Convex Preoptimization for Photonic and Microwave Inverse Design

Inverse design (InvDes) uses simulation and optimization to algorithmically discover unintuitive physical device layouts that outperform traditional rational designs, especially under complex performance and fabrication constraints. However, current InvDes methods—whether conventional gradient- and heuristic-based or AI-driven—are fundamentally constrained by non-convex, highly complex optimization landscapes, rendering global optimality in large-scale design problems unattainable. Here, we propose a new approach that uses convex preoptimization to circumvent the non-convexity barrier. By shifting the optimizable variables from material-based device structures to continuous-valued physical fields, mapping the original problem to closely related, convex semidefinite programs (SDPs), and fine-tuning the result with conventional InvDes methods, we can reliably identify near-globally optimal designs without broad, randomized initialization sweeps. We apply this method to design practical, fully three-dimensional, and fabricable integrated photonic and planar microwave devices, and demonstrate consistently better performance with SDP preoptimization than classic, randomized initialization sweeps. Our results establish a practical method to efficiently approach global optimality in electromagnetic InvDes.