Analytical results for 2-D non-rectilinear waveguides based on a Greens function

We consider the problem of wave propagation for a 2-D rectilinear optical waveguide which presents some perturbation. We construct a mathematical framework to study such a problem and prove the existence of a solution for the case of small imperfections. Our results are based on the knowledge of a Greenʹs function for the rectilinear case.