High-Order Small Perturbation Method of Arbitrary Order for Conducting Rough Surface Scattering under TE Incidence

A novel closed-form high-order small perturbation method (HOSPM) for the analysis of scattering from 1-D conducting random rough surfaces under TE incidence is developed. The main theoretical contributions of the HOSPM are as follows: (1) our method yields a general high-order SPM form for scattered fields of arbitrary orders, (2) Fad di Bruno's formula is introduced into computational electromagnetics (CEM) for the first time to expand a tapered incident wave and its partial derivatives in power series form, and (3) the form is simple and easy to program and does not require any mathematical pretreatment. Comparisons are made between the method of moments (MOM) and different-order HOSPMs in terms of several aspects, including accuracy and time efficiency. The order convergence of the HOSPM is discussed, the regions of validity with regard to correlation lengths and root mean square (RMS) heights are demonstrated for the 2nd-order HOSPM, and the robustness of the 2nd-order HOSPM is proven over a broad range of frequencies.