIGN

Figure 3.5.4: Reflection coefficients of the lens strip with varied chamfering on the 2nd bend

As can be observed in Figures 3.5.3 and 3.5.4 there is a resonant behaviour which disappears when the chamfer is applied, this is more apparent when modifying the 1st bend. Choosing chamfer1 = 0.5 mm and chamfer2 = 0.35 mm the resulting profile and the reflection coefficients of a strip of the modified lens profile are shown in Figure 3.5.5

Figure 3.5.5: Reflection coefficients of the original lens strip and the lens strip with chamfer1 = 0.5 mm and chamfer2 = 0.35 mm

24 CHAPTER 3. LENS DESIGN

3.5.1 The Modified Water Drop Lens

With the modified lens the same layout as in Figure 3.4.1 is simulated. The reflection coefficients when feeding the center port of the original lens and the modified chamfered lens are shown in Figure 3.5.6 (a). There is a clear difference in the reflection coefficients, before the modification a standing wave pattern could be observed which has now disappeared. Additionally selected coupling coefficients are shown in in Figure 3.5.6 (b) and a significant improved can be seen.

Crosstalk and reflection coefficients are shown in Figure 3.5.7 when the center port is excited. As can be observed the reflection coefficient is well below -15 dB and the coupling coefficients are below -18 dB. Here all the S-parameters are included and as can be seen crosstalk of symmetric ports are identical. Port 1 was also excited and reflection and coupling coefficients can be seen in Figure 3.5.8. Again the reflection coefficient is below -15 dB and the coupling coefficients below -18 dB. Figure 3.5.9 shows how the spherical waves from the waveguide ports are transformed into plane waves at the opposite end of the feeding.

Far field results are shown in Figure 3.5.10 when feeding port 1 and port 6. Even though some modifications were made to the lens profile there is no loss in directivity and the beam shape looks promising. There are no scanning losses and the side lobes present at the lower frequency before the modification have disappeared. Hence, the modified lens profile will replace the original one due to significant improvement in S-parameters without degrading the radiation performance.

Table 3.5.1: Radiation pattern for port 1 and port 6 of the modified water drop lens

Port 1 Port 6 Frequency [GHz] 25.2 28 30.8 25.2 28 30.8 Directivity [dBi] 18.9 19.7 20.5 19.0 19.7 20.4 3dB Beam Width [°] 6.7 6.2 5.7 6.8 6.5 6.0 SLL [dB] -15.3 -17.6 -19.1 -17.7 -18.7 -18.9

25 CHAPTER 3. LENS DESIGN

Figure 3.5.6: Comparison Between S-parameters of original lens profile and modified (a) Reflection Coefficients (b) Selected Crosstalk

26 CHAPTER 3. LENS DESIGN

Figure 3.5.7: S-parameters of modified lens when feeding port 6

Figure 3.5.8: S-parameters of modified lens when feeding port 1

27 CHAPTER 3. LENS DESIGN

Figure 3.5.9: Electric field at 28 GHz on the lens (a) Port 1 being fed - Bottom plate (b) Port 6 being fed - Bottom plate (c) Port 1 being fed - Top plate (d) Port 6 being fed - Bottom plate

Figure 3.5.10: Far field results of the modified water drop lens.

28 Chapter 4

Polarizer

Polarizers are commonly used with antennas to alter the polarization of the radiated aperture. For this work, the interest is in a polarizer that rotates the electric field from vertical polarization to ± 45° linear polarization. Figure 4.0.1 shows the general idea of the functionality of the polarizer. The polarizer must have proper functionality in the operating frequency range, meaning it has to rotate the electric field without distorting the electric field. In general, two different methods have been employed to achieve different polarization states in lens antennas. Firstly, the feeding of the antenna determines the polarization states. This is not an option for metallic PPW lenses since only the TEM mode is supported, but can be used for dielectric lenses. Secondly, it is possible to have an array of polarizers positioned some distance away from the antenna as an independent structure. If one wants the polarizer to be operational for the whole scanning range, the polarizer array becomes very large. In this work we will design a polarizer to be integrated to the antenna implemented in the previous chapter.

