幅值可控的逆反射和镜像反射双通道超表面结构拓扑优化设计

史鹏飞; 马馨莹; 向川; 赵宏革; 李渊; 高仁璟; 刘书田

doi:10.7498/aps.72.20230775

摘要

对斜入射电磁波产生包含逆反射通道的双反射通道, 对于提高目标识别性能、导航性能等具有重要意义. 在双通道反射中, 控制逆反射与镜像反射占比则是实现反射功率分配的关键. 为实现双通道反射功率占比的可控, 本文提出了一种双通道反射超表面微结构拓扑优化设计方法. 构建了包括逆反射的双通道反射超表面实现机理及物理模型, 建立了具有特定逆反射与镜像反射幅值比值或占比的超表面微结构拓扑优化模型. 作为数值算例, 针对TE模式下频率为10 GHz俯仰角$-30^\circ$方向入射平面波, 对逆反射与镜像反射功率比1∶1的双通道反射器进行设计, 所设计超表面在$ \pm 30^\circ $方向表现出较强的方向性, 两方向反射幅值大小相等. 同时, 对具有最大逆反射占比的反射超表面进行设计, 逆反射功率占总功率比值为0.093, 无镜像反射及其他方向奇异反射, 超表面强反射集中在$-30^\circ $, 主波束功率占总反射功率比为0.900. 仿真及实验测试结构均验证了所提方法的可行性.

关键词:

超表面 /
双通道 /
拓扑优化

Abstract

For oblique incident electromagnetic waves, the generation of double reflection channels including retroreflection channel is of great significance in improving target recognition performance and navigation performance. In double channel reflection, controlling the ratio of retroreflection to specular reflection is the key to realizing reflection power distribution. In order to realize the control of the proportion of the reflected power in each channel, a topology optimization method for designing the reflective metasurface microstructure with dual channel is proposed in this paper. The implementation mechanism is investigated, physical model of metasurface with dual reflection channel including retroreflection channel is established, and the topology optimization model of metasurface microstructure with specific power ratio of the retroreflection to specular reflection is established. As a numerical example, a dual channel metasurface reflector with a 1∶1 ratio of retroreflection power to specular reflection power is designed for a 10 GHz plane wave in the TE mode with a pitch angle of –30°. The designed metasurface exhibits strong directionality in the retroreflective direction, and the reflection amplitudes in both directions are similar. The retroreflective metasurface with the maximum retroreflection ratio is designed. The retroreflection ratio of the designed metasurface is 0.093. There is no specular reflection or other singular reflection, and the strong reflection on the metasurface is concentrated at –30°. The ratio of the main beam power to the total reflection power is 0.900. The simulated and experimental results verify the feasibility of the proposed method.

Keywords:

作者及机构信息

1.
大连海事大学船舶电气工程学院, 大连　116023

2.
武汉理工大学, 光纤传感技术国家工程实验室, 武汉　430070

3.
大连理工大学, 工业装备结构分析优化与CAE软件全国重点实验室, 大连　116023

通信作者: 赵宏革, zhaohg@dlmu.edu.cn ; 高仁璟, renjing@dlut.edu.cn ;

基金项目: 国家自然科学基金(批准号: U1808215)、湖北省教育厅科学研究计划指导项目(批准号: B2022620)和深圳市科技计划(批准号: JSGG20200102155001779)资助的课题.

Authors and contacts

1.
School of Marine Electrical Engineering, Dalian Maritime University, Dalian 116023, China

2.
National Engineering Research Center of Fiber Optic Sensing Technology and Networks, Wuhan University of Technology, Wuhan 430070, China

3.
State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Dalian University of Technology, Dalian 116023, China

Corresponding author: Zhao Hong-Ge, zhaohg@dlmu.edu.cn ; Gao Ren-Jing, renjing@dlut.edu.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant No. U1808215), the Guidance Project of Scientific Research Program of Department of Education of Hubei Province, China (Grant No. B2022620), and the Program of Science and Technology of Shenzhen, China (Grant No. JSGG20200102155001779).

