Correlations and Fluctuations of Coherent Wave Transmission through Disordered Media

Abstract

The correlation functions of the transmission coefficients for scalar wave propagation through disordered media are calculated by use of both diagrammatic techniques and numerical simulations. The calculation is valid in the diff'usive regime: multiple elastic scattering with negligible absorption or inelastic scattering and a scattering length much longer than the wavelength. In addition to the familiar large local intensity fluctuations we find a novel memory eA'ect and long-range correlations in the transmission coefficients which decay to a positive background value. Implications for light-scattering experiments are discussed.PACS numbers: 42.20. -y Coherent waves propagating through a disordered medium' will emerge from that medium with a phase that varies in an effectively random manner along the wave front. If one assumes that the outgoing wave amplitude at a given point (or in a given mode) is a sum of a large number of uncorrelated amplitudes and that the total amplitudes at points separated by more than a few wavelengths are uncorrelated, then it is easy to show that the wave intensity will fluctuate by an amount of the order of its average. 2 3 The most familiar example of this is the speckle pattern created by a laser beam reflected off' a rough surface.It has recently been understood, however, that waves propagating through an inhomogeneous medium by multiple elastic scattering will create a fluctuating intensity pattern which is not nearly as "random" as intuition suggests. First, such patterns will show on average a higher intensity for backscattering as a result of constructive interference of time-reversed pairs of scattering sequences, '4 an eff'ect that has been observed recently in several experiments. 56 Second, although there are large intensity fluctuations observed, 67 the fluctuations at different points (or in different modes) must be statistically correlated. The theoretical and experimental evidence for this comes from the study of conductance fluctuations in small metal circuits.It is now understood that these fluctuations occur because of the high sensitivity of the complex interference pattern of the (coherent) electron wave function to changes in impurity scattering potentials. It is found that the fluctuations in the total transmission of electrons through the circuit summed over all incident and outgoing channels (which is proportional to the conductance) is always of order unity. s ' It is easy to show that such a result cannot be obtained if the fluctuations in each mode are uncorrelated. " It should be stressed that the statistical behavior encountered here is only quantum mechanical in that it derives from the wavelike behavior of electrons, and thus analogous statistical correlations should be present in any system in which waves propagate by coherent multiple elastic scattering. In this Letter we explicitly calculate the statistical correlation function in different transmitted modes and uncover both the correlations responsible for the "universal conductance fluctuations" ...

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