4.1 Polarizer Unit Cell

The polarizer unit cell, which is a complementary split ring resonator (CSRR), can be seen in Figure 4.1.1. Figure 4.1.2 shows the polarizer in a layered configuration where the unit cells are fully metallic and are separated by air and the center bar is rotated which rotates the electric field traveling through the polarizer. In the study done in [33], an array of dielectric CSRRs was studied in a layered configuration. Reported results showed an efficient broadband linear polarization transformation where the direction of the polarization state could be controlled by rotating the CSRR

29 CHAPTER 4. POLARIZER

Figure 4.0.1: General view of the polarizer functionality

in the corresponding direction. Transmission efficiency of 96 % was reported and a bandwidth of 24 % of the central frequency. A fully metallic version of the array of CSRRs was studied in [34]. Metallic sheets were perforated to get the geometry of the CSRR, the metallic sheets were then stacked with air gap between them to make a flat lens which was used for a phase correction of a radiating waveguide. Since the polarization state can be so easily manipulated and previous work shows a good transmission can also be achieved with the fully metallic CSRR this unit cell will be investigated for this project.

Figure 4.1.1: Polarizer unit cell

30 CHAPTER 4. POLARIZER

Figure 4.1.2: 3-Layered polarizer configuration

4.2 Floquet Study

The unit cell is investigated in a periodic environment using Floquet ports. Using the Floquet ports it is possible to excite two orthogonal fundamental TEM modes, named TE(0,0) (transverse electric) and TM(0,0) (transverse magnetic) in CST. Here, we are interested in exciting the TE(0,0) mode and then evaluating the transmission to the TE(0,0) and TM(0,0) ports at the opposite side. Figure 4.2.2 shows an illustration of the TE(0,0) and TM(0,0) modes. To get a 45° linearly polarized wave the transmission magnitude to the TE and the TM must be equal and in phase. Let’s name the transmitted wave from TE to TE, Sy2,y1, and for TE to TM, Sx2,y1. Figure 4.3.1 demonstrates how the transmittivity between the ports changes when the last bar is 1 rotated. That is when φ2 is varied. Here we couple φ1 and φ2 by setting φ1 = 2 φ2 It is quite clear that when increasing the rotation of the last bar there is increased transmittance to Sx2 and when φ2 = 45° we can see the transmittance to TE and TM is almost the same.

The 3-layered polarizer was optimized in the unit cell environment. The φ2 variable, the rotation of the last polarizer, was set to a fixed value of 45°. Rest of the parameters could then be tuned for an efficient transmission through the layers.

31 CHAPTER 4. POLARIZER

Figure 4.2.1: Polarizer in CST with unit cell boundary conditions

Figure 4.2.2: Visualisation of the TE(0,0) and TM(0,0) modes of the Floquet ports

4.3 Integrating Lens and Polarizer

Next step in the design is integrating the polarizer and the lens to evaluate the overall performance. We start by simulating the integrated design as a PEC, this will allow for a smaller simulation domain since the lens can be simulated as a sheet metal. For this model the center port (port 6) and one of the outermost ports (port 1) are excited. This corresponds to a scanning direction of 0° and -50°. Reflection coefficients can be seen in Figure 4.3.2 and selected crosstalk in Figure 4.3.3. The reflection coefficients are below -15 dB but some of the crosstalk is above -20 dB range but never above -17 dB.

32 CHAPTER 4. POLARIZER

Far field results can be seen in Figure 4.3.4 and detailed performance is listed in table 4.3.1.

Figure 4.3.1: Transmittivity of TM and TE waves with varying rotation on the last polarizer.

The aperture size is smaller with the polarizers which explains the decrease in directivity from the antenna presented in previous chapter. To compare the radiation pattern between the lens with the flare and the lens with the polarizer, normalized radiation pattern of both design is plotted as seen in Figure 4.3.5. The radiation pattern are quite similar between designs and the beams at 25.2 GHz and 28 GHz follow each other closely. Some widening of the beam is observed at 30.8 GHz.

