Spatial beam dynamics in graded-index multimode fibers under Raman amplification:a variational approach

TL;DR

This paper presents a semi-analytical variational approach to study spatial beam dynamics in graded-index multimode fibers under Raman amplification, providing faster insights into nonlinear effects like self-focusing and cross-phase modulation.

Contribution

The paper introduces a variational method that simplifies the complex wave equations into coupled ODEs, enabling faster analysis of beam dynamics under Raman gain with physical insights.

Findings

Variational results agree well with full numerical simulations.

The method helps identify conditions to improve signal quality without beam collapse.

It offers a faster alternative for studying beam behavior under various parameters.

Abstract

We investigate the spatial beam dynamics inside a multimode graded-index fiber under Raman amplification by adopting a semi-analytical variational approach. The variational analysis provides us with four coupled ordinary differential equations that govern the beam's dynamics under Raman gain and are much faster to solve numerically compared to the full nonlinear wave equation. Their solution also provides considerable physical insight and allows us to study the impact of important nonlinear phenomena such as self-focusing and cross-phase modulation. We first show that the variational results corroborate well with full numerical simulations and then use them to investigate the signal's dynamics under different initial conditions such as the initial widths of the pump and signal beams. This allows us to quantify the conditions under which the quality of a signal beam can improve, without collapse of the beam owing to self-focusing. While time-consuming full simulations may be needed when gain saturation and pump depletion must be included, the variational method is useful for gaining valuable physical insight and for studying dependence of the amplified beam's width and amplitude on various physical parameters in a faster fashion.