A New Type of Intensity Correlation in Random Media

A monochromatic point source, embedded in a three-dimensional disordered medium, is considered. The resulting intensity pattern exhibits a new type of long-range correlations. The range of these correlations is infinite and their magnitude, normalized to the average intensity, is of order 1/k0l, where k0 and l are the wave number and the mean free path respectively. 42.25.Dd, 71.55.Jv Typeset using REVTEX 1 A wave propagating in a random medium undergoes multiple scattering and produces a complicated, irregular intensity pattern. Such a pattern is described in statistical terms and one of its important characteristics is the correlation function 〈I(~r1)I(~r2)〉, where I(~r) is the wave intensity at point ~r and the angular brackets designate the ensemble average. This correlation function has been studied in recent years, both theoretically and experimentally, and various types of correlations has been identified. There are large short-range correlations, due to interference among the waves arriving, via all possible scattering sequences, to a neighborhood of a given point; this interference is responsible for the large spatial fluctuations in intensity (speckles). There exist also weak long-range correlations, due to diffusion which propagates the locally large fluctuations to distant regions in space. The purpose of this note is to identify and study a new type of long-range correlation which, under appropriate circumstances, can dominate the “standard” long-range correlations. I consider a monochromatic point source embedded in an infinite three-dimensional random medium. The position of the source is ~r0 and its frequency is ω. Assuming a scalar wave, one has the following equation for the field (the Green’s function) at point ~r: