The Implementation of the Symbolic-Numerical Method for Finding the Adiabatic Waveguide Modes of Integrated Optical Waveguides in CAS Maple

Computational problems of electrodynamics require an approximate solution of the system of Maxwell’s vector equations for regions with different geometries. The main methods for solving problems with the Maxwell equations are either finite difference methods or methods based on the Galerkin and Kantorovich expansions, or the finite element method. Each of the classes of methods is characterised by a wide range of permissible objects, but in each of the methods, the solution contains a large number of quantities known only in numerical form. We have chosen a different approach, in which to describe the waveguide propagation of electromagnetic radiation we propose using the model of adiabatic waveguide modes. This model allows reducing Maxwell equations to a system of ordinary differential equations, which allows analysis of its solutions at the symbolic level. A fundamental system of solutions of the system is constructed in symbolic form. A numerical method for computing the guided modes of a planar three-layer open waveguide is formulated and implemented using a vector model of the adiabatic waveguide modes. Phase constants calculated in the framework of the model of adiabatic waveguide modes were verified by comparison with those calculated in the framework of the scalar model. © 2019, Springer Nature Switzerland AG.