超穎透鏡(metalens)的逆向設計(inverse design)能探索簡單幾何形狀之外的結構，並跳脫局部週期近似(Local Periodic Approximation， LPA)所假設的週期環境，進入更廣的設計空間。然而在大面積、大尺度下，以有限時域差分法(Finite-Difference Time-Domain， FDTD)結合自動微分(Automatic Differentiation， AD)取得設計梯度會受記憶體所限，使全域優化難以實行，逆向設計的便利性往往因而侷限於小尺度結構。 本研究以區域分解法(Domain Decomposition Method， DDM)結合 Schwarz 交替法為途徑，將大域切成可並行求解的子域，於子域間交換邊界場以逼近全域解，並把全域目標函數的梯度耦合納入同一流程，藉此建立一套大面積 FDTD 自動微分超穎透鏡逆向設計的可行流程。 本研究以一個寬頻長波紅外收光超穎透鏡為案例，端到端驗證此流程:分解後的場與梯度能逼近未分解的全域結果，遠場目標函數亦可在近場分區下進行分區自動微分。結果顯示，以區域分解可使大面積 FDTD 自動微分逆向設計成為可行，為後續大尺度超穎透鏡的優化奠定基礎。;Inverse design enables metalenses with structures beyond simple geometric shapes and opens a design space broader than the periodic-neighbour assumption of the local periodic approximation (LPA). At large area and large scale， however， obtaining design gradients with the finite-difference time-domain (FDTD) method and automatic differentiation (AD) is limited by memory， making global optimization impractical and confining the convenience of inverse design to small structures. This work pursues a domain decomposition method (DDM) combined with the Schwarz alternating method: the global domain is partitioned into subdomains that can be solved in parallel， boundary fields are exchanged between subdomains to approach the global solution， and the gradient of the global figure of merit is coupled into the same workflow， thereby establishing a feasible pipeline for large-area FDTD automatic-differentiation metalens inverse design. Using a broadband long-wave-infrared collecting metalens as the case study， the pipeline is validated end to end: the decomposed fields and gradients approach the undecomposed global results， and the far-field figure of merit admits partitioned automatic differentiation over the near-field subdomains. The results show that domain decomposition makes large-area FDTD automatic-differentiation inverse design feasible， laying a foundation for subsequent large-scale metalens optimization.
