Longwave properties of the orientation averaged Mueller scattering matrix for particles of arbitrary shape. I. Dependence on wavelength and scattering angle

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Abstract
Starting from a dipole array theory of elastic light scattering by particles of arbitrary shape and composition, we develop long-wave asymptotic formulas for all sixteen elements of the Mueller scattering matrix, valid after orientation averaging. The six dipole elements have long been known to be asymptotically proportional to k4 where k is the wave vector length of the light. However, the remaining ten nondipole elements experience intricate cancellations within the averaging operation that cause the asymptotic behavior to go like k5, k8, or k9; or at certain angles, like k6. For example, we show that (M34)=Ck9 sin2(θ), where C is a constant dependent on particle properties, and θ is the scattering angle. We find analogous simple angular basis functions for all 16 of the formulas and we show that they agree with numerical results from the exact algorithm. We contrast dipole array theory with central multipole expansion theory, which fails to account correctly for six of the Mueller elements, no matter how many multipoles are used.