Diffusion of Classical Waves in Random Media with Internal Reflection and Microstructure Resonances

The goal of the present thesis is to provide a description of transport in a finite system utilizing the diffusion formalism. We report results on the analysis of total transmission, reflection and surface intensity profiles of classical waves propagating in random media. Performed experiments allow us to parameterize interfacial optical interactions within the framework of the photon diffusion model and to determine the regime of validity of the model. Moreover, such measurements provide a remarkably simple method for determining propagation parameters: transport mean free path, diffusion coefficient, absorption length and internal reflection coefficients at sample's interfaces. Our results not only confirm the adequacy of diffusion theory but make possible a detailed study of the transition from ballistic to diffusive transport. We also study the effect of internal reflection on the spatial and spectral intensity-intensity correlation functions of classical waves propagating in absorbing random media. Both short- and long-range correlation functions are considered. Our results demonstrate that internal reflection causes dramatic changes in the functional behavior of the correlation functions. In the case of low absorption the spatial correlation function undergoes a crossover from quadratic to a linear falloff with separation as the internal reflection increases. The spectral correlation function varies with the frequency shift as (Delta omega)^{-1} for a medium with highly reflecting boundaries instead of ( Deltaomega)^{-1/2} as in the case of weak reflection. Finally, we examine wave diffusion in a random medium with the scatterers of a finite size. The general expression for the diffusion coefficient of classical waves is obtained. We find strong resonant structure in the diffusion constant as a function of the wave vector of incident wave. The location of peaks coincides with the location of principal Mie resonances. We find growth of the transport mean free path in the vicinity of the principal Mie resonances. The effect of absorption on resonances is also considered. It is found that absorption tends to smear out resonances.