How to detect the pseudospin-1/2 Berry 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 (= 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.

arXiv comment6 pages, 6 figures; v2: section added, figure added

References in corpus (11)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Veselago Lens for Electrons: Focusing and Caustics in Graphene p-n Junctions
• Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal
• Focussing Light Using Negative Refraction
• Extremal transmission at the Dirac point of a photonic band structure
• Resource Letter GPP-1: Geometric Phases in Physics
• Berry phase in graphene: a semiclassical perspective
• Correspondence between Andreev reflection and Klein tunneling in bipolar graphene
• Demonstration of a New Transport Regime of Photon in Two-dimensional Photonic Crystal

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