Application of variational-difference methods to dielectric waveguide calculations

Modern variational-difference methods of calculating dielectric waveguides, in particular lightguides, are reviewed. Consideration is given to the main problems that arise when the method of finite elements and the method of finite differences in the variational formulation are used to study the propagation of electromagnetic waves in straight dielectric waveguides homogeneous along the guiding axis, having a complex shape of the cross section and a complicated profile of permittivity. The paper describes various types of variational formulation, various ways of bounding the region and taking into account the behavior of the field at infinity, as well as methods of reducing the initial problem to the algebraic problem of eigenvalues and calculating eigenvalues and eigenvectors. Special attention is paid to the elimination of physically meaningless spurious solutions, the so called "ghosts".