Leaky mode dispersions of Goubau lines

Abstract

The leaky dispersion characteristics of a Goubau line were numerically investigated for three lower‐order transverse magnetic (TM) modes by determining a complex propagation constant using Davidenko's method. As a result, physically meaningful spectral ranges of leaky modes were found to exist below the cutoff frequency of the Goubau line. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 523–525, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23136

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

“…Except for this mode, our results are consistent with Ref. 9. We have assumed that the outside region is air and thus ǫ 3 = µ 3 = 1.…”

“…2 the parameters ǫ 2 = 5, µ 2 = 1, a = 5 mm, b = 10 mm were used to compare our results with those in Ref. 9. In particular, note the lowest-order TM 00 mode (black curve) that has no cutoff frequency and α = 0.…”

“…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 G-Line 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.…”

“…Upon calculating the EM field components associated with certain leaky wave solutions in Fig. 2, all discrete complex solutions of the standard Gline (with Region 2 index of refraction greater than one) are improper [6,9]. Because the outside region is air, cutoff occurs when γ = 1 or s = 0.…”

The Transition Between Reactive and Radiative Regimes for Leaky Modes in Planar Waveguides Based on Homogenized Partially Reflecting Surfaces

“…Among the few studies on this aspect, in [8] the condition of leaky cutoff β = α was first introduced for the fundamental leaky mode of a microstrip line, as the boundary between a low-frequency, reactive regime (where β < α) and a high-frequency, radiative regime (where β > α). The same condition was also derived in [9] by means of a simple effective-dielectric-constant approach, and has been applied over the years to a number of cases, such as microstrips operated on higher leaky modes [10], circular dielectric rods and waveguides [11], [12], Goubau lines [13], modified microstrip lines [14], etc.…”