We were the first to report that both the bound and leaky dominant modes can propagate simultaneously on conductor-backed coplanar strips over a frequency range. We have recently studied this interesting and initially unexpected effect in more detail, and we have made two important discoveries: First, the simultaneous-propagation effect can actually occur on most, if not all, printed-circuit transmission lines (its presence depending on the relative line dimensions), so that, contrary to earlier belief, the effect is rather general. Second, we have discovered the surprising presence of a new improper (or nonspectral) real solution, which is nonphysical but whose evolution as a function of dimensional change serves to explain how the simultaneous-propagation effect can occur. The new solution, and its behavior in a completely nonphysical region, thus governs otherwise-mysterious large changes in the physical, measurable solutions.

Simultaneous propagation of bound and leaky dominant modes on printed-circuit lines: a new general effect

The frequency evolution of dominant (quasi-TEM) and higher order modes on an open printed-circuit structure such as a microstrip is examined. Three different mode types are considered, including bound modes (BMs), leaky modes that leak into the surface wave of the background structure, and leaky modes that also leak into space. One of the fundamental goals is to establish the conditions under which one type of mode can transition into another type as the frequency changes. One important conclusion is that the dominant BM can never transition into a leaky mode for a microstrip structure with an isotropic substrate, but such a transition is possible for an anisotropic substrate, observed originally by Tsuji et al. and Shigesawa et al. However, higher order BMs can directly transition into leaky modes, as shown by Oliner and Michalski and Zheng. On other structures such as coplanar strips, where the bound dominant mode exhibits odd symmetry, a transition from a bound dominant mode to a leaky mode is possible, as shown by Shigesawa et al. and Tsjui et al. In addition to examining the mathematical transitions that are possible, the physical continuation of modes is also investigated, by examining the frequency evolution of the currents excited by a practical source. It is concluded that there may be physical continuity between modes, even if there is no mathematical continuity.

Evolution of leaky modes on printed-circuit lines

In the optical regime, surface plasmon polaritons (SPPs) are attractive topics for physicists, chemists, biologists, and material scientists [1]-[13]. The concept of SPPs, which is widely applied in the field of surface science, can be dated to the 1950s [14]. SPPs are surface wave modes that propagate along the interface between a dielectric and a conductor (usually a metal) at optical frequencies. They are formed by interaction between the light or other electromagnetic (EM) waves trapped on the surface and the free electrons of the metal [1], [2]. Because of this interaction, the EM energy is tightly confined around the interface.

Planar Spoof SPP Transmission Lines: Applications in Microwave Circuits

Leaky dominant mode propagation regimes of a conductor-backed coplanar strip line are rigorously analyzed using the concept of critical or equilibrium points from catastrophe and bifurcation theories, in conjunction with a full-wave integral equation solution. The existence of nondegenerate or Morse critical points (MCPs) and degenerate or fold (turning) critical points (FPs) in coupling and leakage regions are associated with the occurrence of improper real and complex (leaky) solutions. The locations and types of critical points determine the stability and instability of the transmission line system with respect to small changes in geometrical parameters. The dispersion behavior of improper real and complex (leaky) solutions are efficiently reproduced in the local neighborhood of MCPs and FPs using a Taylor series expansion about those points. The qualitative and quantitative dynamic behavior of the transmission line modes can be investigated by examining the evolution of nondegenerate and degenerate points versus some structural parameter, such as strip width. The proposed analysis enables the prediction of bifurcation situations and the existence of improper real and complex solutions and gives a complete description of the system's structural behavior.

On the nature of critical points in leakage regimes of a conductor-backed coplanar strip line

Leaky waves have been known for many years in the context of leaky-wave antennas, but it is only within the past dozen years or so that it was realized that the dominant mode on printed-circuit transmission lines used in microwave and millimeter-wave integrated circuits can also leak. Such leakage is extremely important because it may cause power loss, cross talk between neighboring parts of the circuit, and various undesired package effects. These effects can ruin the performance of the circuit, so we must know when leakage can occur and how to avoid it. In most cases, these transmission lines leak only at high frequencies, but some lines leak at all frequencies. However, those lines can be modified to avoid the leakage. This paper explains why and when leakage occurs, and shows how the dominant mode behaves on different lines. The paper also examines certain less well known but important features involving unexpected new physical effects. These include an additional dominant mode on microstrip line that is leaky at higher frequencies, and a simultaneous propagation effect, which is rather general and which occurs when the line’s relative cross-sectional dimensions are changed. The final section of the paper is concerned with three important recent developments: (a) the new effects that arise when the frequency is raised still higher and leakage occurs into an additional surface wave, (b) a basic and unexpected discovery relating to improper real modes, which are nonphysical but which can strongly influence the total physical field under the right circumstances, and (c) the important practical issue of how leakage behavior is modified when the circuit is placed into a package. key words: leakage into surface waves, microwave and

Types and Basic Properties of Leaky Modes in Microwave and Millimeter-Wave Integrated Circuits

Surface wave leakage phenomena of coupled slot lines are investigated with spectral domain analysis. When the guided mode in the coupled slot lines changes from bound mode to leaky mode, there is a frequency range, called "spectral gap," where only nonspectral solutions exist. If the width of the center conductor or slots is increased beyond a certain value this spectral gap may disappear, resulting in a frequency range where both bound mode and leaky mode can exist simultaneously. >

https://ir.nctu.edu.tw:443/bitstream/11536/2301/1/A1994PK41200008.pdf

You-Bo Tsai

Papers

Surface wave leakage phenomena in coupled slot lines