Numerical test of the theory of pseudo-diffusive transmission at the Dirac point of a photonic band structure

It has recently been predicted that a conical singularity (= Dirac point) in the band structure of a photonic crystal produces an unusual 1/L scaling of the photon flux transmitted through a slab of thickness L. This inverse-linear scaling is unusual, because it is characteristic of radiative transport via diffusion modes through a disordered medium -- while here it appears for propagation of Bloch modes in an ideal crystal without any disorder. We present a quantitative numerical test of the predicted scaling, by calculating the scattering of transverse-electric (TE) modes by a two-dimensional triangular lattice of dielectric rods in air. We verify the 1/L scaling and show that the slope differs by less than 10% from the value predicted for maximal coupling of the Bloch modes in the photonic crystal to the plane waves in free space.Comment: 4 pages, 7 figures. Figure adde

Photonic realization of the relativistic Kronig-Penney model and relativistic Tamm surface states

Photonic analogues of the relativistic Kronig-Penney model and of relativistic surface Tamm states are proposed for light propagation in fibre Bragg gratings (FBGs) with phase defects. A periodic sequence of phase slips in the FBG realizes the relativistic Kronig-Penney model, the band structure of which being mapped into the spectral response of the FBG. For the semi-infinite FBG Tamm surface states can appear and can be visualized as narrow resonance peaks in the transmission spectrum of the grating

Classical Simulation of Relativistic Quantum Mechanics in Periodic Optical Structures

Spatial and/or temporal propagation of light waves in periodic optical structures offers a rather unique possibility to realize in a purely classical setting the optical analogues of a wide variety of quantum phenomena rooted in relativistic wave equations. In this work a brief overview of a few optical analogues of relativistic quantum phenomena, based on either spatial light transport in engineered photonic lattices or on temporal pulse propagation in Bragg grating structures, is presented. Examples include spatial and temporal photonic analogues of the Zitterbewegung of a relativistic electron, Klein tunneling, vacuum decay and pair-production, the Dirac oscillator, the relativistic Kronig-Penney model, and optical realizations of non-Hermitian extensions of relativistic wave equations.Comment: review article (invited), 14 pages, 7 figures, 105 reference