Faraday effect and multiple scattering of light

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Abstract
The presence of a magnetic field in an optically active medium produces a rotation of the polarization of light: it is the well-known Faraday effect, which breaks the time-reversal symmetry. The averaged light intensity in the multiple scattering of light by disordered systems is described by the weak-localization theory based on the direct and reverse sequences of scatterings, which are founded on the time-reversal symmetry. The multiple scattering of electromagnetic (vectorial) waves by spherical particles is considered in the presence of a magnetic field. We have shown that the electric field of the reversed path can be obtained from the direct one by a simple matrix transposition. In systems of reduced dimensionality (1 and 2), we have shown that for the same polarization channel, the peak of the backscattering cone is not affected by the Faraday effect even though the time-reversal symmetry is broken. The intensity correlation function is obtained for a one-dimensional system. This simple model furnishes two results: (i) even though the wave vector is randomized, there is no decorrelation of the polarization for paths of the same length and (ii) the correlation function has an oscillatory behavior as a function of the magnetic field. In three dimensions, we have calculated analytically the attenuation of the backscattering cone as well as the decorrelation length for the multiple Rayleigh scattering. Mie scattering has been considered by Monte Carlo simulations. In the diffusion regime (thick slabs) our results are in accord with previous results and with experiments. Nevertheless, for the intermediate regime in transmission, we have found oscillations of the intensity correlation as a function of the magnetic field. For reflection and strong magnetic field, we have observed the convergence of the enhancement factor to nontrivial asymptotic values.