Rigorous modeling of electrostrictively excited acoustic fields and SBS gain spectra in single-mode optical fibers

Mitigating the stimulated Brillouin scattering (SBS) problem in single-mode optical fibers is often based on complex doping allowing to create and spread multiple Brillouin resonances over a wide acoustic frequency range lowering an overall SBS gain maximum. Co-doping with Al<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>O<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> is often used for it. However, it creates the “antiguiding” conditions for, at least, some of the acoustic waves electrostrictively excited in a vicinity of the fiber core. Conventional eigen-mode solvers have a fundamental restriction on guided acoustic modes and, thus, cannot allow one to calculate the SBS gain spectrum properly in a frequency region near and beyond the Brillouin frequency of pure silica. It requires the use of special approaches including an explicit account on the driving optical field. Here we provide a rigorous and, at the same time, relatively simple and fast method based on a development of the well-known infinite power-series expansion of a solution to the scalar inhomogeneous ordinary differential equation of the electrostrictively excited acoustic field, which has no requirement of specially fitting parameters and allows one to model exactly SBS gain spectra for arbitrarily doped (including different dopant species) conventional optical fibers. To complete the calculation framework, we also provide an experimental investigation of all required acousto-optical material parameters for GeO<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>, P<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>O<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub>, Al<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>O<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> and F dopants in MCVD-made fibers, on a base of which an Al<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>O<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub>/GeO<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>/P<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>O<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub>/F doping design of a single-mode optical fiber at 1.55μm was proposed and experimentally verified featuring a multi-resonant BGS providing ∼11dB of the SBS gain suppression relative to a standard single-mode germanosilicate fiber.