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Ka-Band 2D Luneburg Lens Design with Glide-Symmetric Metasurface

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Ka-Band 2D Luneburg Lens Design with Glide-Symmetric Metasurface DEGREE PROJECT IN ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2017 Ka-band 2D Luneburg Lens Design with Glide-symmetric Metasurface JINGWEI MIAO KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL ENGINEERING TRITA 2017:115 ISSN 1653-5146 www.kth.se Ka-band 2D Luneburg Lens Design with Glide-symmetric Metasurface Jingwei Miao Supervisors: Astrid Algaba Brazalez, Lars Manholm, Martin Johansson N (Ericsson) Fatemeh Ghasemifard (KTH) Examiner: Oscar Quevedo-Teruel (KTH) A thesis submitted for the degree of Master of Science July 2017 Abstract A Luneburg lens is a beam former that has two focal points where one is at the surface and the other lies at infinity. It is a cheap passive steerable antenna at high frequencies. In this thesis, a 2D flat-profile Luneburg lens with all-metal structure is designed for Ka band. Commercial soft- ware CST Microwave Studio Suite and Ansys Electronic Desktop (HFSS) are used for simulations. The lens is composed of two glide-symmetric metasurface layers with a small gap in between. The high order symmetry, glide symmetry, could provide ultra wide band property for the lens. Each layer contains many unit cells. Different unit cells are tested in this thesis to find the best solu- tion taking into account both electromagnetic properties and the easiness of manufacturing. A flare is designed to achieve better matching between the air gap of the lens and free space. A self-designed waveguide feeding is also used, including a transition from coaxial cable to TE10 mode of rectangular waveguide at the focus of the lens. The prototype will be built in the future and measurements will be done to compare with simulation results in this thesis. Abstract En Luneburg-lins ¨ar en lobformare som har tv˚afokalpunkter, en vid lin- sens yta och en i o¨andligheten. Den ¨ar en billig passiv styrbar antenn vid h¨oga frekvenser. I detta examensarbete konstrueras en plan Luneburg-lins i metall f¨or Ka-bandet. De kommersiella programvarorna CST Microwave Studio Suite och Ansys Electronic Desktop (HFSS) anv¨ands f¨or elektro- magnetiska simuleringar. Linsen best˚arav tv˚aglidsymmetriska metaytor med ett litet mellanrum. En h¨ogre ordnings symmetri, glidsymmetri, kan ge linsen ultrabred band- bredd. Metaytorna best˚arav ett stort antal enhetsceller. Olika typer av enhetsceller testas f¨or att hitta den b¨asta l¨osningen med h¨ansyn till b˚ade elektromagnetiska egenskaper och tillverkningsbarhet. En tv˚adimensionell hornstruktur konstrueras f¨or att uppn˚agod matchning mellan linsens luft- gap och frirymd. En v˚agledarmatningdesignas ocks˚a,inklusive ¨overg˚ang fr˚ankoaxialledning till TE10-moden i en rektangul¨ar v˚agledare,som an- sluter till linsens fokalpunkt. En prototyp kommer att byggas i ett senare skede och m¨atningar g¨oras f¨or att j¨amf¨ora med simuleringsresultaten i detta examensarbete. Acknowledgements This study was done at Ericsson Research in Gothenburg Sweden during the spring of 2017. I would like to express my sincere gratitude to my supervisors Astrid Algaba Brazalez, Lars Manholm and Martin Johansson N in Ericsson. They supported me greatly with valuable comments, suggestions and ex- planations in all problems I met during the procedure. In addition, they gave me a lot of care and concern in life during my staying in Gothenburg. I would also like to thank my supervisor Fatemeh Ghasemifard in KTH. She gave me much technical support and many advices as a PhD student. And my examiner Professor Oscar Quevedo-Teruel, he is always there dur- ing my entire study in KTH. I appreciate it a lot for his monthly visiting to Ericsson Gothenburg, to discuss the progress and give advices. Furthermore I want to say thanks to all my colleagues in Ericsson. Their warm help and company make my life in Gothenburg happy and pleasant. In the end I would like to thank my family and friends, who are always willing to help and encourage me when I face troubles. Gothenburg, July 2017 Jingwei Miao Contents 1 Introduction 1 1.1 Background Information . 1 1.2 Luneburg Lens . 3 1.3 Antenna Design Specifications . 4 1.4 The State of Art . 5 1.5 Thesis Outline . 6 2 Theory 8 2.1 Metasurface . 8 2.2 Glide Symmetry . 9 2.3 Unit Cell Properties . 10 2.3.1 Brillouin Zone . 10 2.3.2 Effective Refractive Index . 