Beam broadening in dense scattering media

The full 3-D integral equation for the spherically symmetric scattering of light in a medium of densely packed uniformly distributed scattering centers is solved for the case of a cylindrically symmetric laser beam (Gaussian profile) directed normally at the slab. After reduction to a 2-D problem, the discretized integral equation for the intensity (irradiance) of the scattered light is solved by a standard iteration procedure. The resulting 2-D distribution is reconverted to 3-D to obtain the r and z dependence of the irradiance. From the solution the angular distribution of backward and forward scattered light is calculated; special emphasis is placed on the radial dependence of the scattered light emerging normal to the surface in both directions. Spot sizes are defined and calculated for various values of beam radius and material parameters, nominally chosen to represent irradiation of white (translucent) biological tissue by a Nd:YAG laser. The effect of increasing the scattering coefficient on the spot profiles and radii is studied.