Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard

TL;DR

This study investigates wave transmission and edge states in a microwave photonic crystal near a Dirac point, revealing pseudodiffusive behavior and edge localization analogous to graphene phenomena.

Contribution

It provides the first experimental observation of extremal transmission and edge states in a microwave photonic crystal near a Dirac point.

Findings

Transmission near the Dirac point follows a 1/L dependence.

Edge states are localized at zigzag edges of the photonic crystal.

Edge states resemble those observed in graphene.

Abstract

This article presents experimental results on properties of waves propagating in an unbounded and a bounded photonic crystal consisting of metallic cylinders which are arranged in a triangular lattice. First, we present transmission measurements of plane waves traversing a photonic crystal. The experiments are performed in the vicinity of a Dirac point, i.e., an isolated conical singularity of the photonic band structure. There, the transmission shows a pseudodiffusive 1/L dependence, with $L$ being the thickness of the crystal, a phenomenon also observed in graphene. Second, eigenmode intensity distributions measured in a microwave analog of a relativistic Dirac billiard, a rectangular microwave billiard that contains a photonic crystal, are discussed. Close to the Dirac point states have been detected which are localized at the straight edge of the photonic crystal corresponding to a zigzag edge in graphene.