Region of validity of perturbation theory for dielectrics and finite conductors

Abstract

We present a study of region of validity of first-order perturbation theory applied to rough surface scattering. The scattering problem is solved numerically for the case of periodic surface or gratings varying in one dimension. Scattering of electromagnetic waves from an ensemble of gratings of sufficiently long period will give a good approximation to the case of an infinite rough surface. We use this to test the validity of the first-order perturbation theory. Use of an infinite periodic surface allows us to give results for a range of angle of incidence covering those representing a low grazing angle, near 90° from the mean surface normal. We consider the case for perfect dielectrics and finite conductors. The real and imaginary parts of the refractive index used were limited to less than three due to the numerical instability of the numerical calculation method involved. We find that for perfect dielectrics the first-order small perturbation theory remains for TE polarization valid for all incidence angles, while for TM polarization it seems to fail if the incidence angle approaches the Brewster angle.