Analytical expression and experimental validation of the Brillouin gain spectral broadening at any sensing spatial resolution

A novel and simple analytical expression to describe the Brillouin gain spectral broadening as a function of the spatial resolution in time-domain Brillouin distributed fiber sensors is deduced. The proposed model is experimentally validated using a pump-probe Brillouin sensing setup and also compared with numerical and approximate results. In addition, a compact mathematical form is presented for the peak gain reduction resulting from incomplete acoustic-wave activation in Brillouin sensors with short spatial resolution. Both mathematical expressions can be used together to quantitatively predict the impact of the spatial resolution on the signal-to-noise ratio and frequency uncertainty of the sensor.