Transmittance Quantities Probability Distributions of Waves through Disordered Systems
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Transmittance Quantities Probability Distributions of Waves through Disordered Systems GABRIEL CWILICH and FREDY R ZYPMAN Yeshiva University, Department of Physics, New York, NY 10033-3201 ABSTRACT Waves propagate through disordered systems in a variety of regimes. There is a threshold of disorder beyond which waves become localized and transport becomes restricted. The intensity I of the wave transmitted through a system has a dependence on the length L of the sample that is characteristic of the regime. For example, I decays as L−1 in the diffusive regime. It is of current interest to characterize the transport regime of a wave, from statistical studies of the transmittance quantities through it. Studies suggest that the probability distribution of the intensity could be used to characterize the localized regime.1 There is an ongoing debate on what deviations from the classical Rayleigh distribution are to be expected. In this numerical work, we use scalar waves to obtain the intensity, transmission, and conductance of waves through a disordered system. We calculate the intensity, by setting an incoming plane wave towards the sample from a fixed direction. The outgoing intensity is then calculated at one point in space. This process is repeated for a collection of samples belonging to the same ensemble that characterizes the disorder, and we construct the probability distribution of the intensity. In the case of transmission, we evaluate the field arriving to a series of points distributed in the far field, and repeat the same statistical analysis. For the conductance, we calculate the field at the same series of points for incoming waves in different directions. We analyze the distribution of the transmittance quantities and their change with the degree of disorder. INTRODUCTION The propagation of waves in disordered systems has interested scientists since Lord Rayleigh studied the diffusion of light in the atmosphere to explain the color of the sky2, and led to the development of the theory of Radiative Transfer3. A pivotal advance was the work of Anderson4 raising the possibility that disorder can lead to non-diffusive behavior in which the intensity transmitted decreases exponentially as a function of the length of the sample the so-called localized regime. New theoretical ideas like the scaling theory of localization5, weak localization6,7, universal conductance fluctuations8 and Wigner dwelling times9,10, were followed, and the new field of Mesoscopic Physics reached and influenced many experimental areas: among them electronic systems11,12, microwaves13, optics14,15, acoustics16, geophysics17, laser physics18,19, medical physics20 and atomic physics21. One particular problem that remains central to this field is to understand the signature of the propagation of a signal in the different regimes (after all localization is the absence of transmission!), since disagreement persists about the interpretation of experimental results22. Theoretical analyses of certain characteristics of the propagation, in particu
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