Gokhan, Fikri Serdar2026-01-242026-01-2420252770-0208https://doi.org/10.1364/OPTCON.555636https://hdl.handle.net/20.500.12868/5191Thanks to the LambertW function, the gain of a Brillouin fiber amplifier operating in the depleted pump regime is solved numerically using the Newton-Raphson method. Unlike traditional boundary value problem solvers, which rely on shooting or relaxation techniques and often pose challenges such as high computational complexity and convergence issues, the Newton-Raphson method offers a simpler and more efficient numerical approach. The result obtained can be used to optimize the performance of Brillouin fiber amplifiers. (c) 2025 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreementeninfo:eu-repo/semantics/openAccessScatteringAmplificationLightSlowArticle10.1364/OPTCON.555636449519572-s2.0-105007292472Q2WOS:001502108400014Q3