Vector theory of the waveguide scattering of laser radiation in the presence of noise (method of modes and method of the Green's function)

A vector theory of the laser radiation scattering in an integrated optical waveguide with arbitrary 3D irregularities is proposed. A 3D problem of electrodynamics regarding the laser radiation scattering in an irregular waveguide is solved with allowance for noise using the method of coupled modes in the first approximation of perturbation theory. An approximate solution of a 3D inhomogeneous wave equation is inferred using the method of modes and the method of the Green's function. Analytical expressions for the radiation fields are derived for the propagating and evanescent modes. A preliminary analysis of the results is presented.