透镜天线能将馈源发射的球面电磁波通过相位补偿转变为平面电磁波，具有低成本的优势，广泛地应用于卫星通信、雷达探测等领域。但透镜天线存在介质透镜剖面高，重量大，以及波束扫描范围小、扫描速度不够快等问题。超表面单元是一种二维结构，能够调控电磁波的相位、幅度和极化等属性，使用超表面单元构成的平面透镜具有低剖面、低重量和易加工的优点。另一方面，相控阵具有电扫描能力，使用相控阵作为透镜天线的馈源，透镜天线能够进行快速灵活的波束扫描。本论文针对超表面透镜天线以及超表面透镜相控阵天线的研究，开展了以下工作：

一、设计了一款基于极化转换超表面结构的高增益平面透镜天线。首先，设计了极化转换单元，该单元能将线极化波转换为交叉的线极化波，且能形成两个谐振点。基于类法布里-珀罗谐振腔结构，在单元的底层和顶层分别加载正交的金属栅格，提高了单元的透射性能，并形成了两个新的谐振点，拓宽了工作带宽，设计成了宽带极化转换超表面单元。对超表面单元进行仿真，通过控制中间金属层尺寸参数和镜像单元，在10 - 19 GHz内，单元实现了360°的交叉极化透射相位变化，且交叉极化透射幅度大于-1 dB，相对带宽为62.1%。然后，基于广义斯涅尔定律，设计了相位梯度超表面，在平面波垂直入射下，该超表面实现34°的波束偏转。最后，基于平面透镜相位分布公式，使用超表面结构设计了22 × 22平面透镜，降低了透镜剖面，并使用矩形微带天线作为馈源，仿真了超表面平面透镜天线，天线增益为21.2 dBi，口径效率为42.8%，将馈源的增益提高了14.3 dB，验证了本章设计的可行性。

二、设计了一款宽角扫描的宽带高增益低副瓣超表面透镜相控阵天线。为了解决透镜天线扫描慢的问题，使用相控阵作为馈源进行波束扫描。首先，设计了印刷偶极子天线，该天线在13.3 - 16.9 GHz内|S₁₁| < -10 dB，将其组成10 × 10的相控阵。为了降低扫描损耗，设计了多焦点透镜，并使用遗传算法优化透镜口径面上的相位分布，提高透镜天线的扫描性能，并使用超表面单元排布成相应的54 × 54平面透镜。再应用共轭场匹配法计算出馈源的激励幅度和相位。将超表面透镜和相控阵馈源装配在一起组成超表面透镜相控阵天线，仿真该天线，在15 GHz处，天线能实现方位角0 - 360°和俯仰角±30°的波束扫描，最大增益为27.4 dBi，口径效率为29.6%，增益扫描损耗为3.6 dB。在13.5 - 16.5 GHz内，法向增益变化1.7 dB。然后，基于共轭场匹配法和泰勒综合法，提出一种降低副瓣的方法，将第一副瓣电平降低了5.3 dB。最后，加工测试了超表面透镜相控阵天线，实测与仿真结果吻合良好，验证了设计的可行性。

The lens antenna can transform the spherical electromagnetic wave emitted from the feed source into planar electromagnetic wave through phase compensation, which has the advantage of low cost and has been widely used in satellite communication, radar detection and other fields. However, the lens antenna has the problems of high profile and weight of dielectric lens, as well as small beam scanning range and not fast enough scanning speed. The metasurface is a two-dimensional structure that can modulate the phase, amplitude and polarization properties of electromagnetic waves, and the metasurface lens antenna has the advantages of low profile, low weight and easy processing. On the other hand, phased arrays have electrical scanning capability, and using phased arrays as the feed source of the lens antenna, the lens antenna can perform fast and flexible beam scanning. In this thesis, for the study of the metasurface lens antenna as well as the metasurface lens phased array antenna, the following work is carried out:

1. A high-gain planar lens antenna antenna based on polarization conversion metasurface is designed. First, a polarization conversion unit is designed, which can convert the line polarization wave to crossed line polarization wave and can form two resonance points. Based on the Fabry-Perot-like resonant cavity, orthogonal metal grids are loaded on the bottom and top layers of the unit to improve the transmission performance of the unit, and two new resonant points are formed to broaden the operating bandwidth, which is designed as a broadband polarization conversion metasurface. The metasurface is simulated, and by controlling size parameters of the intermediate metal layer and mirroring the unit, the metasurface achieves a 360° cross-polarization transmission phase change in the 10 - 19 GHz with a cross-polarization transmission amplitude greater than -1 dB and a relative bandwidth of 62.1%. Then, based on the generalized Snell's law, a phase gradient metasurface is designed, which achieves a beam deflection of 34° at the vertical incidence of a plane wave. Finally, on the phase distribution formula of the planar lens, a 22 × 22 metasurface lens antenna is designed to reduce the lens profile. And a rectangular microstrip antenna is used as the feed source, and the metasurface lens antenna is simulated with an antenna gain of 21.2 dBi and an aperture efficiency of 42.8%, which improves the gain of the feed source by 14.3 dB, verifying the feasibility of the design in this chapter.

