Modelling the depletion length induced by modulation instability in distributed optical fibre sensors

An analytical model for the depletion length of modulation instability in single-mode optical fibres is proposed. The model gives the possibility to determine the maximum sensing distance that distributed optical fibre sensors can reach before being limited by the pump depletion induced by modulation instability. The important role of the noise level in the evolution of both modulation instability and the respective power depletion is clarified. The model gives a closed form expression helpful for a predictive design and is validated comparing the analytical results obtained by the model with measurements in a 25 km long Brillouin fibre sensor.