A POD-DeepONet Framework for Forward and Inverse Design of 2D Photonic Crystals

TL;DR

This paper introduces a POD-DeepONet framework for efficient forward and inverse design of 2D photonic crystals, combining reduced-order modeling with neural networks to enable accurate predictions and stable inverse design.

Contribution

The paper presents a novel POD-DeepONet surrogate model tailored for photonic crystal band-structure prediction and inverse design, with theoretical guarantees and practical effectiveness.

Findings

Accurate forward band-structure predictions for 2D photonic crystals.

Effective inverse design procedures for dispersion and band-gap targeting.

The framework achieves high accuracy on high-contrast, pixel-based layouts.

Abstract

We develop a reduced-order operator-learning framework for forward and inverse band-structure design of two-dimensional photonic crystals with binary, pixel-based $p4m$-symmetric unit cells. We construct a POD--DeepONet surrogate for the discrete band map along the standard high-symmetry path by coupling a POD trunk extracted from high-fidelity finite-element band snapshots with a neural branch network that predicts reduced coefficients. This architecture yields a compact and differentiable forward model that is tailored to the underlying Bloch eigenvalue discretization. We establish continuity of the discrete band map on the relaxed design space and prove a uniform approximation property of the POD--DeepONet surrogate, leading to a natural decomposition of the total surrogate error into POD truncation and network approximation contributions. Building on this forward surrogate, we formulate two end-to-end neural inverse design procedures, namely dispersion-to-structure and band-gap inverse design, with training objectives that combine data misfit, binarity promotion, and supervised regularization to address the intrinsic non-uniqueness of the inverse mapping and to enable stable gradient-based optimization in the relaxed space. Our numerical results show that the proposed framework achieves accurate forward predictions and produces effective inverse designs on practical high-contrast, pixel-based photonic layouts.