2. A broadband wide-angle scanning metasurface lens phased array antenna with high gain and low sidelobe is designed. In order to solve the problem of slow scanning of the lens antenna, a phased array is used as the feed source for scanning. Firstly, a printed dipole antenna, which has |S11| < -10 dB in 13.3 - 16.9 GHz, is designed to form a 10 × 10 phased array. To reduce the scanning loss, a multifocal lens is designed and a genetic algorithm is used to optimize the phase distribution on the aperture of the lens to improve the scanning performance of the lens antenna, and the metasurface is used to arrange the 54 × 54 planar lens. Then the conjugate field matching method is applied to calculate the excitation amplitude and phase of the feed source. The metasurface lens and phased array feed source are assembled together to form a metasurface lens phased array antenna, which is simulated. At 15 GHz, the metasurface lens phased array antenna achieves beam scanning with azimuth 0 - 360° and elevation ±30° with a maximum gain of 27.4 dBi, an aperture efficiency of 29.6% and a gain scanning loss of 3.6 dB. The normal gain varies by 1.7 dB in 13.5 - 16.5 GHz. Then, based on the conjugate field matching method and Taylor synthesis method, a method is proposed to reduce the sidelobe level, and the first sidelobe level of the metasurface lens phased array antenna is reduced by 5.3 dB. Finally, the metasurface lens phased array antenna is processed and tested, and the measured and simulated results are in good agreement, which verifies the feasibility of the design.

[1]克劳斯. 天线(第三版)[M]. 北京: 电子工业出版社, 2006.
[2]John Thornton, Kao-Cheng Huang. Modern lens antennas for communications engineering[M]. John Wiley and Sons, 2013.
[3]Sun Shulin, He Qiong, Hao Jiaming, et al. Electromagnetic metasurfaces: physics and applications[J]. Advances in Optics and Photonics, 2019, 11(2): 380-479.
[4]Karim Achouri, Christophe Caloz. Electromagnetic Metasurfaces: Theory and Applications[M]. IEEE, 2021.
[5]Ke Chen, Yijun Feng. A review of recent progress on directional metasurfaces: concept, design, and application[J]. Journal of Physics D: Applied Physics. 2022.
[6]赵晓鹏, 刘亚红. 微波超材料与超表面中波的行为[M]. 北京：科学出版社, 2016.
[7]Raul H. Barroso, Wilmer Malpica. An Overview of Electromagnetic Metamaterials[J]. IEEE Latin America Transactions, 2020, 18(11): 1862-1873.
[8]张玉龙, 李萍, 石磊. 超材料[M]. 北京: 化学工业出版社, 2019.
[9]Richard W. Ziolkowski. Design, fabrication, and testing of double negative metamaterials[J]. IEEE Transactions on Antennas and Propagation, 2003, 51(7): 1516-1529.
[10]Sheng Xi, Hongsheng Chen, Tao Jiang, et al. Experimental verification of reversed Cherenkov radiation in left-handed metamaterial[J]. Physical Review Letters, 2009, 103(19): 194801.
[11]Xueying Lu, Michael A. Shapiro, Ivan Mastovsky, et al. Generation of high-power, reversed-cherenkov wakefield radiation in a metamaterial structure[J]. Physical Review Letters, 2019, 122(1): 014801.
[12]N. Seddon, T. Bearpark. Observation of the Inverse Doppler Effect[J]. Science, 2003, 302(5650): 1537-1540.
