The problem of numerical simulation of propagation of guided waveguide modes in a regular homogeneous open waveguide

The work is dedicated to the problem of numerical simulation of the propagation of guided modes in a planar three-layer dielectric waveguide. Maxwell's equations in a Gaussian system of units, material equations for linear isotropic dielectric media and boundary conditions corresponding to guided TE modes were chosen as a mathematical model of the waveguide propagation of polarized monochromatic electromagnetic radiation. Properties of this regular homogeneous open waveguide with three layers having different refractive indices were investigated. The formulation of such waveguide task consists of the Helmholtz equation obtained by reducing the Maxwell equations, the boundary conditions for the TE modes and the asymptotic conditions for the guided modes for the Helmholtz equation. To solve such waveguide problem, we used the wave coupling method which consists of the following steps: The method of separation of variables is used to solve the Helmholtz equation, after that the solution represented as a product of two functions (each depends only on one variable) and then we substitute it into the boundary coupling conditions and form a system of linear algebraic equations for further solving and finding the coefficients of phase deceleration and amplitude coefficients. In addition to this method we used the method of separation of variables used to solve the Helmholtz equation, the Gauss method, adapted for solving homogeneous system of linear algebraic equations. The work presents a scheme of a three-layer planar open waveguide, a graph of dispersion curves showing the dependence of the phase deceleration coefficients on the thickness of the waveguide and the graph of the transverse parts of the guided waveguide modes. All numerical calculations and the described algorithm of symbolic numerical simulation are presented in the computer algebra system called Maple. © Copyright 2017 for the individual papers by the papers' authors.