Field Transformation in a Multimode Optical Waveguide with Random Irregularities of the Film Surface

Abstract

A self-consistent mathematical model for the transformation of the average intensity of the mode spectrum I(z) of a waveguide field in a multimode planar optical waveguide with a step profile and rough surface is developed. This model is based on the matrix model for multiple scattering of modes in an optical waveguide. The elements of the intermode scattering matrix are found, which describe the process of mutual transfer of the energy of modes along a waveguide and their transformation into radiation modes. The transformation of the I(z) modes in waveguides with large-and small-scale inhomogeneities is investigated. It is shown that the largest qualitative differences in the noted dependences manifest themselves only in the initial portions of the optical waveguide. The length z of these portions is much smaller than the characteristic scale length Lk at which the fundamental energy of the kth mode excited in the optical waveguide is renewed. The effect of self-filtration of the mode spectrum I(z) is described, as a result of which a stable (normalized), independent of distance z, distribution I* is formed. It is established that irregularities of the optical waveguide boundaries exert a depolarizing effect on a guided light beam. The specific features of the normalization of the radiative dissipation of a group of modes Ii(z) in an optical waveguide are investigated. It is ascertained that, in the case of small-scale irregularities, the attenuation coefficient is described by a nonlinear monotonic dependence α(z), which asymptotically converges to the value α*, characteristic of the normalized field I*. When the optical-waveguide film has large irregularities, the dependence α(z) is characterized by a pronounced maximum due to the formation of alternative channels of radiative dissipation of the energy of waveguide modes.