Iterative series for calculating the scattering of waves from a hard corrugated surface

Abstract

We present an iterative series expansion in closed form that satisfies all the analytical equations proposed for solving the scattering of waves from a hard corrugated surface. The series converges to the good solution up to $h\lesssim 0.20$ when the corrugation of the surface is $D\left(x\right)=2\mathrm{}\pi hcos2\pi x$.