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

Abstract

We present a general formulation for multiple scattering of classical electromagnetic waves by volume gratings. Fujiwara's electron multiple scattering theory is modi®ed and extended to the case of both, the transmission and the re¯ection geometries. The analytical solution for the amplitude C n 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 di raction of a classical electromagnetic wave by a thin periodical slab, as previously given by A Â lvarez-Estrada and Calvo, the solution for the back scattered ®eld amplitude is derived and shown to coincide with that obtained within the framework of the multiple scattering theory. IntroductionThe di raction of an electromagnetic wave by a volume di raction grating is a phenomenon which has been extensively studied within various di erent theoretical frameworks and for various applications. The coupled wave theories [1±3], the modal theories [4,5], and the electromagnetic theory of gratings [6] have been succesfully used to solve a great variety of physical problems related to the volume grating di raction. However, owing to the mathematical complexity of the di raction problem, rigorous analytical solutions are still not su ciently developed and various numerical algorithms are currently employed in order to solve the problem. Moreover, the application of the numerical methods is often restricted to periodic, homogeneous and planar volume gratings.In 1977 Calvo [7] demonstrated that multiple scattering theories (MSTs) based on integral equation formalism for the electromagnetic ®eld, lead to general analytical solutions for the scattered ®eld amplitude. The multiple scattering theories developed for volume holography [8, 9] and acousto-optic di raction gratings [10±14] are based on the Batterman and Cole theory [15] for X-ray di raction by crystals, and on the Cowley and Moodie [16, 17] and Fujiwara's [18] theories for scattering of electrons by atoms and crystal's lattices. Their main

Light scattering by an array of birefringent optical waveguides: theoretical foundations

“…4 Also, multiple scattering by volume gratings has been solved through a modified Fujiwara's theory. 5 However, to our knowledge, none of these formalisms have yet been applied to study multiple scattering by an array of N isotropic optical waveguides. Moreover, scattering by multiple anisotropic waveguides, which is the subject of this work, has scarcely been considered.…”