Distribution of average intensity in a closed quasioptical waveguide with impedance fluctuations on one wall

Abstract

UDC 621.372.8 The mutual coherence function of the field in a waveguide with impedance fluctuations on one wall is considered. Calculations are made in the parabolic-equation approximation using the local perturbation method. It is shown that components of the mutual coherence function with different periods of longitudinal interference oscillations propagate independently along the waveguide. This circumstance makes it possible to greatly simplify the general integral equation of the second kind that the mutual coherence function of the field in the waveguide satisfies, and to obtain (in the case of one-mode excitation of small-scale irregularities) the distribution of the mean intensity at large distances. At sufficiently large distances the mean intensity is uniformly distributed over the waveguide cross section, except for narrow zones adjacent to the boundaries. With increasing distance, the scale of these zones decreases as a power law. 1. Reference ]1] uses a modification of the local perturbation method (extensively employed in computing the statistical moments of the field in an inhomogeneous medium [2]) to obtain an integral equation of the second kind for the mutual coherence function of the field in a waveguide with an impedance fluctuation on one wall. This equation qualitatively describes the same multiple scattering process as the Bethe- Salpeter equation in the ladder approximation, obtained in [3] by using Feynman diagrams. However, the structure of this equation is simpler, since it is formulated relative to the coherence function, which has only transverse spacing of the observation points. For the case of large-scale nonuaiformities in the impedance, [1] obtained a solution of this equation that describes the mutual coherence function in the region of multiple scattering. In this paper, with allowance for spatial filtration, we will greatly simplify the integral equation. We will consider in detail the case of small-scale nonuniformities. For single-mode excitation of the waveguide, we obtain the distribution of the mean field intensity in the waveguide cross section at large distances.