Proposed method for detection of the pseudospin-12Berry phase in a photonic crystal with a Dirac spectrum

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 ($=\text{Dirac}$ point) with a pair of nearly degenerate modes near that singularity described by a spin-$\frac{1}{2}$ degree of freedom $(=\text{pseudospin})$. 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 $\ensuremath{\pi}$ acquired by rotation of the pseudospin over $360\ifmmode^\circ\else\textdegree\fi{}$ around a perpendicular axis. We support our analytical theory based on the Dirac equation by a numerical solution of the full Maxwell equations.