%0 Journal Article
%T Dirac Dispersion in Two-Dimensional Photonic Crystals
%A C. T. Chan
%A Zhi Hong Hang
%A Xueqin Huang
%J Advances in OptoElectronics
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/313984
%X We show how one may obtain conical (Dirac) dispersions in photonic crystals, and in some cases, such conical dispersions can be used to create a metamaterial with an effective zero refractive index. We show specifically that in two-dimensional photonic crystals with symmetry, we can adjust the system parameters to obtain accidental triple degeneracy at 忙 point, whose band dispersion comprises two linear bands that generate conical dispersion surfaces and an additional flat band crossing the Dirac-like point. If this triply degenerate state is formed by monopole and dipole excitations, the system can be mapped to an effective medium with permittivity and permeability equal to zero simultaneously, and this system can transport wave as if the refractive index is effectively zero. However, not all the triply degenerate states can be described by monopole and dipole excitations and in those cases, the conical dispersion may not be related to an effective zero refractive index. Using multiple scattering theory, we calculate the Berry phase of the eigenmodes in the Dirac-like cone to be equal to zero for modes in the Dirac-like cone at the zone center, in contrast with the Berry phase of for Dirac cones at the zone boundary. 1. Introduction The Dirac equation is the wave equation formulated to describe relativistic spin 1/2 particles [1]. In the special case where the effective mass of the spin 1/2 particle is zero, and the solution to Dirac equation has a linear dispersion in the sense that the energy is linearly proportional to the wave vector . The electric band structure of graphene near the Fermi level can be described by the massless Dirac equation and hence exhibit the Dirac dispersion [2每15]. The electronic band dispersion is linear near the six corners of the two-dimensional (2D) hexagonal Brillouin zone at the and points, and the dispersion close to the Fermi energy at each of these corner -points can be visualized as two cones meeting at the Fermi level at one point called the Dirac point, and the conical dispersion near the Dirac point is usually referred to as Dirac cones. This rather singular electronic band structure of graphene near the Fermi level gives rise to many unusual transport properties [2每15], including quantum hall effect [4每6], Zitterbewegung [7每11], and Klein paradox [12]. Dirac cone dispersions are not limited to graphene but can also be found in classical wave periodic systems such as photonic crystals [16每24]. In fact, linear dispersions at the Brillouin zone boundary for 2D triangular photonic crystals appeared in the photonic
%U http://www.hindawi.com/journals/aoe/2012/313984/