Closed-form Mueller scattering matrix for a random ensemble of long, thin cylinders

Abstract

We present a closed-form solution to the problem of elastic light scattering by a randomly oriented ensemble of cylinders of finite length. All the Mueller scattering matrix elements are calculated, so the solution is complete in the sense that all possible polarization effects are treated. The cylinders are assumed to be made of an isotropic material, which may be transparent or absorbing. Cylinder radius a and length L must obey a≤λmed/2π≤L, where λmed is the wavelength in the supporting fluid medium. Our solution includes all multipole effects due to the length of the cylinder, as well as all internal reflections at the boundary between the cylinder and the supporting medium. Nonzero values of the retardation elements M34 and M43 may be caused either by retardative internal reflections, or by absorption, or both. These elements are easily observable in experiments on scattering by rod-like viruses, but are completely missing in theories that ignore retardative contributions to the scattered amplitude. The curve M34(θ) is affected strongly in distinct ways by rod length, by index of refraction, and by absorptivity.