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

We present a general formulation for multiple scattering of classical electromagnetic waves by volume gratings. Fujiwara's electron multiple scattering theory is modified and extended to the case of both, the transmission and the reflection geometries. The analytical solution for the amplitude Φn corresponding to the nth scattering order is given. The convergence of the solution is proved for the transmission by a sinusoidal symmetric phase grating. By employing a structural Green's function and a vectorial formulation for diffraction of a classical electromagnetic wave by a thin periodical slab, as previously given by Alvarez-Estrada and Calvo, the solution for the back scattered field amplitude is derived and shown to coincide with that obtained within the framework of the multiple scattering theory.