Dispersion relation reconstruction for 2D Photonic Crystals based on polynomial interpolation

TL;DR

This paper introduces an efficient method for reconstructing dispersion relations in 2D photonic crystals using polynomial interpolation, significantly reducing computational costs while maintaining accuracy.

Contribution

The paper presents a novel global polynomial interpolation scheme for fast dispersion relation reconstruction in 2D photonic band structures.

Findings

Method achieves high accuracy with fewer sampling points

Significantly reduces computational time compared to traditional methods

Applicable to various 2D photonic crystal configurations

Abstract

Dispersion relation reflects the dependence of wave frequency on its wave vector when the wave passes through certain material. It demonstrates the properties of this material and thus it is critical. However, dispersion relation reconstruction is very time consuming and expensive. To address this bottleneck, we propose in this paper an efficient dispersion relation reconstruction scheme based on global polynomial interpolation for the approximation of 2D photonic band functions. Our method relies on the fact that the band functions are piecewise analytic with respect to the wave vector in the first Brillouin zone. We utilize suitable sampling points in the first Brillouin zone at which we solve the eigenvalue problem involved in the band function calculation, and then employ Lagrange interpolation to approximate the band functions on the whole first Brillouin zone. Numerical results show that our proposed methods can significantly improve the computational efficiency.