12 3 Unit Cell Design 14 3.1 Holey Structure . 14 3.1.1 Deciding Air Gap Thickness g . 15 3.1.2 Deciding Layer Thickness t .................... 16 3.1.3 Deciding Periodicity p and Hole Diameter D . 17 3.1.4 Theoretically Further Exploring . 18 3.1.5 Comparison with Ordinary Unit Cells . 19 3.2 Hole with One Pin . 19 3.2.1 Feasible Solutions . 21 3.2.2 Manufacturing Considerations . 23 3.3 Hole with Four Pins . 24 3.3.1 Round Pins . 24 3.3.2 Square Pins . 25 3.4 Final Unit Cell Choice . 26 i 3.4.1 Dispersion Exploration . 27 4 Lens Layout 31 4.1 Design Frequency Shift . 31 4.2 Metasurface Lens Design . 33 5 Flare and Feeding Design 36 5.1 Flare Design . 36 5.1.1 A Sliced Model . 36 5.1.2 Flare with Circular Parallel Plate . 38 5.1.3 Flare with Metasurface Lens . 40 5.2 Feeding Design . 40 5.2.1 Coaxial Probe to Rectangular Waveguide . 42 5.2.2 Stepped Horn Connection . 45 6 Complete Design Results 47 6.1 Focal Point Determination . 47 6.2 Single Feeding Result . 49 6.3 Multiple Feedings Result . 51 7 Tolerance Evaluation 55 7.1 Feeding Parameters Investigation . 55 7.2 Flare edge Smoothness Investigation . 57 7.3 Gap Height Investigation . 60 8 Conclusions and Future Work 64 Bibliography 66 ii List of Figures 1.1 Cross-section of a standard Luneburg lens. 3 1.2 Refractive index variation of a standard Luneburg lens. 4 2.1 Illustration of glide symmetry. 9 2.2 A typical unit cell in periodic metasurface. 10 2.3 Irreducible Brillouin zone. 11 2.4 Dispersion diagram in x- direction. 12 3.1 Holey unit cell configuration. 14 3.2 neff versus frequency for different height of hole. g = 0:2 . 15 mm, t = 2 mm, p = 3:6 mm, D = 3:06 mm. 3.3 neff versus h at 28 GHz for different g. 16 3.4 neff versus h at 28 GHz. g = 0:2 mm, t = 2 mm . 17 3.5 neff versus D=p at 28 GHz. g = 0:2 mm; t = 2 mm; h = 1:8 mm . 18 3.6 neff versus g at 28 GHz. t = 2 mm, p = 3:6 mm, D = . 19 3:06 mm, h = 1:8 mm 3.7 Unit cell configurations without glide symmetry. 20 3.8 neff versus frequency for different unit cell configurations. 20 3.9 Hole-with-one-pin unit cell configuration. 21 3.10 neff versus frequency for different height of hole. Solution 1. 22 3.11 neff versus frequency for different height of hole. Solution 2. 22 3.12 neff versus D at 28 GHz. Solution 2, h =1.1 mm. 23 3.13 Milling illustration. 24 3.14 Hole-with-four-pin (round) unit cell configuration. 25 3.15 neff versus frequency for different height of hole. Unit . 26 cell with four round pins. 3.16 Hole-with-four-pin (square) unit cell configuration. 27 3.17 neff versus frequency for different height of hole. Unit . 28 cell with four square pins. 3.18 Luneburg lens with 10 dielectric layers . 29 3.19 neff versus h at three typical frequencies. Solution 1. 29 iii 3.20 Far field Gain Abs (θ = 90◦) based on unit cell in Solution 1. 30 4.1 Dispersion comparison for different center frequencies. 32 4.2 Wire frame view of two glide-symmetric layers. 34 4.3 One layer of the glide-symmetric metasurface lens. 34 4.4 E-field in x-y plane. 35 5.1 A slice of parallel plate with flare. 37 5.2 Reflection coefficient of a sliced flare. 37 5.3 Circular parallel plate with the flare. 38 5.4 Reflection coefficient of circular parallel plate with flare. 39 5.5 E-field in x-y plane at 28 GHz. 39 5.6 Metasurface lens with the flare. 40 5.7 Reflection coefficient of metasurface lens with flare. 41 5.8 Feeding structure, x-y cut plane view. 41 5.9 Coaxial Probe data sheet. 42 5.10 Coaxial probe to waveguide transition structure. 43 5.11 Coaxial to waveguide transition, S-parameter impedance view. 44 5.12 Stepped horn structure, x-z cut plane view. 45 5.13 Stepped horn, S-parameter impedance view. 46 5.14 Reflection coefficient of whole feeding. 46 6.1 Bottom layer of integrated lens. 47 6.2 Far field comparison of different feed position. 48 6.3 Electric field in x-y plane at 28 GHz, for full lens with one feeding. 49 6.4 Reflection coefficient of full lens with one feeding. 50 6.5 Far field Gain Abs (θ = 90◦) of full lens with one feeding. 50 6.6 Bottom layer of full lens with 11 ports. 51 6.7 Enlarged view of adjacent feedings and probe flanges. 51 6.8 Reflection coefficient of all 11 ports. 52 6.9 Crosstalk between typical feedings. 53 6.10 Far field Gain Abs (θ = 90◦) at different frequencies. 54 7.1 x-y cut plane view of stepped horn. 55 7.2 S11 impedance view comparison of round- and sharp-corner stepped horn. 56 7.3 Coaxial probe to waveguide transition structure.
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