Mathematical Modeling of Smoothly-Irregular Integrated-Optical Waveguide and Mathematical Synthesis of Waveguide Luneburg Lens

In this paper we consider a class of multilayer integrated-optical waveguides consisting of homogeneous dielectric layers of constant or variable thickness, which are being systematically numerically studied using the cross-section method. The method is based on the adiabatic approximation of the asymptotic expansion on the one hand and the expansion in the complete system of modes of regular comparison waveguide. The paper discusses the problems of numerical implementation of the cross-section method to the transformation of particular mode in a smooth transition from one planar regular open waveguide to another.