Analytical Solution of Brillouin Amplifier Equations for lossless medium

TL;DR

This paper derives an analytical solution for the coupled pump and Stokes wave equations in a lossless Brillouin medium, introducing a novel gain approximation for the Brillouin Fiber Amplifier in the saturation region.

Contribution

It provides an exact analytical solution to the coupled equations in a lossless medium and introduces a new gain approximation for the saturation region of Brillouin Fiber Amplifiers.

Findings

Analytical solution based on conserved quantities

New gain approximation for saturation region

Enhanced understanding of pump depletion dynamics

Abstract

In order to explain pump depletion in Stimulated Brillouin scattering (SBS), coupled intensity equations describing the interaction of pump and stokes waves in Brillouin medium, must be solved simultaneously. Since this problem has well-defined boundary conditions, such a mathematical problem is known as the two-point boundary value problem. Conventional solution techniques leads transcendental equation which results implicit solution. In this paper, we accurately define Pump and Stokes evolution in lossless medium in terms of conserved quantity and proposed the solution of this conserved quantity using the asymptotic theory. Regarding with the saturation region, the gain approximation of Brillouin Fiber Amplifier (BFA) for the lossless medium, is introduced for the first time to our best of knowledge.