Propagator model including multipole fields for discrete random media

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Abstract
A propagator model using Feynman diagrams is presented for studying the first and the second moments of the electromagnetic field in a discrete random medium. The major difference between our work and previous treatments of this type is that all diagrams are in a basis of vector spherical functions. Each propagator or infinite-medium Green’s function is the translation matrix for spherical functions, and each scatterer is characterized by a T matrix that, in turn, is a representation of the Green’s function of the scatterer in a basis of spherical functions. All orders of multipoles are formally retained, in contrast to previous work involving the dipole approximation. Partial resummations of the scattering diagrams are shown to be related to the quasi-crystalline approximation and the first-order smoothing approximation. The lowest-order term of the ladder approximation for the incoherent intensity is evaluated. Sample numerical results are presented and compared with available experimental results.