A Perturbative Solution to Plane Wave Scattering From a Rough Dielectric Cylinder

We present an analytical, second-order perturbative solution to the problem of electromagnetic plane-wave scattering from a dielectric cylinder with a randomly rough surface. In contrast to previous integral equation-based approaches, we perturb the electromagnetic boundary conditions at the cylinder interface. Doing so affords us tractable expressions for the fields internal and external to the cylinder. We validate our results by comparing them with rigorous, but computationally intensive solutions obtained from the method of moments, and numerically estimate a region of validity for our results. We report this region as h₀ <; λ/20 and l > 4 h₀, where h₀ and l are the root-mean-square surface roughness and surface correlation length, respectively, for scattering at a wavelength λ.