Influence of the Rayleigh backscattering on the mode composition of radiation in multimode graded-index waveguides with a quadratic refractive-index profile

A method of coherent states is used to describe the process of Rayleigh scattering in a multimode graded-index waveguide with a quadratic refractive-index profile. Explicit expressions are obtained for the coefficients representing excitation of Gaussian–Hermite backscattering modes in two cases of practical importance: excitation of a waveguide by an extended noncoherent light source and selective excitation of different modes at the entry to a waveguide. An analysis is also made of the coefficients of coupling between forward and backward modes. Explicit expressions for the coefficients representing capture of backscattered radiation by a waveguide are obtained for two special cases of excitation (extended light source and zeroth mode).