Application of adiabatic modes method for calculation and design of thin-film waveguide generalized Luneburg lens

The propagation of polarized light in integrated-optical multilayer waveguides is investigated. In the case of a regular homogeneous films Maxwell's equations are reduced to a pair of systems of ordinary differential equations for the TE- and TM-modes by the method of separation of variables. In the case of irregular layers the method of separation of variables is not applicable. Method of adiabatic modes is developed which is a generalization of the Kantorovich reduction of the differential equation in partial derivatives to a system of ordinary differential equations.