文章全文 : translate this paragraph

参考文献

[1]	Kuga Y, Ishimaru A 1984 J. Opt. Soc. Am. A 1 831 Google Scholar
[2]	杨丹青, 王莉, 王新龙 2015 物理学报 64 054301 Google Scholar Yang D Q, Wang L, Wang X L 2015 Acta Phys. Sin. 64 054301 Google Scholar
[3]	盛泉, 耿婧旎, 王爱华, 王盟, 齐岳, 刘俊杰, 付士杰, 史伟, 姚建铨 2023 物理学报 72 044203 Google Scholar Sheng Q, Geng J N, Wang A H, Wang M, Qi Y, Liu J J, Fu S J, Shi W, Yao J Q 2023 Acta Phys. Sin. 72 044203 Google Scholar
[4]	Yang R, Fan Y, Zhu W, Hu C, Chen S, Wei H, Chen W, Chang C T, Zhao Q, Zhou J, Zhang F, Qiu C W 2023 Laser Photonics Rev. 17 2200975 Google Scholar
[5]	Jin X, Holzman J F 2010 IEEE Sens. J. 10 1875 Google Scholar
[6]	Vitaz J A, Buerkle A M, Sarabandi K 2010 IEEE Trans. Antennas Propag. 58 3539 Google Scholar
[7]	Deroba J C, Sobczak K D, Good A, Larimore Z, Mirotznik M 2019 IEEE Aero. El. Sys. Mag. 34 20 Google Scholar
[8]	Kim H, Lee B 2007 Opt. Eng. 46 094002 Google Scholar
[9]	Kadera P, Jimenez-Saez A, Burmeister T, Lacik J, Jakoby R 2020 IEEE Access 8 212765 Google Scholar
[10]	Chang C C, Chen T Y, Tsai J C 2016 IEEE Photonics Technol. Lett. 28 554 Google Scholar
[11]	Pon C Y 1964 IEEE Trans. Antennas Propag. 12 176 Google Scholar
[12]	Yan L, Shen Z 2020 IEEE Antennas Wirel. Propag. Lett. 19 736 Google Scholar
[13]	Yu N, Genevet P, Kats M A, Aieta F, Tetienne J P, Capasso F, Gaburro Z 2011 Science 334 333 Google Scholar
[14]	Hessel A, Schmoys J, Tseng D Y 1975 J. Opt. Soc. Am. 65 380 Google Scholar
[15]	Jull E V, Heath J W, Ebbeson G R 1977 J. Opt. Soc. Am. 67 557 Google Scholar
[16]	Ra'Di Y, Sounas D L, Alu A 2017 Phys. Rev. Lett. 119 067404 Google Scholar
[17]	Hoang T V, Lee C H, Lee J H 2019 IEEE Trans. Antennas Propag. 68 2451 Google Scholar
[18]	Wong A M H, Eleftheriades G V 2017 Phys. Rev. X 8 011036 Google Scholar
[19]	Wong A M H, Christian P, Eleftheriades G V 2018 IEEE Trans. Antennas Propag. 66 2892 Google Scholar
[20]	Lee S G, Lee J H 2020 IEEE Trans. Antennas Propag. 69 3588 Google Scholar
[21]	Tao C, Itoh T U 2020 IEEE Trans. Antennas Propag. 68 6193 Google Scholar
[22]	Estakhri N M, Alù A 2016 Phys. Rev. X 6 041008 Google Scholar
[23]	Wang X C, Díaz-Rubio A, Li H, Tretyakov S A, Alù A 2020 Phys. Rev. Appl. 13 044040 Google Scholar
[24]	Wang X, Díaz-Rubio A, Tretyakov S A 2020 Phys. Rev. Appl. 14 024089 Google Scholar
[25]	Asadchy V S, Díaz-Rubio A, Tcvetkova S N, et al. 2017 Phys. Rev. X 7 031046 Google Scholar

施引文献

图 1 介质表面镜像反射通道和逆反射通道

Fig. 1. Specular reflection and retroreflection of medium surface.

