Multiple scattering of classical electromagnetic waves by volume gratings:completion of Fujiwara's solution

We present a general formulation for multiple scattering of classical elect romagnetic waves by volume gratings. Fujiwara's electron multiple scatterin g theory is modified and extended to the case of both, the transmission and the reflection geometries. The analytical solution for the amplitude Psi(n ) corresponding to the nth scattering order is given. The convergence of th e solution is proved for the transmission by a sinusoidal symmetric phase g rating. By employing a structural Green's function and a vectorial formulat ion for diffraction of a classical electromagnetic wave by a thin periodica l slab, as previously given by Alvarez-Estrada and Calvo, the solution for the back scattered field amplitude is derived and shown to coincide with th at obtained within the framework of the multiple scattering theory.