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In this paper, an ingenious reverse design method is applied to the design and optimization of terahertz bandpass filters in order to achieve standardized design of high-performance terahertz functional devices. An equivalent model of subwavelength metasurface mapped to digital space is established. Based on ideal objective functions and constraints, intelligent algorithms begin a bold journey to explore the vast potential structure in the solution space. Through iterative refinement, the algorithm reveals optimal structural patterns, unlocking areas of unparalleled performance. The direct binary search (DBS) algorithm and the binary particle swarm optimization (BPSO) algorithm are compared in optimization process. When using the DBS algorithm to optimize the design area, it takes a long time to poll the logic states of all pixel units point by point, and it is easy to get stuck in the local optimal value. However, BPSO algorithm has stronger global search capabilities, faster convergence speed, and higher accuracy. Through a comprehensive comparison of the device performance optimized by the two algorithms, the solution optimized by BPSO algorithm has better out-of-band suppression performance and a narrower full width at half peak, but slightly lower transmittance at the center frequency. The bandpass filter has a center frequency of 0.51 THz, a bandwidth of 41.5 GHz, and an insertion loss of -0.1071 dB. When considering computational efficiency, DBS algorithm lags behind, the simulation time is 11550 s, while BPSO algorithm only needs 9750 s. Compared with the traditional forward design, the reverse design method can achieve the narrower band, lower insertion loss, better out-of-band suppression and polarization stability. The fine structural changes of the optimal results have a significant influence on spectral performance, demonstrating the superiority and uniqueness of reverse design. This technology contributes to the design and optimization of high-performance and novel functional devices.
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Keywords:
- reverse design /
- terahertz metasurface /
- digital encoding /
- mapping and modeling
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图 1 (a)传统的十字型FSS; (b)数字型THz BPFs中像素点分布和1/8对称结构示意图(红三角形虚线框所示)
Figure 1. (a) A traditional cross-type FSS; (b) schematic diagram of the pixel distribution and 1/8 symmetrical unit structure surrounded by red triangle in a digital THz BPFs.
图 2 (a)理想性能的目标函数; (b)逆向设计方法流程图
Figure 2. (a) Ideal performance indicators; (b) the flow chart of reverse design method.
图 3 DBS和BPSO两种算法优化后的单元结构和相应透射率曲线
Figure 3. Unit structure and corresponding transmittance curve optimized by DBS and BPSO algorithms, respectively.
图 4 (a) DBS和(b) BPSO两种算法在优化过程中FOM值随迭代次数的变化
Figure 4. Variation curve of FOM value versus iteration number in the optimization process of (a) DBS and (b) BPSO algorithms, respectively.
图 5 (a) BPSO算法在迭代寻优过程中不同FOM值对应的透射率曲线; (b) BPSO算法设计不同中心频率处THz BPFs的透射率曲线
Figure 5. (a) Transmittance curves corresponding to different FOM values in optimization process of BPSO algorithm; (b) transmittance curves of THz BPFs at different center frequencies designed by BPSO algorithm.
图 6 逆向设计和传统设计优化后的单元结构及其透射率曲线
Figure 6. Unit structure and its transmittance curve optimized by reverse design and traditional design.
图 7 (a)—(d)结构简化过程; (e)—(h)相应的透射率光谱
Figure 7. (a)–(d) Process of structural simplification; (e)–(h) corresponding transmittance spectra.
