本研究針對超穎透鏡逆向設計中「單一超穎原子生成」與「透鏡級系統設計」之間的斷層，提出一套以資料驅動、結合深度生成模型與前向優化之完整逆向設計流程，對象為工作波長 940 nm、TM 偏振聚焦的非晶矽超穎透鏡，符合近紅外 3D 感測需求。流程涵蓋四個環節：首先，以嚴格耦合波分析（RCWA）建立涵蓋週期 460 ~ 500 nm、高度 450 ~ 550 nm 的 60005 筆超穎原子資料集，並以 snaphu 工具解包修正 2π 跳變，奠定符合物理的訓練基礎。接著，以殘差網路取代全連接架構並設立多頭預測分支，建立前向代理模型，其包含穿透率與相位的五項光學響應 R2 score 都在 0.981 以上，平均絕對誤差較基準模型降低 29.95 至 48.67%。再來，在條件變分自編碼器 ( cVAE ) 與條件生成對抗網路 ( cGAN ) 的輸入端加入結構條件，並提出融合幾何距離、動態物理一致性與絕對最近鄰三階段驗證演算法，剔除跳變區的不穩定結構，生成約十五萬筆解析度 5 nm 的可靠候選超穎原子。最後，結合前向模型與角譜法 ( ASM ) 建構可微分排佈系統，以貪婪搜尋作為初始排佈，進行端對端優化。結果顯示，短焦透鏡經前向優化後，TM 透鏡效率由 81.3% 升至 84.1%、TM/TE 消光比由 24.9 dB 升至 46.5 dB；長焦透鏡雖然只用貪婪搜尋，其透鏡效率與消光比也高達 85.3% 與 39.6 dB ，證實流程跨數值孔徑的泛化能力。核心貢獻在於將結構生成、物理驗證與全域排佈優化串接為環環相扣的整體流程，並確立前向模型精度為整體可信度上限之關鍵原則。

Metasurface-based metalenses promise to replace bulky refractive optics, yet a persistent gap separates the generation of individual meta-atoms from lens-level system design. This study proposes a data-driven inverse-design pipeline that couples deep generative models with forward optimization, targeting amorphous-silicon metalenses operating at 940 nm under TM-polarized focusing for near-infrared 3D sensing. Rigorous coupled-wave analysis was employed to construct a 60005-entry meta-atom dataset, with snaphu phase unwrapping correcting 2π discontinuities to establish a physically consistent training manifold. A residual forward surrogate model with multi-head branches replaced conventional fully connected architectures, achieving R2 scores 0.981 and above across five optical responses while reducing mean absolute error by 29.95–48.67% relative to the baseline. Conditional variational autoencoder and conditional generative adversarial network models, augmented with structural conditions and coupled with a three-stage validation algorithm, each yielded roughly 150000 reliable candidate meta-atoms at 5 nm resolution. A differentiable arrangement system integrating the forward model with the angular spectrum method then refined greedy-search layouts through end-to-end optimization. For the short-focal lens, forward optimization raised TM efficiency from 81.3% to 84.1% and the TM/TE extinction ratio from 24.9 to 46.5 dB; the long-focal lens attained 85.3% efficiency and 39.6 dB, confirming generalizability across numerical apertures. The principal contribution lies in unifying structure generation, physical validation, and global arrangement into a coherent pipeline, and in establishing forward-model fidelity as the ceiling of overall design credibility.

[1] N. Yu and F. Capasso, "Flat optics with designer metasurfaces," Nature Materials, vol. 13, no. 2, pp. 139-150, 2014.
[2] M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu and F. Capasso, "Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging," Science, vol. 352, no. 6290, pp. 1190-1194, 2016.
[3] A. Arbabi, Y. Horie, M. Bagheri and A. Faraon, "Dielectric Metasurfaces for Complete Control of Phase and Polarization with Subwavelength Spatial Resolution and High Transmission," arXiv:1411.1494v2, pp. 1-27, 2015.
[4] T. Hu, Q. Zhong, N. Li, Y. Dong, Z. Xu, Y. H. Fu, D. Li, V. Bliznetsov, Y. Zhou, K. H. Lai, Q. Lin, S. Zhu and N. Singh, "CMOS-compatible a-Si metalenses on a 12-inch glass wafer for fingerprint imaging," Nanophotonics, vol. 9, no. 4, pp. 823-830, 2020.
