A flexible Bloch mode method for computing complex band structures and impedances of two-dimensional photonic crystals

TL;DR

This paper introduces a versatile numerical method for computing Bloch modes, complex band structures, and impedances of 2D photonic crystals from scattering data, overcoming limitations of previous specialized techniques.

Contribution

The method generalizes existing approaches by using scattering data from common numerical tools, enabling analysis at challenging frequencies where other methods fail.

Findings

Successfully computed complex band structures at difficult frequencies.

Designed photonic crystal antireflection coatings using the method.

Demonstrated the method's flexibility and practical applicability.

Abstract

We present a flexible method that can calculate Bloch modes, complex band structures, and impedances of two-dimensional photonic crystals from scattering data produced by widely available numerical tools. The method generalizes previous work which relied on specialized multipole and FEM techniques underpinning transfer matrix methods. We describe the numerical technique for mode extraction, and apply it to calculate a complex band structure and to design two photonic crystal antireflection coatings. We do this for frequencies at which other methods fail, but which nevertheless are of significant practical interest.