Method of adiabatic waveguide modes formulation for open layered dielectric planar waveguides in symbolic form

Computational problems of electrodynamics require an approximate solution of the system of Maxwells 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, firstly, allows for the vector character of electromagnetic radiation and, secondly, involves the amplitude vector function and the scalar function describing the phase as the main desired quantities. This model allows reducing Maxwell's equations to a system of ordinary differential equations, which allows analysis of its solutions at the symbolic level. © 2019 Author(s).