Degeneracy analysis for a super cell of a photonic crystal and its application to the creation of band gaps

TL;DR

This paper presents a method to analyze degeneracies in the band structure of photonic crystals using super cells, explaining how to create band gaps by lifting degeneracies through symmetry transformations.

Contribution

It introduces a novel degeneracy analysis method for super cells in photonic crystals and proves theorems on degeneracy lifting to generate band gaps.

Findings

Degeneracies occur at Brillouin zone edges due to symmetry.

Transforming the super cell can lift degeneracies.

Many known 2D photonic crystals' band gaps are explained by this analysis.

Abstract

A method is introduced to analyze the degeneracy properties of the band structure of a photonic crystal making use of the super cells. The band structure associated with a super cell of a photonic crystal has degeneracies at the edge of the Brillouin zone if the photonic crystal has some kind of point group symmetry. Both E-polarization and H-polarization cases have the same degeneracies for a 2-dimensional (2D) photonic crystal. Two theorems are given and proved. These degeneracies can be lifted to create photonic band gaps by changing the transform matrix between the super cell and the smallest unit cell. The existence of the photonic band gaps for many known 2D photonic crystals is explained through the degeneracy analysis.