Mode-dependent characteristics of Rayleigh backscattering in weakly-coupled few-mode fiber

We theoretically investigate the mode-dependent characteristics of Rayleigh backscattering arising in weakly-coupled few-mode fibers (FMFs). Based on the theory of Lorentz reciprocity and surface wave excitation, we derive a general analytical equation of excitation efficiency and power distribution of Rayleigh backscattering light among backward propagation modes under the condition of impulse response. Thus, we are able to characterize the Rayleigh backscattering of weakly-coupled FMF with arbitrary refractive index profile. As for the weakly-coupled FMF with a step-index profile, the power distribution ratio of individual modes in the Rayleigh backscattering light is mainly determined by the forward propagation mode. In particular, the backscattering mode with the same profile as the forward propagation one has the highest excitation efficiency. The FMF parameters have influence on the total backscattering power, but little effect on the mode power distribution ratio.