下载: 全尺寸图片幻灯片

图 2 双通道超表面阵列及超胞　(a) 平面型二维超表面阵列; (b) 超表面超胞; (c) 超表面超胞结构

Fig. 2. Double-channel metasurface array and super unit: (a) 2D planar metasurface array; (b) metasurface super unit; (c) the microstructure of the super unit.

下载: 全尺寸图片幻灯片

图 3 逆反射超表面拓扑优化流程图

Fig. 3. Flow chart of topology optimization for retroreflection metasurface.

下载: 全尺寸图片幻灯片

图 4 所设计双通道反射功率1∶1超表面反射器及反射特性　(a) 超胞; (b) 微结构; (c) 反射器俯仰向归一化双站RCS; (d) 三维双站RCS

Fig. 4. Designed double-channel metasurface reflector with a 1∶1 ratio of retroreflection power to specular reflection power and its reflection characteristics: (a) The unit cell; (b) the microstructure; (c) the normalized bistatic RCS in the elevation coordinate; (d) the three-dimensional bistatic RCS of the designed reflector.

下载: 全尺寸图片幻灯片

图 5 仅金属接地板归一化双站RCS

Fig. 5. Normalized bistatic RCS of the reflector only with metallic ground.

下载: 全尺寸图片幻灯片

图 6 双通道超表面实验测试平台及结果　(a) RCS测试示意图; (b) 所设计超表面试件; (c)测试所得反射特性

Fig. 6. Experimental platform for the double-channel metasurface reflector testing and the tested results: (a) The schematic diagram of the RCS testing platform; (b) the designed metasurface specimen; (c) the tested reflection characteristics.

下载: 全尺寸图片幻灯片

图 7 入射角度偏差下的反射功率1∶1超表面反射特性　(a) 归一化双站RCS; (b) 负反射角度及镜像反射与负反射幅值比

Fig. 7. Reflection characteristics of the metasurface with a 1∶1 ratio of retroreflection power to specular reflection power when the incident angle is adjusted: (a) The normalized bistatic RCS of the metasurface; (b) the retroreflection angle and ratio between the specular reflection and retroreflection.

下载: 全尺寸图片幻灯片

图 8 入射波频率偏差下的反射功率1∶1超表面反射特性　(a) 归一化双站RCS; (b) 负反射角度及镜像反射与负反射幅值比

Fig. 8. Reflection characteristics of the metasurface with a 1∶1 ratio of retroreflection power to specular reflection power when the frequency of the incident wave is biased: (a) The normalized bistatic RCS of the designed metasurface; (b) the retroreflection angle and the ratio between the specular reflection and retroreflection.

下载: 全尺寸图片幻灯片

图 9 所设计的逆反射占比最大超表面反射器及反射特性　(a) 超胞; (b) 微结构; (c) 俯仰向归一化双站RCS; (d) 测试所得反射特性及所设计超表面试件

Fig. 9. Designed metasurface reflector with the maximum retroreflection ratio and its reflection characteristics: (a) The unit cell; (b) the microstructure; (c) the normalized bistatic RCS in the elevation coordinate; (d) the tested radiation pattern and the metasurface retroreflector prototype.

下载: 全尺寸图片幻灯片

图 10 入射角度偏差下的逆反射占比最大超表面反射特性　(a) 归一化双站RCS; (b) 负反射角度及逆反射功率占比

Fig. 10. Reflection characteristics of the metasurface with the maximum retroreflection ratio when the incident angle is adjusted: (a) The normalized bistatic RCS of the metasurface; (b) the retroreflection angle and retroreflection ratio under excitation of incident waves with different incident angle.

下载: 全尺寸图片幻灯片

图 11 入射波频率偏差下的逆反射占比最大超表面反射特性　(a) 归一化双站RCS; (b) 负反射角度及逆反射功率占比

Fig. 11. Reflection characteristics of the metasurface with the maximum retroreflection ratio when the frequency of the incident wave is biased: (a) The normalized bistatic RCS of the designed metasurface; (b) the retroreflection angle and retroreflection ratio under excitation of incident waves with different frequencies.