Figure 4.3.2: Reflection coefficients of the integrated aperture

33 CHAPTER 4. POLARIZER

Figure 4.3.3: Selected crosstalk of integrated aperture

Table 4.3.1: Radiation pattern performance for integrated lens. Port 1 and port 6

Port 1 Port 6 Frequency [GHz] 25.2 28 30.8 25.2 28 30.8 Directivity [dBi] 17.2 17.6 17.9 17.3 17.3 17.7 3dB Beam Width [°] 6.1 6.5 5.8 6.9 7.4 6.7 X-Pol level [dB] -17.4 -23.8 -30.4 -18.1 -24.0 -33.0 SLL [dB] -15.8 -16.7 -15.0 -18.3 -18.1 -18.0

34 CHAPTER 4. POLARIZER

Figure 4.3.4: Far field results for port 1 and port 6 at 25.2, 28 and 30.8 GHz

35 CHAPTER 4. POLARIZER

Figure 4.3.5: Normalized radiation pattern of the lens with a flare and the lens with polarizers when feeding the center port.

36 Chapter 5

Manufacturing and Adjustments

5.1 Polarizer

A little adjustment has to be made on the center circle of the polarizer since a sharp transition from the circle to the bar is not possible. Therefore, a blended curve has to be applied. The difference can be seen in Figure 5.1.1.

Figure 5.1.1: Smooth bend added to polarizer

The radius of the bend is r = 0.25 mm, in accordance with manufacturing constraints. It has no effect on the performance.

37 CHAPTER 5. MANUFACTURING AND ADJUSTMENTS

5.2 Stepped Horn

A slight modification has to be made to the stepped horn due to manufacturing constraints. Corners of the stepped sections are smoothed since the milling machine has some milling radius. Here, a study is made as can be seen in Figure 5.2.2, and there is no effect on the reflection coefficients when having a milling radius up to 0.8 mm.

Figure 5.2.1: Corner Radius in stepped horn

Figure 5.2.2: Reflection coefficient, stepped horn to lens profile w. corner radius

38 CHAPTER 5. MANUFACTURING AND ADJUSTMENTS

5.3 Feeding Network

As discussed in section 3.5.1 the lens will be excited using standard WR28 waveguides. For manufacturing the width of the flanges have to be taken into account as well as proper mounting for the waveguides. The bottom and top plate can be seen in Figure 5.3.1

Figure 5.3.1: (a) Top and bottom plate assembled (b) Top plate (c) Bottom plate

In Figure 5.3.1 (b) and (c) it can be seen that after the stepped horn section the waveguide is extended to the edges of the plates. Four waveguides opening on the sides and seven on the backside. This is done so there is enough space to place all the waveguides on the lens at the same time. To make sure the extension of the waveguides do not introduce reflections, this model was simulated with waveguide ports at the waveguide openings. Since having the polarizers and the bottom and top plate resulted

39 CHAPTER 5. MANUFACTURING AND ADJUSTMENTS in a simulation domain too large for the computer, the simulation was done using the flare employed in Section 3.5.1.

Figure 5.3.2: Top and bottom plate combined showing four ports on the sides and seven on the backside.

Figure 5.3.3: Reflection coefficients of lens with feeding network

40 CHAPTER 5. MANUFACTURING AND ADJUSTMENTS

Figure 5.3.4: Crosstalk with feeding network

The reflection coefficients are below -15 dB and the coupling coefficients below -19 dB similar to the results presented in section 3.5.1.

41 Chapter 6

Results

Here simulation results are presented for the assembled design with the manufacturing adjustments. This includes S-parameters, far field and losses in the lens. The material used is aluminium from CST material library.

6.1 S-Parameters

Simulated reflection coefficients for all 11 ports are shown in Figure 6.1.1. All reflection coefficients are below -15 dB over the frequency range of interest and it can be seen due to the symmetry of the design that all reflection coefficients show similar behaviour. Figure 6.1.2 shows selected coupling coefficients, the ones chosen are the ”neighbouring ports” of the excited ports since those experience the most coupling effects. As previously mentioned, it would have been preferred to have the cross-talk below -20 dB but evidently that was not accomplished. A better matching could have been accomplished on the cost of a higher X-pol levels. Crosstalk between all ports can be seen in Figure 6.1.2.

