Simple far-field model for lateral leakage in printed transmission lines

A simple far-field phased-line model for the lateral leakage (e.g. the surface-wave one) in printed transmission lines is presented. It is based on replacing the guiding strip(s) and/or guiding slot(s) by a phased line radiating in the background structure (usually a simple dielectric-slab guide or a partially filled parallel plate waveguide). Both full-line (infinitely extended) and half-line (semi-infinite) structures are considered. The model predicts the impossibility of real (bounded) modes that are faster than the corresponding background mode (into which leakage can take place) in both full-line and half-line structures. On the other hand, complex (leaky-wave) modes are shown to behave properly (improperly) outside their sector of definition in half-line (full-line) structures. Far-field distributions for a number of cases are given for the sake of illustration.