Random groups in the optical waveguides theory

TL;DR

This paper introduces a novel mathematical approach using random group theory to analyze light propagation in single-mode fiber light-guides with random inhomogeneities, focusing on the behavior of the electric field's coherence and polarization.

Contribution

It develops a new theoretical framework for describing light in fibers with randomness, providing insights into the asymptotic polarization behavior.

Findings

Limit polarization degree tends to zero as fiber length increases.

Analyzes the statistics of electric field amplitudes in random inhomogeneous fibers.

Provides a mathematical basis for understanding light coherence in complex fibers.

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.