[5] M. G. Moharam, E. B. Grann and D. A. Pommet, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings," Journal of the Optical Society of America A, vol. 12, no. 5, pp. 1068-1076, 1995.
[6] S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vu˘ckovi´ and A. W. Rodriguez, "Outlook for inverse design in nanophotonics," arXiv:1801.06715v1, pp. 1-13, 2018.
[7] J. Jiang, M. Chen and J. A. Fan, "Deep neural networks for the evaluation and design of photonic devices," arXiv:2007.00084v1, pp. 1-29, 2020.
[8] T. Ma, M. Tobah, H. Wang and L. J. Guo, "Benchmarking deep learning-based models on nanophotonic inverse design problems," Opto-Electronic Science, vol. 1, no. 1, p. 210012, 2022.
[9] E. Tseng, S. Colburn, J. Whitehead, L. Huang, S.-H. Baek, A. Majumdar and F. Heide, "Neural Nano-Optics for High-quality Thin Lens Imaging," arXiv:2102.11579v1, pp. 1-13, 2021.
[10] "SNAPHU: Statistical-Cost, Network-Flow Algorithm for Phase Unwrapping," Stanford Radar Interferometry Research Group, 2024. [Online]. Available: https://web.stanford.edu/group/radar/softwareandlinks/sw/snaphu/.
[11] C. W. Chen and H. A. Zebker, "Network approaches to two-dimensional phase unwrapping: intractability and two new algorithms," Journal of the Optical Society of America A, vol. 17, pp. 401-414, 2000.
[12] C. W. Chen and H. A. Zebker, "Two-dimensional phase unwrapping with use of statistical models for cost functions in nonlinear optimization," Journal of the Optical Society of America A, vol. 18, pp. 338-351, 2001.
[13] J. W. Goodman, Introduction to Fourier Optics, 4th ed., W. H. Freeman, 2017, pp. 68-73, 88-96.
[14] S. K. Pal and S. Mitra, "Multilayer Perceptron, Fuzzy Sets, and Classification," IEEE Transactions on Neural Networks, vol. 3, no. 5, pp. 683-697, September 1992.
[15] I. Goodfellow, Y. Bengio and A. Courville, Deep Learning, MIT Press, 2016.
[16] Y. A. LeCun, L. Bottou, G. B. Orr and K.-R. Müller, "Efficient BackProp," in Neural Networks: Tricks of the Trade, Springer, 1998, pp. 9-50.
[17] X. Glorot, A. Bordes and Y. Bengio, "Deep Sparse Rectifier Neural Networks," in Proceedings of the 14th International Conference on Artificial Intelligence and Statistics (AISTATS), 2011.
[18] S. Ioffe and C. Szegedy, "Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift," in Proceedings of the 32nd International Conference on Machine Learning, 2015.
[19] D. E. Rumelhart, G. E. Hinton and R. J. Williams, "Learning representations by back-propagating errors," Nature, vol. 323, no. 6088, pp. 533-536, October 1986.
[20] D. P. Kingma and J. L. Ba, "Adam: A Method for Stochastic Optimization," in International Conference on Learning Representations (ICLR), 2015.
[21] K. He, X. Zhang, S. Ren and J. Sun, "Deep Residual Learning for Image Recognition," arXiv:1512.03385, pp. 1-12, 2015.
[22] D. P. Kingma and M. Welling, "Auto-Encoding Variational Bayes," arXiv:1312.6114, pp. 1-14, 2013.
[23] K. Sohn, X. Yan and H. Lee, "Learning Structured Output Representation using Deep Conditional Generative Models," in Advances in Neural Information Processing Systems 28 (NIPS 2015), 2015.
[24] I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville and Y. Bengio, "Generative Adversarial Nets," arXiv:1406.2661, pp. 1-9, 2014.
[25] M. Mirza and S. Osindero, "Conditional Generative Adversarial Nets," arXiv:1411.1784v1, pp. 1-7, 2014.
[26] "PlanOpSim: Metasurface and Metalens Simulation Software," PlanOpSim NV, [Online]. Available: https://www.planopsim.com/. [Accessed 2026].