[13]Hongya Chen, Jiafu Wang, Hua Ma, et al. Ultra-wideband polarization conversion metasurfaces based on multiple plasmon resonances[J]. Journal of Applied Physics, 2014, 115(15): 154504-154504-5.
[14]Hongya Chen, Hua Ma, Jiafu Wang, et al. Ultra-wideband transparent 90 degrees polarization conversion metasurfaces[J]. Applied physics A., 2016.
[15]Pei Yang, Ruirong Dang, Lipin Li. Dual-Linear-to-Circular Polarization Converter Based Polarization-Twisting Metasurface Antenna for Generating Dual Band Dual Circularly Polarized Radiation in Ku-Band[J]. IEEE Transactions on Antennas and Propagation, 2022, 70(10): 9877-9881.
[16]Xiaoming Liu, Yixin Zhou, Chen Wang, et al. Dual-Band Dual-Rotational-Direction Angular Stable Linear-to-Circular Polarization Converter[J]. IEEE Transactions on Antennas and Propagation, 2022, 70(7): 6054-6059.
[17]Fengxia Li, Haiyan Chen, Yang Zhou, et al. Generation and Focusing of Orbital Angular Momentum Based on Polarized Reflectarray at Microwave Frequency[J]. IEEE Transactions on Microwave Theory and Techniques, 2021, 69(3): 1829-1837.
[18]Ling-Jun Yang, Sheng Sun and Wei E. I. Sha. Ultrawideband Reflection-Type Metasurface for Generating Integer and Fractional Orbital Angular Momentum[J]. IEEE Transactions on Antennas and Propagation, 2020, 68(3): 2166-2175.
[19]Amrollah Amini, Homayoon Oraizi. Control of Orbital Angular Momentum Regimen by Modulated Metasurface Leaky-Wave Antennas[J]. IEEE Transactions on Antennas and Propagation, 2022, 70(11): 10166-10176.
[20]Tao Hong, Shuai Wang, Zhengyan Liu, et al. RCS Reduction and Gain Enhancement for the Circularly Polarized Array by Polarization Conversion Metasurface Coating[J]. IEEE Antennas and Wireless Propagation Letters, 2019, 18(1): 167-171.
[21]Yongqiang Pang, Yongfeng Li, Bingyue Qu, et al. Wideband RCS Reduction Metasurface with a Transmission Window[J]. IEEE Transactions on Antennas and Propagation, 2020, 68(10): 7079-7087.
[22]Qi Zheng, Chenjiang Guo, Jun Ding, et al. A Broadband Low-RCS Metasurface for CP Patch Antennas[J]. IEEE Transactions on Antennas and Propagation, 2021, 69(6): 3529-3534.
[23]Feng Liu, Jiayin Guo, Luyu Zhao, et al. Dual-Band Metasurface-Based Decoupling Method for Two Closely Packed Dual-Band Antennas[J]. IEEE Transactions on Antennas and Propagation, 2020, 68(1): 552-557.
[24]Jiongjian Fang, Jinxin Li, Pei Xiao, et al. Coupling Mode Transformation-Based Dielectric Surface and Metasurface for Antenna Decoupler[J]. IEEE Transactions on Antennas and Propagation, 2023, 71(1): 1123-1128.
[25]Chunhua Xue, Qun Lou, Zhi Ning Chen. Broadband Double-Layered Huygens’ Metasurface Lens Antenna for 5G Millimeter-Wave Systems[J]. IEEE Transactions on Antennas and Propagation, 2020, 68(3): 1468-1476.
[26]Omer Yesilyurt, Gonul Turhan-Sayan. Metasurface Lens for Ultra-Wideband Planar Antenna[J]. IEEE Transactions on Antennas and Propagation, 2020, 68(2): 719-726.
[27]Robert Mailloux. Phased Array Antenna Handbook[M]. Boston: Artech House, 2005.
[28]李知新. 相控阵天线理论和技术[M]. 北京: 国防工业出版社, 2015.
[29]Viktor G. Veselago. The electrodynamics of substances with simultaneously negative values of ε and μ[J]. Physics-Uspekhi, 1968, 10(4): 509-514.
