Rayleigh backscattering induces mode hopping of DFB fiber lasers in the sensor array, and the critical length related to Rayleigh backscattering limits the size of DFB fiber laser sensor networking. Based on three-mirror cavity model, the critical length for DFB fiber lasers are derived. It increases nearly exponentially with the coupling coefficient for the ideal π-shifted DFB fiber lasers. While the reflectivity of the sub-FBG at lasing wavelength is the main factor to resist Rayleigh backscattering for a non-ideal DFB fiber laser. The corresponding experiments have been carried out, and the results agree with the predictions.

Coupling coefficient; Critical length; Distributed feedback fiber lasers; Fiber laser sensors; Lasing wavelength; Mode-hopping; Rayleigh backscattering; Three-mirror cavity

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