Scattering from a Periodic Corrugated Structure: Thin Comb with Soft Boundaries

Abstract

An incident plane wave is scattered from a surface, corrugated in one dimension, and given by an infinite number of periodic, finite-depth, infinitesimally thin parallel plates (thin comb) having soft boundary conditions. The solutions of the Helmholtz equation are assumed to be upgoing plane waves above the plates and standing waves in the plate wells. Both have unknown amplitude coefficients. Continuity of the solutions and their derivatives across the common boundary yields a doubly infinite set of linear equations for the unknown amplitudes. The equations are solved using the modified residue calculus technique due to Mittra. The amplitudes are expressed as values or residues of a certain meromorphic function. The residue calculus and Wiener-Hopf techniques are related; thus, an example of a solvable finite-range Wiener-Hopf-type problem is presented. Numerical evaluations of reflection coefficients are presented as a function of frequency, depth, and incident angle. The Wood P anomaly and the Brewsterangle anomaly are demonstrated. Results for backscatter at near-grazing incidence are also presented, and correspondences between the reflection coefficients and amplitude phases, as a function of depth, are indicated.