The Fermi beam solution generalized to oblique incidence

We consider the time-independent, monoenergetic searchlight problem for a purely scattering, homogeneous slab of finite thickness. This problem corresponds to a pencil beam of radiation impinging upon one surface of a source-free slab at an arbitrary oblique angle of incidence. The scattering process is assumed sufficiently peaked in the forward direction so that the Fokker-Planck differential scattering operator can be used. Further, the slab is assumed sufficiently thin so that radiation backscattering is negligibly small. Under these assumptions, we obtain the full three-dimensional solution for the angular flux of radiation. This solution is a generalization of the classic Fermi solution, obtained in the special case of perpendicular beam incidence.