Analysis of the weak localization of photons in fractal aggregated structures and its applications

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By means of optical experiments and computer simulations on the basis of two different models, the following properties were revealed for the weak localization of photons in fractal aggregated structures.1. In one simulation, scattering of photons were traced in fractal media with fractal dimension 1<D<2 generated by means of the Weierstrass function in a two-dimensional plane. It is found that the coherent cone in the enhanced backscattering light obeys approximately a power law with the exponent of 1-D.Simulated probability density of the scattering free path was approximately equal to the theoretical density. A self-similar algorithm was developed to extend the simulation to the three-dimensional space.2. In the other simulation, the scattering process was simulated by calculating a free path by using random numbers at each scattering event. In this simulation, the fractality of the media was assumed only in the probability density of the free path, which we derived analytically in this study. This simulation revealed that the shape of the coherent cone depends on the fractal dimension of the media, and that this dependence is different for different polarization components of the detected light.3. The optical experiment using the fractal aggregates produced from the aqueous solution of PMMA particles showed the shape of the coherent backscattered cone to obey the power law with fractional exponent given approximately by 1-D.It is also found that the height of the coherent cone depends on the average size of fractal clusters of the media.