Electromagnetic Waves in Random Media: A Supersymmetric Approach

Abstract

A general method is set up, which casts problems of electromagnetic waves in random media into a systematic formalism akin to that of supersymmetric quantum field theory, by analogy with electrons in disordered metals. The characteristic functional of the field is related to that of trie medium by means of a diagrammatic expansion; for a linear medium, trie vertices are trie cumulants of trie permittivity, conductivity and permeability. Among trie auxiliary fields introduced to account for trie field equations, fermionic ones can be eliminated by discarding closed loops m the diagrams. A matrix Green function relates the expectation value of trie field to electric and magnetic monopole sources; its general structure and properties are reviewed. The versatility of trie approach, which allows us to take advantage of perturbative and variational techniques drawn from quantum field theory or statistical mechamcs, is fllustrated by examples: electromagnetic response of a weakly disordered medium, representation of correlations and of energy dissipation by means of four-leg diagrams. The couphng induced by disorder between long- and short-range effects, between transverse and longitudinal parts of the wave, is accounted for. The convergence of the expansions can be improved by making them self-consistent, and also by charactenzing the medium by the statistics of its polarizability rather than that of its permittivity, which partly accounts for screemng or depolanzation. The resulting expansions are of Pade type. Bruggeman's approximation is recovered in the low-frequency, weak-disorder limit; corrections are evaluated. An intricate structure for the electromagnetic response, involving several potes and a transition fine, anses in the high-frequency, weak-disorder limit.