Direct realization of the pseudospectral method of calculating waveguide mode

Often in the applied problems of integrated optics we use regular open gradient (general) planar waveguides. Waveguides perform conversion, amplification and transmission of light signals, similar to how it occurs with electrical signals in integrated circuits, but the speed of information transfer through such devices is much higher. The mathematical model of light propagation in a waveguide is described by Maxwell's equations and the corresponding boundary conditions. The Maxwell's equations in Cartesian coordinates are separated into two independent sets for the TE and TM polarizations. Systems for the TE and TM polarizations can be transformed into ODEs of the second order. The boundary conditions for equations are reduced to two pairs of boundary conditions. The problem of finding modes in regular open gradient planar waveguide is described in terms of an eigenvalue problem (The generalized eigenvalue problem of two matrices). Numerical simulation of these waveguides requires modern numerical methods with high efficiency and accuracy. © Copyright 2017 for the individual papers by the papers' authors.