Wave transformation in transmission lines with rapid connection and disconnection of reactive elements

Rapid switching of transmission line parameters has emerged as a way to manipulate signals and as a testbed for various electromagnetic processes in time-varying media, including metamaterials. In general, the switching results in wave reflection and transmission similar to that for a spatial interface but at new frequencies. Here, various realizations of parameter switching are studied: connection and disconnection of reactive elements (capacitors and inductors) in series and in parallel. The temporal boundary conditions for the current and voltage distributions are derived rigorously based on the telegrapher’s equations that explicitly model additional elements, instead of taking the equivalent values. It is shown that the temporal boundary conditions depend not only on the parameter values before and after switching but on its specific realization. Connecting or disconnecting reactive elements always involves energy losses. When new elements are added, two types of losses are identified. The first type is related to the creation of static magnetic and electric fields in the elements after switching. The second type is related to a very rapid energy dissipation during switching even for a vanishingly small resistivity in the line. When elements are removed, their energy is also removed from the waves. The effects of finite switching times are discussed. This study defines some serious constraints in using switchable transmission lines for the realization of photonic time crystals and efficient wave manipulation without externally added energy. The results are also applicable to wave propagation phenomena in other media with time-varying parameters.