[30]Pendry J. B., Holden A. J., Stewart W. J., et al. Extremely Low Frequency Plasmons in Metallic Mesostructures[J]. Physical Review Letters, 1996, 76(25): 4773-4776.
[31]Pendry J. B., Holden A. J., Robbins D. J., et al. Magnetism from conductors and enhanced nonlinear phenomena[J]. IEEE Transactions on Microwave Theory Techniques, 1999, 47(11): 2075-2084.
[32]R. A. Shelby, D. R. Smith, S. Schultz. Experimental verification of negative index of refraction[J]. Science, 2001, 292(5514): 77-79.
[33]Pendry J. B.. Negative Refraction Makes a Perfect Lens[J]. Physical Review Letters, 2000, 85(18):3966-3969.
[34]Nicholas Fang, Hyesog Lee, Cheng Sun, et al. Sub-Diffraction-Limited Optical Imaging with a Silver Superlens[J]. Science, 2005, 308(5721):534-537.
[35]J. B. Pendry, D. Schurig and D. R. Smith. Controlling electromagnetic fields[J]. Science, 2006, 312(5781): 1780-1782.
[36]D. Schurig, J. J. Mock, B. J. Justice, et al. Metamaterial electromagnetic cloak at microwave frequencies[J]. Science, 2006, 314(5801): 977-980.
[37]F. Falcone, T. Lopetegi, M. A. G. Laso, et al. Babinet principle applied to the design of metasurfaces and metamaterials[J]. Physical review letters, 2004, 93(19): 197401.
[38]Nanfang Yu, Patrice Genevet, Mikhail A. Kats, et al. Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction.[J]. Science, 2011, 334(6054): 333-337.
[39]Carl Pfeiffer, Anthony Grbic. Metamaterial Huygens’ Surfaces: Tailoring Wave Fronts with Reflectionless Sheets[J]. Physical review letters, 2013, 110(19): 197401.
[40]D. Berry, R. Malech, W. Kennedy. The reflectarray antenna[J]. IEEE Transactions on Antennas and Propagation, 1963, 11(6): 645-651.
[41]Daniel McGrath. Planar three-dimensional constrained lenses[J]. IEEE Transactions on Antennas and Propagation, 1986, 34(1): 46-50.
[42]Hamza Kaouach, Laurent Dussopt, Jérome Lanteri. Wideband low-loss linear and circular polarization transmit-arrays in V-Band[J]. IEEE Transactions on Antennas and Propagation, 2011, 59(7): 2513-2523.
[43]Luca Di Palma, Antonio Clemente, Laurent Dussopt, et al. Circularly Polarized Transmitarray With Sequential Rotation in Ka-Band[J]. IEEE Transactions on Antennas and Propagation, 2015, 63(11):5118-5124.
[44]Mudar A. Al-Joumayly, Nader Behdad. Wideband Planar Microwave Lenses Using Sub-Wavelength Spatial Phase Shifters[J]. IEEE Transactions On Antennas And Propagation, 2011, 59(12): 4542-4552.
[45]Meng Li, Nader Behdad. Wideband True-Time-Delay Microwave Lenses Based on Metallo-Dielectric and All-Dielectric Lowpass Frequency Selective Surfaces[J]. IEEE Transactions on Antennas and Propagation, 2013, 61(8):4109-4119.
[46]Ahmed H. Abdelrahman, Atef Z. Elsherbeni, Fan Yang. Transmitarray Antenna Design Using Cross-Slot Elements With No Dielectric Substrate[J]. IEEE Antennas and Wireless Propagation Letters, 2014, 13: 177-180.
[47]Peng Mei, Gert Frolund Pedersen, Shuai Zhang. A Broadband and FSS-Based Transmitarray Antenna for 5G Millimeter-Wave Applications[J]. IEEE Antennas and Wireless Propagation Letters, 2021, 20(1): 103-107.
[48]Haipeng Li, Guangming Wang, He-Xiu Xu, et al. X-Band Phase-Gradient Metasurface for High-Gain Lens Antenna Application[J]. IEEE Transactions on Antennas and Propagation, 2015, 63(11): 5144-5149.
[49]Elham Erfani, Mahmoud Niroo-Jazi, Serioja Tatu. A High-Gain Broadband Gradient Refractive Index Metasurface Lens Antenna[J]. IEEE Transactions on Antennas and Propagation, 2016, 64(5): 1968-1973.
