The electric and magnetic disordered Maxwell equations as eigenvalue problem

TL;DR

This paper reformulates Maxwell's equations with electric and magnetic disorder as a Hermitian eigenvalue problem and uses CPA to analyze photon localization, revealing a larger localization range than previously known.

Contribution

It introduces a Hermitian reformulation of disordered Maxwell equations and applies CPA to explore photon localization, expanding understanding of Anderson localization in 3D.

Findings

Spectral range of Anderson localization is larger with combined electric and magnetic disorder.

Reformulation as eigenvalue problem facilitates analysis of disordered electromagnetic systems.

Results may explain why 3D Anderson localization of light has not been observed experimentally.

Abstract

We consider Maxwell's equations in a 3-dimensional material, in which both, the electric permittivity, as well as the magnetic permeability, fluctuate in space. Differently from all previous treatments of the disordered electromagnetic problem, we transform Maxwell's equations and the electric and magnetic fields in such a way that the linear operator in the resulting secular equations is manifestly Hermitian, in order to deal with a proper eigenvalue problem. As an application of our general formalism, we use an appropriate version of the Coherent-Potential approximation (CPA) to calculate the photon density of states and scattering-mean-free path. Applying standard localization theory, we find that in the presence of both electric and magnetic disorder the spectral range of Anderson localization appears to be much larger than in the case of electric (or magnetic) disorder only. Our result could explain the absence of experimental evidence of 3D Anderson localization of light (all the existing experiments has been performed with electric disorder only) and pave the way towards a successful search of this, up to now, elusive phenomenon.