Solution to the Eigenvalue Problem of Rectangular Waveguides with Partial Dielectric Filling by Fourier Transform

Introduction. Modern computer simulation tools can be used to analyze complex waveguide structures channeling electromagnetic energy. In order to verify the obtained calculation results, they should be compared with a known "exact" value followed by calibration of the considered electrodynamic model. The desired value can be found using the method of Fourier transform, which allows the propagation constant in a regular rectangular waveguide with partial filling with a dielectric to be determined and its channeling properties in various wavelength ranges to be evaluated. Aim. Construction of a computational model for calculating a regular waveguide with an arbitrary arrangement of the dielectric on the cross section by the Fourier method, determination of the dispersion characteristics of the analyzed structures in the millimeter wavelength range. Materials and methods. A mathematical model for the analysis of a waveguide with partial dielectric filling is based on Maxwell’s equations using boundary conditions for tangential and normal components of the electromagnetic field. Results. A numerical analysis of the dispersion characteristics of structures with complex dielectric filling was carried out. A methodological approach to constructing a computational model for searching for the propagation constant in a rectangular waveguide with an arbitrary arrangement of dielectric filling is proposed. This approach can serve as the basis for analyzing layered dielectric structures with a complex cross-sectional shape and different values of relative permittivity. Conclusion. The developed mathematical models made it possible to numerically evaluate the channeling properties of waveguides with dielectric filling in the microwave range.