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[1] Yang X, Zhao X, Yang K, Liu Y, Fu W, Luo Y. Biomedical applications of terahertz spectroscopy and imaging 2016 Trends Biotechnol. 34 810
Google Scholar
[2] Pengnoo M, Barros M T, Wuttisittikulkij L, Butler B, Davy A, Balasubramaniam S 2020 IEEE Access 8 114580
Google Scholar
[3] Kumar A, Gupta M, Pitchappa P, Wang N, Szriftgiser P, Ducournau G, Singh R 2022 Nat. Commun. 13 5404
Google Scholar
[4] Lee E S, Jeon T I. 2012 Opt. Express 20 29605
Google Scholar
[5] Savel’ev S, Rakhmanov A L, Nori F 2005 Phys. Rev. Lett. 94 157004
Google Scholar
[6] Lin Y, Yao H, Ju X, Chen Y, Zhong S, Wang X 2017 Opt. Express 25 25125
Google Scholar
[7] Gao T, Huang F, Chen Y, Zhu W, Ju X 2020 Appl. Sci. 10 5030
Google Scholar
[8] Hu F, Fan Y, Zhang X, Jiang W, Chen Y, Li P, Yin X, Zhang W 2018 Opt. Lett. 43 17
Google Scholar
[9] 洪鹏, 胡珑夏雨, 周子昕, 秦浩然, 陈佳乐, 范烨, 殷同宇, 寇君龙, 陆延青 2023 光子学报 52 0623001
Google Scholar
Hong P, Hu L X Y, Zhou Z X, Qin H R, Chen J L, Fan Y, Yin T Y, Kou J L, Lu Y Q 2023 Acta Photonnica Sin. 52 0623001
Google Scholar
[10] 常红伟, 马华, 张介秋, 张志远, 徐卓, 王甲富, 屈绍波 2014 63 087804
Google Scholar
Chang H W, Ma H, Zhang J Q, Zhang Z Y, Xu Z, Wang J F, Qu S B 2014 Acta Phys. Sin. 63 087804
Google Scholar
[11] Sui S, Ma H, Wang J, Pang Y, Feng M, Xu Z, Qu S 2018 J. Phys. D 51 065603
Google Scholar
[12] Zhu R, Wang J, Sui S, Meng Y, Qiu T, Jia Y, Wang X, Han Y, Feng M, Zheng L, Qu S 2020 Front. Phys. 8 231
Google Scholar
[13] Liu Z H, Liu X H, Xiao Z Y, Lu C C, Wang H Q, Wu Y, Hu X Y, Liu Y C, Zhang H Y, Zhang X D 2019 Optica 6 1367
Google Scholar
[14] Ma W, Cheng F, Liu Y M 2018 ACS Nano 12 6326
Google Scholar
[15] Ma H, Kim J S, Choe J H, Park Q H 2023 Nanophotonics 12 2415
Google Scholar
[16] Zhang T, Liu Q, Dan Y H, Yu S, Han X, Dai J, Xu K 2020 Opt. Express 28 18899
Google Scholar
[17] Wang Y Z, Zeng Q L, Wang J Z, Li Y, Fang D N 2022 Comput. Methods Appl. Mech. Eng. 401 115571
Google Scholar
[18] Piggott A Y, Lu J, Lagoudakis K G, Petykiewicz J, Babinec T M, Vučković J 2015 Nat. Photonics 9 374
Google Scholar
[19] Chang W J, Ren X S, Ao Y Q, Lu L H, Cheng M F, Deng L, Liu D M, Zhang M M 2018 Opt. Express 26 24135
Google Scholar
[20] Fallahi A, Mishrikey M, Hafner C, Vahldieck R 2008 IEEE Trans. Antennas Propag. 56 1340
Google Scholar
[21] Ordal M A, Long L L, Bell R J, Bell S E, Bell R R, Alexander R W, Ward C A 1983 Appl. Opt. 22 1099
Google Scholar
[22] Zhu G Y, Ju X W, Zhang W B 2018 Int. J. Prod. Res. 56 4017
Google Scholar
[23] Hajian M, Ranjbar A M, Amraee T, Mozafari B 2011 Int. J. Electr. Power Energy Syst. 33 28
Google Scholar
[24] Ju X W, Hu Z Q, Huang F, Wu H B, Belyanin A, Kono J, Wang X F 2021 Opt. Express 29 9261
Google Scholar
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