Photonic and microwave devices are foundational elements of both precision physics experiments and modern telecommunications and sensing technology. Electromagnetic inverse design intelligently searches for devices that optimally fulfill a particular task. However, most realistic design tasks are highly nonconvex problems. Thus, when treated as generic optimization tasks, they require extensive initialization sweeps to identify high-performing topologies. Here, we introduce convex preoptimization, a data-free, physics-informed alternative for intelligent design search. By lifting the electromagnetic fields to an outer-product representation and relaxing the local Maxwell constraints, we convert the original nonconvex problem to a convex one that can be solved to global optimality. The solution provides a physics-informed prior for the original task: a material choice at every pixel, together with a spatial map of the ambiguity of each choice, which guides subsequent refinement. We show that, for a wide range of photonic and microwave devices, convex preoptimization consistently dominates conventional initialization sweeps in both best and average performance while using a fraction of the compute. Convex preoptimization thus provides a physics-informed, interpretable, and training-free front end for inverse design.

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• Electromagnetic field calculations
• Inverse problems
• Mathematical physics
• Nanophotonics
• Optical & microwave phenomena
• Optimization problems
• Radio frequency techniques
• Maxwell's equations