Theoretical study of the effect of slow light on BOTDA spatial resolution

Due to the resonant nature of Brillouin scattering, delay occurs while pulse is propagating in an optical fiber. This effect influences the location accuracy of distributed Brillouin sensors. The maximum delay in sensing fibers depends on length, position, pump and Stokes powers. Considering pump depletion, we have obtained integral solutions for the coupled amplitude equations under steady state conditions and then calculated the group delay. The results show that moderate pump depletion (which is the optimized sensor working range) mitigates significantly the delay, and the maximum delay induced at resonance is only a fraction of Brillouin Optical Time Domain (BOTDA) spatial resolution, which means that the use of pulse width to define the spatial resolution is valid when Brillouin slow light is considered. We have shown that uniform strain and temperature distribution in a fiber gives the maximum delay induced uncertainty.