Probability distribution functions for transmission of waves through random media: A new numerical method

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Abstract
We present a new numerical method for calculating interference phenomena for waves propagating through random media. The model is applied to calculate probability distribution functions for the transmission P(T) in one and two dimensions, T being the transmission coefficient. The model reproduces the analytical predictions for one dimension, and yields new results for two-dimensional systems. The distribution function P(T) in two dimensions, in the diffusive regime, is found to be close to a Gaussian with a variance proportional to the mean, in agreement with the results of diagrammatic calculations. A crossover of the distribution to log-normal behavior typical for strong localization is obtained.