Mode bifurcation and fold points of complex dispersion curves for the negative index metamaterial Goubau line

Abstract

In this paper the complex dispersion curves of the four lowest-order transverse magnetic modes of a dielectric Goubau line (ǫ > 0, µ > 0) are compared with those of a dispersive metamaterial Goubau line. The vastly different dispersion curve structure for the metamaterial Goubau line is characterized by unusual features such as mode bifurcation, complex fold points, both proper and improper complex modes, and merging of complex and real modes.The Goubau line (G-Line) has been known and studied since Sommerfeld and later Goubau considered applications using non-radiating surface waves on transmission lines [1,2]. While Sommerfeld analyzed a long cylindrical metallic wire as the transmission line of interest, Goubau realized that adding a dielectric outer sheath to the wire reduced the radial extent of the electromagnetic (EM) field and thus the dimensions of the associated excitation device. Interestingly, while the Sommerfeld wave can exist only on a conductor of finite conductivity, the Goubau wave can exist even when the inner conductor is assumed to have perfect conductivity. The G-Line has been investigated since the first part of the twentieth century, and its guided modes are well known [1,2,3,4,5]. As with all open waveguide structures, the G-Line spectrum consists of a finite discrete set of guided modes with purely real longitudinal propagation constants and an infinite continuum of radiation modes. Also present on open lossless structures are leaky waves [6,7] characterized by discrete complex longitudinal propagation constant solutions to the dispersion equation, but which are improper solutions of Maxwell's equations in that these solutions decay longitudinally but do not obey the transverse radiation condition and thus may only be used in restricted regions of space. Improper waves are not considered part of an open waveguide spectrum and are often referred to as "nonmodal" or "nonspectral" [6]. Despite this fact, leaky waves have found great usefulness in certain applications, particularly those related to leaky wave antennas [8]. Some authors have referred to the complex solutions of the circular dielectric rod and the standard G-Line dispersion equations as leaky modes and have considered them on a more or less equal footing with the guided modes [9,10]. The leaky waves of even the standard GLine are still not well characterized (only the transverse magnetic (TM) solutions have been considered in detail [9]) but on that structure, all complex leaky wave solutions of the characteristic equation have EM field components that diverge as the radial coordinate increases to infinity and are thus improper.In this Letter the G-Line geometry (see Fig. 1) is used with a negative index of refraction dispersive meta- material (NIM) [11,12] replacing the usual dielectric layer. Under these circumstances the metamaterial GLine spectrum consists of guided modes, radiation modes, improper complex waves, and proper complex modes. In the following we consider only the symmetric transverse magnetic (TM 0n ) solutio...

Analysis and design of efficient passive components for the millimeter-wave and THz bands

“…In addition, a fine control on the energy coupling process may be achieved if the grooves are manufactured with enough precision. A curious work is found in [521], where a DCSWW with a metamaterial dielectric is analyzed and the propagation behavior is compared with the classical DCSWW. The phenomena involved are quite singular, thus being, at this moment, hard to visualize future applications.…”