Two-dimensional anisotropic scattering in a semi-infinite cylindrical medium exposed to a laser beam

Abstract

A modified Ambarzumian's method is used to develop a system of nonlinear integral equations for the source functions at the boundary of a two-dimensional cylindrical medium with a scattering phase function represented by a series of Legendre polynomials. The scattering medium is infinite in both the r- and z-directions. The incident radiation is collimated and normal to the surface of the medium and is Bessel-varying in the radial coordinate. Superposition is used to construct the solution for the Gaussian shaped laser beam from the Bessel-varying solution. The back-scattered intensity and flux are calculated for three and five term phase functions which are characterized by moderately strong forward scattering. Appreciable differences are observed between the results for these phase functions and the results for the isotropic, linear, and Rayleigh phase functions. A simple scaling procedure is introduced that collapses the results for different phase functions into the results for isotropic scattering at large optical distances from the laser beam.