42 CHAPTER 6. RESULTS

Figure 6.1.1: Reflection coefficients of all 11 ports

Figure 6.1.2: Selected crosstalk of neighbouring ports.

6.2 Far Field Scanning Results

Radiation pattern which correspond to the center, upper and lower frequencies are shown in Figure 6.2.2, here the realized gain of the Co-pol is plotted. The cross-over level between beams is about 7 dB. The total efficiency for each port is shown in Figure 6.2.1, at 28 GHz the efficiency is about 90 % and over the band of interest the efficiency is above 87 %. The radiation patterns generally look good and show very little scanning losses,the beam shape gets worse when moving up in frequency. At 30.8 GHz we do not see the sharp dip of the beam as at 25.2 GHz and 28 GHz. The results shown here are superimposed beams not combined results. Figure 6.2.3 shows a surface plot of the radiation pattern of the co-pol and X-pol at 28 GHz.

43 CHAPTER 6. RESULTS

Figure 6.1.3: Crosstalk between all ports

Figure 6.2.1: Total efficiency of all ports of the radiating antenna.

6.3 Losses

All losses in the lens are metallic losses since the use of dielectrics was avoided. Figure 6.3.1 shows the powers in the lens from the simulation. The loss in metals is only about 6 % which is quite low, indicating that a PPW height of 2 mm for the lens is sufficient to avoid large ohmic losses. In previous thesis where a metasurface lens was designed larger metallic losses were present but there the PPW height of the lens was much smaller, 0.1 and 0.3 mm, which was needed to reach the required refractive index. Being able to control the PPW height of the geodesic lens is therefore desirable.

44 CHAPTER 6. RESULTS

Figure 6.2.2: Superimposed far field results of all ports at the center frequency and upper and lower frequencies.

45 CHAPTER 6. RESULTS

Figure 6.2.3: Surface plot of the co-pol and X-pol radiation pattern at 28 GHz

46 CHAPTER 6. RESULTS

Figure 6.3.1: (a) Results from this work (b) Results from [35] (c) Results from [36]

47 Chapter 7

Future Work and Sustainability

7.1 Conslusion and Future work

In this thesis, a dual polarized geodesic Luneburg lens antenna is designed. It consists of a PPW beamformer and a polarizer unit cell. All components fully metallic. The antenna shows good performance in the frequency range of 25.2-30.8 GHz, having reflection coefficients below -15 dB and crosstalk below -18 dB. The beamwidth of the antenna varies from 7.5° to 5.8°, this is a bit higher than the requirements but the main goal of this thesis was to achieve a ±45° polarized antenna which was achieved. This was done by having polarizers in the edge of the flare to rotate the electric field. 11 ports were used to feed the antenna resulting in a scanning angle of ± 50° and good performance was achieved over the whole scanning range.

The future work includes the manufacturing of the lens and polarizers and measurements of the integrated aperture. Further improvements could be done on the feeding network, more accurately how to have the feeds closer together. That way more beams could be produced in the same scanning angle improving the resolution of the device. Additionally, manufacturing a stacked array of the lens would be interesting to see how well it performs but for this work we make do with one aperture to verify the device performance.

48 CHAPTER 7. FUTURE WORK AND SUSTAINABILITY

7.2 Words on Sustainability

With the notable negative effect, humanity is having on the earth’s climate sustainability is becoming the keyword in many scientific fields. There is a clear connection to the fields of transportation and power production but how does it link to electromagnetics. With the 5G revolution, more cellular towers are being built and there will be an increase in mobile users as well as mobile devices. This is bound to increase the energy usage of the telecommunication industry. Then the question arises if this next generation of mobile communication should be abandoned and we should stop funding academic research on the topic. The truth is that the 5G revolution has started and already we have our sights on what will come after 5G. Making it vital to find an efficient way to broadcast super and extremely high radio frequency signals. Additionally, we can make use of this new technology for the benefit of the climate. Having smart cities and smart farms can play a vital role to reduce carbon emission. So even though this work will not make a huge impact on a sustainable future it might a tiny step in the correct direction.

49 Bibliography

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