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Waves propagate through disordered systems in a variety of regimes. There isa threshold of disorder beyond which waves become localized and transportbecomes restricted. The intensity I of the wave transmitted through a systemhas a dependence on the length L of the sample that is characteristic of theregime. For example, I decays as 1/L in the diffusive regime. It is of currentinterest to characterize the transport regime of a wave from statisticalstudies of the transmittance quantities through it. Studies suggest that theprobability distribution of the intensity could be used to characterize thelocalized regime. There is an ongoing debate on what deviations from theclassical Rayleigh distribution are to be expected. In this numerical work, weuse scalar waves to obtain the intensity, transmission, and conductance ofwaves through a disordered system. We calculate the intensity, by setting anincoming plane wave towards the sample from a fixed direction. The outgoingintensity is then calculated at one point in space. This process is repeatedfor a collection of samples belonging to the same ensemble that characterizesthe disorder, and we construct the probability distribution of the intensity.In the case of transmission, we evaluate the field arriving to a series ofpoints distributed in the far field, and repeat the same statistical analysis.For the conductance, we calculate the field at the same series of points forincoming waves in different directions. We analyze the distribution of thetransmittance quantities and their change with the degree of disorder.

Transmittance Quantities Probability Distributions of Waves through Disordered Systems