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We study the effects of random roughness on wave propagation in a parallel plate metallic waveguide with finite conductivity. The rough surface is three dimensional (3D) with roughness heights varying in both horizontal directions. Integral equations are obtained from the extinction theorem formulated with layered medium Green's function. The second order small perturbation method is then applied to solve the integral equations. A closed form expression for the coherent wave is derived, which is expressed in terms of a three-fold Sommerfeld type integral due to the waveguide structure. Approximate methods are applied to calculate the Sommerfeld integral. The results based on the approximations are shown to agree with that of direct integration. The coherent wave enhancement factors of absorption are computed. Results of the present 3D roughness case are compared with the previous results of two dimensional (2D) roughness. The results for waveguides are also compared with the results obtained for a plane wave incident on a metal surface with 3D roughness. Results are illustrated for 3D roughness with a variety of power spectra. It is shown that enhancement factors of 3D roughness are larger than for 2D roughness. We also show that enhancement factors for a waveguide are larger than that of the plane wave case. Comparisons are also made between the theoretical results and measurements.
Date of Publication: Dec. 2012