下载: 全尺寸图片幻灯片

[1]	Kuga Y, Ishimaru A 1984 J. Opt. Soc. Am. A 1 831 Google Scholar
[2]	杨丹青, 王莉, 王新龙 2015 物理学报 64 054301 Google Scholar Yang D Q, Wang L, Wang X L 2015 Acta Phys. Sin. 64 054301 Google Scholar
[3]	盛泉, 耿婧旎, 王爱华, 王盟, 齐岳, 刘俊杰, 付士杰, 史伟, 姚建铨 2023 物理学报 72 044203 Google Scholar Sheng Q, Geng J N, Wang A H, Wang M, Qi Y, Liu J J, Fu S J, Shi W, Yao J Q 2023 Acta Phys. Sin. 72 044203 Google Scholar
[4]	Yang R, Fan Y, Zhu W, Hu C, Chen S, Wei H, Chen W, Chang C T, Zhao Q, Zhou J, Zhang F, Qiu C W 2023 Laser Photonics Rev. 17 2200975 Google Scholar
[5]	Jin X, Holzman J F 2010 IEEE Sens. J. 10 1875 Google Scholar
[6]	Vitaz J A, Buerkle A M, Sarabandi K 2010 IEEE Trans. Antennas Propag. 58 3539 Google Scholar
[7]	Deroba J C, Sobczak K D, Good A, Larimore Z, Mirotznik M 2019 IEEE Aero. El. Sys. Mag. 34 20 Google Scholar
[8]	Kim H, Lee B 2007 Opt. Eng. 46 094002 Google Scholar
[9]	Kadera P, Jimenez-Saez A, Burmeister T, Lacik J, Jakoby R 2020 IEEE Access 8 212765 Google Scholar
[10]	Chang C C, Chen T Y, Tsai J C 2016 IEEE Photonics Technol. Lett. 28 554 Google Scholar
[11]	Pon C Y 1964 IEEE Trans. Antennas Propag. 12 176 Google Scholar
[12]	Yan L, Shen Z 2020 IEEE Antennas Wirel. Propag. Lett. 19 736 Google Scholar
[13]	Yu N, Genevet P, Kats M A, Aieta F, Tetienne J P, Capasso F, Gaburro Z 2011 Science 334 333 Google Scholar
[14]	Hessel A, Schmoys J, Tseng D Y 1975 J. Opt. Soc. Am. 65 380 Google Scholar
[15]	Jull E V, Heath J W, Ebbeson G R 1977 J. Opt. Soc. Am. 67 557 Google Scholar
[16]	Ra'Di Y, Sounas D L, Alu A 2017 Phys. Rev. Lett. 119 067404 Google Scholar
[17]	Hoang T V, Lee C H, Lee J H 2019 IEEE Trans. Antennas Propag. 68 2451 Google Scholar
[18]	Wong A M H, Eleftheriades G V 2017 Phys. Rev. X 8 011036 Google Scholar
[19]	Wong A M H, Christian P, Eleftheriades G V 2018 IEEE Trans. Antennas Propag. 66 2892 Google Scholar
[20]	Lee S G, Lee J H 2020 IEEE Trans. Antennas Propag. 69 3588 Google Scholar
[21]	Tao C, Itoh T U 2020 IEEE Trans. Antennas Propag. 68 6193 Google Scholar
[22]	Estakhri N M, Alù A 2016 Phys. Rev. X 6 041008 Google Scholar
[23]	Wang X C, Díaz-Rubio A, Li H, Tretyakov S A, Alù A 2020 Phys. Rev. Appl. 13 044040 Google Scholar
[24]	Wang X, Díaz-Rubio A, Tretyakov S A 2020 Phys. Rev. Appl. 14 024089 Google Scholar
[25]	Asadchy V S, Díaz-Rubio A, Tcvetkova S N, et al. 2017 Phys. Rev. X 7 031046 Google Scholar

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幅值可控的逆反射和镜像反射双通道超表面结构拓扑优化设计