[50]Lin-Xiao Wu, Na Zhang, Kai Qu, et al. Transmissive Metasurface with Independent Amplitude/Phase Control and Its Application to Low-Side-Lobe Metalens Antenna[J]. IEEE Transactions on Antennas and Propagation, 2022, 70(8): 6526-6536.
[51]Payam Nayeri, Fan Yang, Atef Z. Elsherbeni, et al. Design of Multifocal Transmitarray Antennas for Beamforming Applications[C]. Orlando: 2013 IEEE Antennas and Propagation Society International Symposium, 2013, 1672-1673.
[52]Eduardo B. Lima, Sérgio A. Matos, Jorge R. Costa, et al. Circular Polarization Wide-Angle Beam Steering at Ka-Band by In-Plane Translation of a Plate Lens Antenna[J]. IEEE Transactions on Antennas and Propagation, 2015, 63(12): 5443-5455.
[53]Qingyun Zeng, Zhenghui Xue, Wu Ren, et al. Dual-Band Beam-Scanning Antenna Using Rotatable Planar Phase Gradient Transmit Arrays[J]. IEEE Transactions on Antennas and Propagation, 2020, 68(6): 5021-5026.
[54]Mei Jiang, Zhi Ning Chen, Yan Zhang, et al. Metamaterial-Based Thin Planar Lens Antenna for Spatial Beamforming and Multibeam Massive MIMO[J]. IEEE Transactions on Antennas and Propagation, 2017, 65(2): 464-472.
[55]Laurent Dussopt, Amazir Moknache, Jussi Säily, et al. A V-Band Switched-Beam Linearly-Polarized Transmit-Array Antenna for Wireless Backhaul Applications[J]. IEEE Transactions on Antennas and Propagation, 2017, 65(12): 6788-6793.
[56]Abbas Abbaspour-Tamijani, Lisha Zhang, George Pan, et al. Lens-enhanced phased array antenna system for high directivity beam-steering[C]. Spokane: 2011 IEEE International Symposium on Antennas and Propagation, 2011, 3275-3278.
[57]Abbas Abbaspour-Tamijani, Lisha Zhang, Helen K. Pan. Enhancing the Directivity of Phased Array Antennas Using Lens-Arrays[J]. Progress in Electromagnetics Research, 2013.
[58]Peng-Yu Feng, Shi-Wei Qu, Shiwen Yang. Phased Transmitarray Antennas for 1-D Beam Scanning[J]. IEEE Antennas and Wireless Propagation Letters, 2019, 18(2): 358-362.
[59]Peng-Yu Feng, Shi-Wei Qu, Xiao-Han Chen, et al. Low-Profile High-Gain and Wide-Angle Beam Scanning Phased Transmitarray Antennas[J]. IEEE Access, 2020, 8: 34276-34285.
[60]钟锡华. 现代光学基础[M]. 北京：北京大学出版社, 2003.
[61]王建, 郑一农, 何子远. 阵列天线理论与工程应用[M]. 北京: 电子工业出版社, 2015.
[62]Wen-Long Guo, Guang-Ming Wang, Xin-Yao Luo, et al. Dual-Phase Hybrid Metasurface for Independent Amplitude and Phase Control of Circularly Polarized Wave[J]. IEEE Transactions on Antennas and Propagation, 2020, 68(11): 7705-7710.
[63]David E. Goldberg. Genetic Algorithms in Search, Optimization. Search Optimization Machine Learning[J]. Addison-Wesley Longman Publishing Co., 1989.
[64]Hou-Tong Chen, Jiangfeng Zhou, John F. O’Hara, et al. Antireflection coating using metamaterials and identification of its mechanism[J]. Physical Review Letters, 2010, 105(7): 073901.
[65]Payam Nayeri, Atef Z. Elsherbeni, Fan Yang. Radiation Analysis Approaches for Reflectarray Antennas[J]. Ieee Antennas And Propagation Magazine, 2013, 55(1): 127-134.
[66]Peter T. Lam, Shung-Wu Lee, Donald Chang, et al. Directivity optimization of a reflector antenna with cluster feeds: A closed-form solution[J]. IEEE Transactions on Antennas and Propagation, 1985, 33(11): 1163-1174.