Zero-refractive index and pseudo-spin physics in photonic systems

Abstract

It is know that photonic crystals with Dirac-like conical dispersions at k = 0 derived from monopole and dipole excitations can serve as a “classical system” with zero-refractiveindex [1]. We will show that such a system also behaves as if it is a “quantum-like system” with pseudo-spin 1 [2]. In some dielectric photonic crystals exhibiting conical dispersions at k = 0, the eigenmodes can be described by an effective spin-orbit Hamiltonian with a pseudospin of 1. Here, the pseudospin of 1 does not refer to the intrinsic spin of photons, but an additional quantum number describing the admixing of 3 degrees of freedom of the spatial wave function of the EM wave near the Dirac-like point. As the pseudospin of the conical dispersion in these photonic crystals is different from that of graphene which has pseudospin of 1/2, the transport properties are also different even though both systems have conical disperions. For example, we found that Klein tunneling is more robust and collimation can be realized more easily with pseudospin 1 than pseudospin 1/2. For photonic systems that can be described by pseudospin-1 Hamiltonian, disorder induced localization effect are found to be distinct from ordinary materials. In particular, as disorder increases, the localization length can decrease to a minimum and increase again. Such unusual phenomena is closed related to the notion “complementary material”. The special wave scattering properties of pseudospin-1 photons, coupled with the discovery that the effective photonic “potential” can be varied by a simple change of length scale, may offer new ways to control photon transport. We will also show that conical dispersions will lead to single-mode interface states. In particular, an interface state is guaranteed to exist if an interface is formed such the photonic crystals on either side of the boundary are formed by slightly perturbing the condition to form a Dirac-like cone (zero-refractive index). Near the Brillouin zone center, the existence of the interface state can be explained using effective medium theory. In a deeper level, the origin of the existence of the interface states can be discussed in terms of scattering theory and a bulk-interface correspondence that relates the surface impedance to the geometric phases of the bulk band structure [3, 4].