General proof of optical reciprocity for nonlocal electrodynamics

Abstract

Recent studies have established certain specific results concerning the optical reciprocity of source and observer in the presence of dielectric medium with nonlocal response (i.e. spatial dispersion). These include the case of a linear dielectric response with dependence on the electric field gradient; as well as the case of a general anisotropic nonlocal medium in the long wavelength quasistatic limit. Here we present a more rigorous study of this problem by extending the previous results to the most general case of anisotropic nonlocal medium in the context of exact electrodynamics with reference to the symmetry of the Green dyadic. It is established that for nonmagnetic materials within linear optics, reciprocity will remain valid as long as the dielectric tensor satisfies the condition . Possible applications of the results are briefly discussed. ( ) (1

Reciprocity in quantum, electromagnetic and other wave scattering

“…Reciprocity for nonlocal potentials has been considered in [24][25][26]. The second remark is that a larger family of possible reciprocity operators is also allowed: Those when U of (77) is a Hilbert space operator acting on wave functions as…”

“…The currently typically used condition of reciprocity in linear systems is the self-transpose (also called complex symmetric) property of the matrix of the scattering potential, of the index of refraction, of the dielectric/magnetic permeability tensors, or of the Green's function [24,25]. This condition, however, depends on the frame, on the polarization basis chosen.…”

Impressed sources and fields in the volume-integral-equation formulation of electromagnetic scattering by a finite object: A tutorial

“…[82] for a specific choice of Z; hence we use the former term to avoid ambiguity. Importantly, the free-space dyadic Green's operator G is pseudo self-adjoint, and the same is obviously true of U for isotropic (as considered in this tutorial) or, more generally, for any reciprocal media [83].…”

Switching Reciprocity On and Off in a Magneto-Optical X-Ray Scattering Experiment Using Nuclear Resonance ofα−Fe57Foils

“…The term 'reciprocity' has been introduced by Stokes [1], and the numerous subsequent related publications cover the whole 20 th century, as it is summarized in the review paper of Potton [2]. Reciprocity theorems were derived for various scattering problems, telling under which conditions and limitations the reciprocity principle is valid [3][4][5][6][7], and situations in the field of local and nonlocal electromagnetism [8][9][10][11], sound waves [12], electric circuits [13], radio communication [14], and local and nonlocal quantum mechanical scattering problems [5,15,16] were considered. Nonreciprocal devices (circulators and isolators) with on-chip integration possibility were also suggested [17].…”