Random groups in the optical waveguides theory

Abstract

We propose a new approach to the mathematical description of light propagation in a single-mode fiber light-guide (SMFLG) with random inhomogeneities. We investigate statistics of complex amplitudes of the electric field of light wave by methods of the random group theory. We have analyzed the behavior of the coherence matrix of a monochromatic light wave and the polarization degree of a nonmonochromatic radiation in SMFLG with random inhomogeneities as the length of the fiber tends to infinity; in particular, we prove that limit polarization degree is equal to zero.