Anomalous refractive properties of photonic crystals

Abstract

Abstract:We describe methods of investigation in order to study the behavior of photonic crystals. Our approach establishes a link between the dispersion relation of the Bloch modes for an infinite crystal (which describes the intrinsic properties of the photonic crystal in the absence of an incident field) and the diffraction problem of a grating (finite photonic crystal) illuminated by an incident field. We point out the relationship between the translation operator of the first problem, and the transfer matrix of the second. The eigenvalues of the transfer matrix contain information about the dispersion relation. This approach enables us to answer questions such as: when does ultrarefraction occur? Can the photonic crystal simulate a homogeneous and isotropic material with low effective index? This approach also enables us to determine suitable parameters to obtain ultrarefractive or negative refraction properties and to design optical devices such as highly dispersive microprisms and ultrarefractive microlenses. Rigorous computations add a quantitative aspect, and demonstrate the relevance of our approach.

3d Printed Lattices With Spatially Variant Self-Collimation

“…They are composed of a periodic lattice of physical features that interact with an applied wave to produce new and useful phenomena including negative refractive index [2][3][4], dispersive properties [5][6][7][8][9][10][11], electromagnetic band gaps [12][13][14][15], anisotropy [16][17][18][19][20][21][22][23][24][25][26][27], and more. All of these phenomena depend strongly on the direction of an applied wave and/or the polarization of the field.…”

Electromagnetic Wave Propagation in Media with Indefinite Permittivity and Permeability Tensors

“…Photonic crystals, for example, can modify the radiative density of states associated with nearby electromagnetic sources. Optical effects such as superradiance [1], enhanced or inhibited spontaneous emission [2], ultrarefraction [3] and even negative refraction [4,5] have been predicted for various photonic lattice configurations.…”

Band Gap Formation and Multiple Scattering in Photonic Quasicrystals with a Penrose-Type Lattice

“…Novel exciting phenomena could be exploited in the near future in practical optical circuits. One can cite phenomena such as superprism [6], self-guiding [7], and others effects that are based on the richness of the dispersion relation of photonic crystals [8,9].…”