Homogenization of membrane and pillar photonic crystals

TL;DR

This paper rigorously derives the effective electromagnetic properties of a finite-height, anisotropic photonic crystal with a periodic structure, using two-scale convergence to model wave behavior at large wavelengths.

Contribution

It introduces a rigorous homogenization method for finite-height anisotropic photonic crystals, linking their effective properties to those of an infinite structure.

Findings

Effective permittivity and permeability tensors match those of an infinite crystal.

Homogenized system accurately models wave propagation in finite structures.

Provides a mathematical framework for designing photonic devices with complex geometries.

Abstract

We study wave propagation and diffraction in a bidimensional photonic crystal with finite height, in case where the wavelength is large with respect to the period of the structure. The device is made of materials with anisotropic permittivity and permeability tensors. We derive rigorously the homogenized system, using the concept of two-scale convergence. The effective permittivity and permeability tensors turn out to be that of a two-dimensional photonic crystal with infinite height.