Far roots of dispersion equations for LE- and LM-waves

Waveguides filled with dielectric are usually used as slowing down systems. The partial filling waveguides with dielectric gives the additional degree of freedom for controlling slots energetic parameters such as radiation and reflection coefficients. These parameters are functions of unknown electric field and this field may be represented as a combination of eigen waves fields. The full system of eigen waves in a waveguide with longitudinal dielectric slab consists of LE- and LM-modes. The eigen values can be obtained from the dispersion equations for these waves. The aim is to compare far roots of dispersion equations for LE- and LM-waves in a partly filled with dielectric waveguide and in an empty one. This information may be used for obtaining reliable results in the process of slot admittances calculations. In a waveguide with two-layered dielectric the transversal eigen values for LE higher modes monotonically tend to those of an empty waveguide (nπ/b). In the case of LM-modes they oscillate periodically about (nπ/b) with non-decreasing amplitude. The period T of oscillations highly depends on dimensions of dielectric layers. The cases of very thin layers are mostly difficult for obtaining stable results of slot scattering parameters.