Propagation and localization of random plane waves in two‐dimensional homogeneous and isotropic random medium

Abstract

Random plane wave in two‐dimensional (2D) homogeneous and isotropic random medium is studied by means of stochastic functional approach. The random medium is assumed to be an omnidirectional Gaussian random field with isotropic narrowband spectrum centered at 2k twice as much as the wave number. The approximate stochastic solutions are obtained based on some theoretic considerations of the translation operator associated with the homogeneity of the random medium. The random plane wave is exponentially decaying or expanding with distance in the propagating direction indicating that the wave is in the cutoff state as was expected in the study of random cylindrical waves. Comparisons among these solutions and those obtained earlier by Ogura are given to demonstrate that the statistical behaviors of propagating waves have nothing to do with the shape of the wavefront, but are solely determined by the spectral form of the random medium. The presence of wave localization is verified by computer simulations for such a random plane wave field. Also the average and variance for the phase shift and log‐amplitude of the wave are measured from the simulated data to compare with the theoretical values. The agreements between the theory and the simulation are shown to be satisfactory in spite of the approximate theoretical formulas.