Two dimensional photonic crystals

TL;DR

This paper systematically derives formulas for computing photonic band structures in 2D photonic crystals, applies them to specific lattice structures, and discovers a large complete band gap in high frequencies.

Contribution

It provides a comprehensive derivation of formulas for 2D photonic crystal band structures and demonstrates their application to complex geometries with significant band gaps.

Findings

Large complete photonic band gap found in high frequency regime

Formulas applicable to various lattice structures and symmetries

Application to hollow cross-shaped cylinders in alumina ceramic

Abstract

The topology, the symmetry involving the shape of dielectric cylinders, and the lattice structure are among the most important ingredients in the architecture of photonic crystals. In this paper, we present a systematic derivation of the formulas which are needed in computing the photonic band structures of many commonly used two dimensional lattice structures and dielectric cylinders with various kinds of symmetries and rotations. Further the results are applied to arrays of hollow cross-shaped cylinders embedded in the alumina ceramic background. A large complete photonic band gap is found in the high frequency regime.