Mysterious behavior of the excited near fields on printed-circuit transmission lines: physical contribution of a non-physical solution

It is well known that, when most printed-circuit transmission lines are excited by a practical monochromatic high-frequency source, the near-field amplitude decay exponentially along the line axis due to the excitation of a leaky mode. Such a situation usually occurs when the leaky mode is the only physical solution at a given frequency. However, we sometimes meet with an unexpected situation in which the near-field amplitude decays with a decay constant much smaller than that expected from the leaky-mode eigenvalue, even though the only physical solution at the operating frequency is the leaky-mode solution. No answer to this mysterious situation could be found previously, until when we found that such a slow decay in the near-field-amplitude variation depends strongly on an indirect effect from a nonphysical improper-real solution that exists at the operating frequency. We show several kinds of evidence that prove our interpretation of this mysterious problem, including theoretical discussions and experimental results.