Statistics of mode area for transverse Anderson localization in disordered optical fibers

TL;DR

This paper introduces the mode area probability density function (MA-PDF) as a new statistical tool to analyze transverse Anderson localization in disordered optical fibers, providing insights into system behavior and computational efficiency.

Contribution

The paper presents the MA-PDF as a novel, physics-based statistical measure for TAL, independent of excitation shape, and demonstrates its scaling properties and convergence in small structures.

Findings

MA-PDF captures all relevant statistical information on TAL

MA-PDF converges to a terminal form for small structures

Method reduces computational cost for studying TAL

Abstract

We introduce the mode area probability density function (MA-PDF) as a powerful tool to study transverse Anderson localization (TAL), especially for highly disordered optical fibers. The MA-PDF encompasses all the relevant statistical information on TAL; it relies solely on the physics of the disordered system and is independent of the shape of the external excitation. We explore the scaling of MA-PDF with the transverse dimensions of the system and show that it converges to a terminal form for structures considerably smaller than those used in experiments, hence substantially reducing the computational cost to study TAL.