How to detect the pseudospin-1/2 Berry phase in a photonic crystal with a Dirac spectrum

TL;DR

This paper presents a method to detect the pseudospin-1/2 Berry phase in a photonic crystal with a Dirac spectrum by eliminating dynamical phase effects, enabling direct observation of geometric phase shifts.

Contribution

It introduces a technique using complementary media to isolate and measure the Berry phase in photonic crystals with Dirac points, supported by analytical and numerical analysis.

Findings

Transmission minima indicate Berry phase shifts

Complementary media eliminate dynamical phase

Numerical solutions confirm analytical predictions

Abstract

We propose a method to detect the geometric phase produced by the Dirac-type band structure of a triangular-lattice photonic crystal. The spectrum is known to have a conical singularity (= Dirac point) with a pair of nearly degenerate modes near that singularity described by a spin-1/2 degree of freedom (= pseudospin). The geometric Berry phase acquired upon rotation of the pseudospin is in general obscured by a large and unspecified dynamical phase. We use the analogy with graphene to show how complementary media can eliminate the dynamical phase. A transmission minimum results as a direct consequence of the geometric phase shift of pi acquired by rotation of the pseudospin over 360 degrees around a perpendicular axis. We support our analytical theory based on the Dirac equation by a numerical solution of the full Maxwell equations.