Trapped electromagnetic modes in forked transmission lines

The transmission-line or telegrapher equations for unbounded transmission lines are investigated. It is found that when a transmission line (TL) is forked, there may exist oscillating modes locally trapped or localized on the line. Solutions of these modes are equivalent to eigenproblems. When such a mode is destroyed, a Fano resonance (“peak-dip”-shaped resonance) is seen in the transmission spectrum, and this may provide an alternative point of view for those resonances commonly understood as due to the excitation of dual modes. A theoretical study on these modes is presented.