Wave fronts and packets in 1D models of different meta-materials: Graphene, left-handed media and transmission line

Abstract

A comparative study is made of the propagation of wave packets and fronts in three different meta‐media, i.e. graphene, left‐handed media (LHM) and transmission lines, using one‐dimensional models. It is shown that a potential step in graphene influences only the frequency of the electronic wave, i.e., the particular spectrum branch (electron or hole) to which the wave belongs to, while the envelop function (the wave front or packet form) remains unchanged. Although the model for a vacuum and LHM interface is similar to that of the potential step in graphene, the solutions are quite different due to differences in the chirality of the waves. Comparing the propagation of wave fronts and packets in a standard transmission line and its meta‐analog we demonstrate that the propagating packets in the meta‐line are much more deformed as compared to the standard one, including broadening, asymmetry and even the appearance of fast moving precursors. This influence is seen not only in the case of packets with steep fronts but in soft Gaussian packets as well.

Classical analog to the Airy wave packet

“…Using Eqs. (9) we go back to the laboratory frame and obtain the following solution of the Liouville equation:…”

“…There are more effects of that type in physics. It is worth mentioning the difference in phase and group velocities of the wave in the dispersive media, or precursors [9] moving faster than the wave packets.…”