A numerical research of a proper wave spectrum of an anisotropic dielectric waveguide

Background. The aim of this work is to study the spectrum of the problem of propagating electromagnetic waves of an anisotropic dielectric waveguide with a circular cross section. Materials and methods. To determine the solution, we use the variational formulation of the problem. The physical problem is reduced to solving the eigenvalue problem for a system of ordinary differential equations. To find the numerical solution of the problem, we use the Galerkin method with the use of finite piecewise linear basis functions. Results. A numerical method for solving the problem of propagation of normal waves of an anisotropic dielectric waveguide with a circular cross-section was developed and implemented; a number of numerical experiments were carried out. Conclusion. The proposed numerical method is an effective way of finding an approximate solution to the problem of propagation of electromagnetic waves.