Spectral Prediction and Inverse Design of Multimode-Coupled Topological Photonic Crystal Structures Based on Fourier Feature Encoding

Abstract Customized spectral response of topological photonic crystal (TPC) structure is of great significance for its practical application. However, the complex spectral response of multimode TPC would make both conventional manual optimization and standard deep learning highly challenging. In this work, we propose a Fourier-encoded deep learning strategy that replaces full-spectrum prediction with frequency-conditioned transmittance prediction. The resulting Fourier MLP resolves sharp spectral variations and achieves high prediction accuracy (R² = 0.9836) across rapidly oscillating transmittance profiles. As a differentiable surrogate, this model effectively guides gradient-based inverse design toward prescribed transmission targets. We validate this approach through two examples: spectral suppression at f=105, 106, and 107 THz; spectral enhancement at f=109 and 112 THz, and suppression at f=110 THz. The proposed method may provide a practical route for the design of complex topological photonic devices, such as filters and sensors.