Search

Statements and analysis are presented of nonselfadjoint eigenvalue problems for elliptic equations and systems, including singular Sturm–Liouville problems on the line, that arise in mathematical models of the wave propagation in open metal-dielectric waveguides. Existence of real and complex spectra are proved and their distribution is investigated for canonical structures possessing circular symmetry of boundary contours.

Existence of symmetric complex waves in a metamaterial dielectric rod and a perfectly conducting cylinder of circular cross section covered by a concentric layer of metamaterial, a metamaterial Goubau line, is proved. Analytical investigation and numerical solution of dispersion equations reveal several important properties of running waves inherent to open metal-metamaterial waveguides which have not been reported for waveguides filled with standard media.

Existence of symmetric complex waves in a dielectric rod (DR) - a dielectric waveguide of circular cross section - is proved by analyzing functional properties of the dispersion equations (DEs) usi ...

We consider normal waves in multi-layered dielectric rod and Goubau line that are basic types of open metal-dielectric waveguides. The dispersion equations are analyzed using the notion of generalized cylindrical polynomials and methods of calculating determinants of block-diagonal matrices. Sufficient conditions of the existence of symmetric waves are established.

Existence of symmetric surface complex waves in a Goubau line—a perfectly conducting cylinder of circular cross-section covered by a concentric dielectric layer—is proved by constructing perturbation of the spectrum of symmetric real waves with respect to the imaginary part of the permittivity of the dielectric cover. Closed-form iteration procedures for calculating the roots of the dispersion equation (DE) in the complex domain supplied with efficient choice of initial approximation are developed. Numerical modeling is performed with the help of a parameter-differentiation method applied to the analytical and numerical solution of DEs.

Existence of complex TM and TE waves in a dielectric waveguide of circular cross section and a Goubau line is proved by analyzing functional properties of the dispersion equations (DEs) using the theory of functions of several complex variables and validating the existence of complex roots of DE. The method proceeds from the analysis of general setting involving hybrid nonsymmetric azimuthally dependent real and complex waves.

We consider a homogeneous Goubau line (GL) with a lossy cover. We analyze the dispersion equation for symmetric waves with respect to the problem parameters, find radially symmetric complex waves, and examine their behavior. We show that longitudinal wavenumbers of complex waves are regular perturbations of the propagation constants of eigenwaves of lossless GL, weakly depend om the imaginary part of permittivity of the cover, and that attenuation in GL is low at higher losses.