Scattering of light with angular momentum from an array of particles

Understanding the scattering properties of various media is of critical importance in many applications, from secure high-bandwidth communications to extracting information about biological and mineral particles dissolved in sea water. In this paper we demonstrate how beams carrying orbital angular momentum can be used to detect the presence of symmetric or chiral subsets of particles in disordered media. Using a generalized Mie theory, we calculate analytical expressions for quasimonochromatic structured light scattered by dilute distributions of micro- and nanoparticles. These allow us to determine the angular momentum of the scattered field as a function of the angular momentum of the incident beam and of the spatial distributions of scattering particles. Our numerical results show that we can distinguish structured from random distributions of particles, even when the number density of ordered particles is a few percent of the total distribution. We also find that the signal-to-noise ratio, in the forward direction, is equivalent for all orders of the Laguerre-Gaussian modes in relatively dense (but still dilute) distributions of particles smaller than the beam waist and the Rayleigh range of the beam.