Predicting band structures for 2D Photonic Crystals via Deep Learning

TL;DR

This paper introduces a deep learning model using U-Net to efficiently predict 2D photonic crystal band structures, significantly reducing computational costs while maintaining high accuracy, thus advancing photonic device design.

Contribution

The study presents a novel deep learning framework combining U-Net, transfer learning, and Super-Resolution to predict dispersion relations in 2D photonic crystals more efficiently than traditional methods.

Findings

High accuracy in predicting initial band functions

Significant reduction in computational expenses

Effective simultaneous prediction of multiple bands

Abstract

Photonic crystals (PhCs) are periodic dielectric structures that exhibit unique electromagnetic properties, such as the creation of band gaps where electromagnetic wave propagation is inhibited. Accurately predicting dispersion relations, which describe the frequency and direction of wave propagation, is vital for designing innovative photonic devices. However, traditional numerical methods, like the Finite Element Method (FEM), can encounter significant computational challenges due to the multiple scales present in photonic crystals, especially when calculating band structures across the entire Brillouin zone. To address this, we propose a supervised learning approach utilizing U-Net, along with transfer learning and Super-Resolution techniques, to forecast dispersion relations for 2D PhCs. Our model reduces computational expenses by producing high-resolution band structures from low-resolution data, eliminating the necessity for fine meshes throughout the Brillouin zone. The U-Net architecture enables the simultaneous prediction of multiple band functions, enhancing efficiency and accuracy compared to existing methods that handle each band function independently. Our findings demonstrate that the proposed model achieves high accuracy in predicting the initial band functions of 2D PhCs, while also significantly enhancing computational efficiency. This amalgamation of data-driven and traditional numerical techniques provides a robust framework for expediting the design and optimization of photonic crystals. The approach underscores the potential of integrating deep learning with established computational physics methods to tackle intricate multiscale problems, establishing a new benchmark for future PhC research and applications.