P. Cheben et Ml. Calvo, Multiple scattering of classical electromagnetic waves by volume gratings:completion of Fujiwara's solution, J MOD OPT, 46(2), 1999, pp. 181-198
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.