Novel variational approach for analysis of photonic crystal slabs

TL;DR

This paper introduces a variational method for analyzing photonic crystal slabs that significantly reduces computational resources and enables the calculation of radiation modes, improving efficiency over traditional 3D methods.

Contribution

A novel variational approach that simplifies photonic crystal slab analysis by approximating field amplitudes, enabling faster computation and radiation mode analysis.

Findings

Faster computation of PC slab modes comparable to 2D methods

Ability to calculate radiation modes not feasible with 3D PWE

Reduces time and memory consumption in photonic crystal analysis

Abstract

We propose a new method based on variational principle for analysis of photonic crystal (PC) slabs. Most of the methods used today treat PC slab as a three-dimensional (3D) crystal and this makes them very time and/or memory consuming. In this method we use Bloch theorem to expand the field on infinite plane waves which their amplitudes depend on the component perpendicular to the slab surface. By approximating these amplitudes with appropriate functions, we can find modes of PC slabs almost as fast as we can find modes of a two-dimensional (2D) crystal. Besides this advantage, we can also calculate radiation modes with this method which is not feasible with 3D Plane Wave Expansion (PWE) method.