The evolution of space-wave and surface-wave leaky modes on printed-circuit lines

One of the goals of the present investigation is to determine the mathematical and physical relations between the bound mode and the two types of leaky modes that can exist on a printed-circuit structure. One of the important mathematical questions is when a particular type of modal solution can evolve into another type of modal solution. For example, under what conditions can a bound mode turn into a leaky mode as the frequency changes? Also, can one type of leaky mode turn into another type of leaky mode solution? Another important issue is the physical continuity between the modal solutions that exist. When a practical feed, such as a delta-gap source, is placed on a printed circuit line, the source will launch a bound mode current in addition to a continuous spectrum current on the line. By numerically studying the behavior of the continuous spectrum current on the line as frequency changes, the physical continuity in the continuous-spectrum current can be examined as one particular modal solution evolves into another type of solution, or as one particular leaky-mode solution loses or gains physical significance.