On the behavior of wave numbers beyond the critical value for waves in dielectric waveguides (media with losses)
The solutions of the dispersion equations for waves in plane and circular (symmetrical waves) dielectric waveguides are investigated. Thermal losses in the internal and external media are taken into account. Special attention is devoted to an analysis of the arrangement of the solutions in the complex plane of transverse wave numbers relative to the branchcut that separates the domains of physical and nonphysical solutions. It is shown that for both waveguides the solutions corresponding to backward non-natural waves are situated on the nonphysical sheet of the complex plane. Fundamental differences are noted for plane and circular waveguides in terms of the behavior of the wave numbers for a variation of the field frequency or waveguide parameters.
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