A method of variation of boundaries for waveguide grating couplers

We describe a method for calculating the solution of theelectromagnetic field in a non-rectilinear open waveguide by using aseries expansion, starting from the field of a rectilinearwaveguide. Our approach is based on a method of variation ofboundaries. We prove that the obtained series expansion convergesand we provide a radiation condition at infinity in such a way thatthe problem has a unique solution.Our approach can model several kinds of optical devices which areused in optical integrated circuits. Numerical examples will beshown for the case of finite aperiodic waveguide grating couplers.