Modeling the Brillouin Spectrum in Raman Amplifier-Assisted Brillouin OTDR

A tool for increasing the range of Brillouin optical time domain reflectometry (BOTDR) is distributed in-line Raman amplification. In this article, we model and experimentally verify how a combination of Raman pump depletion, pump-probe walk-off and self- and cross-phase modulation lead to a shift of the Brillouin spectrum, ultimately inducing an error in the sensor reading. The induced error is up to approximately 7 MHz (approx. 7 $^{\circ }$C) for standard BOTDR parameters. We numerically model the propagation of the fields in the fiber using standard propagation equations, and by considering only spontaneous Brillouin scattering as the source of the back-scattered field, we find an expression of the Brillouin spectrum. By using standard parameters of a BOTDR setup, we show how there is a tradeoff between Raman amplifier gain and the spectrally induced error. By comparing the model to experiments, we find that the measurements show the same trend as the simulated spectra.