New Types of Orthonormal Electromagnetic Beams in Complex Media and Free Space
Abstract : Vector plane-wave superpositions defined by a given set of orthonormal scalar functions on a two- or three- dimensional manifold are treated. We present a technique for composing orthonormal electromagnetic beams in complex media and free space. New families of exact time-harmonic solutions of the homogeneous Maxwell equations in linear media (isotropic, chiral, anisotropic, and bianisotropic) and free space, which describe orthonormal electro magnetic beams, are obtained.
Waves with linear, quadratic and cubic coordinate dependence of amplitude in crystals
There exist inhomogeneous electromagnetic and elastic waves with linear, quadratic and cubic coordinate dependence of amplitude, in addition to the usual plane harmonic waves in crystals. This article is concerned with conditions for initiation of such waves and mathematical techniques for their description. New types of electromagnetic waves with quadratic and cubic coordinate dependence of amplitude on the transverse coordinate in a transparent biaxially anisotropic plate are found. Any transparent biaxial crystal is demonstrated to have an infinite set of cuts, each suitable for initiation of one or more such waves.
Macroscopic model of second‐harmonic generation in a dielectric thin‐film helicoidal bianisotropic medium
The oblique propagation problem in a dielectric thin-film helicoidal bianisotropic medium (TFHBM), which has a reference uniaxial basis and exhibits second-harmonic generation (SHG), is solved. First, the linear constitutive relation is set up, followed by a constitutive relation to describe SHG. Then, a homogeneous 4 × 4 matrix ordinary differential equation is solved for the linear electromagnetic field phasors, and an inhomogeneous 4 × 4 matrix ordinary differential equation is solved for the second-harmonic electromagnetic field phasors. Extension to more general nonlinear HBMs shall follow the same route, provided the angular frequency of the nonlinear field generated is different from the angular frequencies of the linear fields that are needed to generate the nonlinear field. © 1996 John Wiley & Sons, Inc.