Wave Propagation in Parallel Plate Metallic Waveguide With Finite Conductivity and Three Dimensional Roughness

Abstract

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.Index Terms-Perturbation method, random rough surface, three dimensional, waveguide structure.

An Application of Sensor Array Processing in Characterizing One Dimensional Surface Roughness

“…In this part, we explain the prototype of surface roughness [15,17,18,19,20] study using a group of arrays of antennas and single transmitter of wave towards the plate with normal incidence, before discussing the implementation of high resolution angle of arrival techniques [1,2], let us describe the type of surface's irregularities we are focused on.…”

“…The roughness of surface is considered as random fluctuations [15,19] of protuberances that compose the material type of the surface, thus the roughness is random, and it can be described by two dimensional [19,20] or one dimensional function [17,18], we focus here on the last category, the statistical description of the randomness states that the height of The plate is placed in ( , ) xyplane, the lines of roughness are parallel to…”

“…Indeed, it was shown in [28] that MVDR spectrum gave better resolution in the case of large number of radiating sources if they are not coherent. Let us illustrate an example in Figure 3, an array of fourteen elements with half wavelength inter-distance, we compare two spectra, the first is for specular reflection 1 P  and the second is for ' 400 P  sources whose angles of arrivals are uniformly distributed in the range 20 …”

“…The study of such surfaces is performed using profilometric [16] and optical techniques [8,16,17], the global shapes of protuberances are analyzed with optical interferomety using reflected laser beams [17]. In the other hand, the random roughness can be classified into one dimensional [17,18], two dimensional profile [19,20] or even three dimensional [20]. Verification of degree of roughness is an important step in many industrial sectors such as the verification of substrate of some electronic devices [21] and the quality of signal transmission over the sea surface which can be under calm and rough states [12].…”

Reconstruction of surface errors of the metallic waveguide based on electromagnetic scattering theory

“…Modelling is currently the predominant method (Guo et al, 2010;Ding et al, 2012). In modelling, sufficient accurate surface measurement data are required.…”