Semi-Dirac dispersion relation in photonic crystals

TL;DR

This paper demonstrates that a square array of elliptical dielectric cylinders in a photonic crystal can produce a semi-Dirac dispersion relation at the Brillouin zone center, revealing unique topological and refractive properties.

Contribution

It introduces a photonic crystal design that exhibits semi-Dirac dispersion and analyzes its properties using perturbation and effective medium theories.

Findings

Realization of semi-Dirac dispersion in photonic crystals

Topological transition in iso-frequency surfaces at the semi-Dirac point

Photonic crystal behaves as zero-refractive-index material along symmetry axis

Abstract

A semi-Dirac cone refers to a peculiar type of dispersion relation that is linear along the symmetry line but quadratic in the perpendicular direction. Here, I demonstrate that a photonic crystal consisting of a square array of elliptical dielectric cylinders is able to produce this particular dispersion relation in the Brillouin zone center. A perturbation method is used to evaluate the linear slope and to affirm that the dispersion relation is a semi-Dirac type. Effective medium parameters calculated from a boundary effective medium theory not only explain the unexpected topological transition in the iso-frequency surfaces occurring at the semi-Dirac point, they also offer a perspective on the property at that point, where the photonic crystal behaves as a zero-refractive-index material along the symmetry axis but functions like at a photonic band edge in the perpendicular direction.