Fourier factorization with complex polarization bases in the plane-wave expansion method applied to two-dimensional photonic crystals

TL;DR

This paper improves the plane wave expansion method for 2D photonic crystals by using Fourier factorization with elliptic polarization bases, resulting in better convergence and broader applicability.

Contribution

It introduces a Fourier factorization approach with complex polarization bases, enhancing convergence over classical methods in photonic crystal analysis.

Findings

Our method shows superior convergence compared to classical approaches.

It effectively handles systems with arbitrary cross-sections.

The approach enables analysis of more complex photonic structures.

Abstract

We demonstrate an enhancement of the plane wave expansion method treating two-dimensional photonic crystals by applying Fourier factorization with generally elliptic polarization bases. By studying three examples of periodically arranged cylindrical elements, we compare our approach to the classical Ho method in which the permittivity function is simply expanded without changing coordinates, and to the normal vector method using a normal-tangential polarization transform. The compared calculations clearly show that our approach yields the best convergence properties owing to the complete continuity of our distribution of polarization bases. The presented methodology enables us to study more general systems such as periodic elements with an arbitrary cross-section or devices such as photonic crystal waveguides.