Helmholtz equations of electromagnetic waves in gyrotropic elliptical waveguides

In the propagation of electromagnetic waves in waveguides, the formulation of boundary value problems is of great importance, the solution of which leads to the derivation of dispersion equations of great practical importance. Analysis of dispersion equations makes it possible to reveal the patterns of propagation of electromagnetic waves in waveguides and on their basis to develop various instruments of the microwave range. The problem of research is considerably complicated if the waveguide is filled with a gyrotropic medium. There is currently no complete mathematical model of the propagation of electromagnetic waves in gyrotropic elliptical waveguides, which includes the Helmholtz equations, the expression for the transverse components and boundary conditions. In this paper, on the basis of general expressions for arbitrarily magnetized regular gyrotropic waveguides with a generalized orthogonal curvilinear cross-sectional shape obtained by solving a system of Maxwell differential equations, the Helm holtz equations for elliptical waveguides filled with longitudinally and transversely magnetized ferrite are obtained. The obtained equations supplement the theoretical basis for the electrodynamic analysis of gyrotropic elliptical waveguides.