Radiation and coupling of guided modes in an optical fiber with a slightly rough boundary: stochastic functional approach

Abstract

The guided waves, or modes, in an optical fiber are perturbed if the boundary of the fiber is statistically irregular (rough). Owing to the accumulated effects of multiple scattering along the entire propagation path, even very slight boundary irregularities can have considerable influence on the propagation characteristics of the guided modes, such as radiation, reflection, and mode coupling. The scattering problem of guided waves in an optical fiber with a slightly rough core boundary is treated by application of the stochastic functional approach, which has been used successfully for similar problems in a planar waveguide with the Dirichlet boundary condition, as reported by us in an earlier paper [ Phys. Rev. E50, 5006 ( 1994)]. A stochastic representation for the Green’s function is given by expansion of the scalar Green’s function of the fiber in terms of the Wiener–Hermite stochastic functionals of a homogeneous Gaussian random boundary. The Wiener expansion coefficients and then the radiation losses and the mode-coupling coefficients of the guided modes caused by the rough boundary are determined from the boundary conditions under the approximation of a slight roughness. To give an idea of how the random rough boundary affects the propagation characteristics of the modes, we present some numerical examples for the Gaussian power spectrum of the random boundary. The numerical results show that the relative dielectric constant of the core and the cladding in an optical fiber should be as close to unity as possible to reduce the radiation loss caused by the rough boundary.