Theoretical optimization of optical fibre Raman-Brillouin hybrid sensors

This paper proposes a hybrid distributed fibre sensor which works on Raman and Brillouin scattering generated simultaneously from the same laser beam source. The problem is solved by an analytical and a numerical method to determine some important parameters associated with Raman-Brillouin hybrid distributed fibre sensors, by solving the governing differential equations. Optimization of the hybrid sensor's length is proposed and discussed. The governing equations consider pump depletion caused by all involved effects: Rayleigh, spontaneous and stimulated Raman and Brillouin. Solutions are discussed for three important cases: spontaneous Raman and Brillouin scattering, Brillouin stimulated and Raman spontaneous scattering, and finally both Raman and Brillouin stimulated scattering. It is demonstrated that the sensor's length can be maximized in order to obtain the maximum scattered intensity in two different cases, one of them in good agreement with the literature. It is discussed that the differences between the full numerical solution and the analytical solutions occur mainly due to the approximations made. Results may be used in the distributed sensor's design whose goal is to optimize the sensor's length to get the most intense scattering signal. The implementation of the sensor and its feasibility in all cases is also argued. All results can be applied to Raman amplification systems where Brillouin scattering also takes place.