Method of separation of fluxes in the theory of light propagation in disordered media

This paper considers the problem of determination of the light-field intensity in conditions of plane geometry of a scattering material layer. Discussing theoretically well-studied problems, namely, small-angle light reflection from media with sharply anisotropic scattering on separate centers, light reflection from a semiinfinite medium in conditions of isotropic scattering, P-1-approximation, and others, we demonstrate considerable difficulties connected with boundary conditions in the solution of different problems in the theory of optical radiation transfer. In order to overcome these difficulties, we propose an original method of separation of light fluxes. The essence of this method is in representing the intensities of both ascending and descending radiation as series. According to this method, instead of expanding the intensities in the multiplicity of collisions, we use expansions in the number of events that imply the sign reversal of the projection of the photon velocity on the direction normal to the boundaries of the scattering medium. We derive equations for independent calculation of ascending and descending radiation fluxes. Moreover, boundary conditions on material surfaces are exactly fulfilled for any approximate method of solving these equations. Taking a simple bidirectional scattering phase function as an example, we analytically calculate the ascending and descending radiation in a material layer with a finite thickness and partial fluxes of various multiplicities. We analytically calculated the Green's function in a medium with isotropic scattering and the Green's function that corresponds to the standard small-angle approximation in media with sharply anisotropic scattering. For the Henyey-Greenstein scattering law, we obtain a simple analytical expression for the intensity of transmitted radiation under oblique incidence of a light flux upon a material surface.