Space-time correlation of the amplitude and phase of the field in a waveguide having a statistically rough boundary

Abstract

The perturbation theory method in the Born approximation is used to solve the problem of the space-time correlation of the amplitude and phase of the field in a plane waveguide having a statistically rough wall. With respect to the boundary roughnesses it is assumed that their height is small in comparison with a wavelength and that Open image in new window , Open image in new window andl y are the correlation radii of the roughnesses along and across the propagation routes, respectively; D is the length of the route; Open image in new window is the longitudinal wave number of the n-th normal wave; Open image in new window , and also that the variation of the boundary shape with time takes place considerably more slowly than a period of the electromagnetic oscillations. It is shown that the coefficient of space-time correlation has an identical form for the amplitude and phase of the field, does not depend on the specific waveguide model, and is determined solely by the statistical characteristics of the boundary roughnesses. The expressions are analyzed for the dispersions of the amplitude and phase fluctuations, their space correlation functions, and their time spectra in a series of limiting cases.