Analytical regularization of a generalized eigenwave problem for weakly guiding step-index optical fibers by Muller boundary integral equations

We investigate surface and leaky natural waves of weakly guiding step-index optical fibers. We reduce the original problem for Helmholtz equation on the plane with Reichardt radiation condition to a nonlinear eigenvalue problem for Muller boundary integral equation with Fredholm operator. We study the spectral properties of this operator and build a theoretically and practically justified collocation algorithm of numerical solution of the problem.