Electromagnetic waves' self-focusing in metamaterials having both LHM and RHM behavior: an application to filter design

Self-focusing, also known as Talbot’s effect had been widely studied by the scientific community. In this paper we show self-focusing as a coherence propagation phenomenon, in particular we studied self-focusing for a pulse propagating in a metamaterial with both behaviors: left handed material (LHM) and right handed material (RHM). These dual behaviors allow the construction of frequency filters in the range of frequency in which the metamaterial stops behaving as a LHM (negative refraction index) and begins an RHM behavior (positive refraction index). The coherence length (CL) for pulses propagating in these metamaterials seems to be larger when its frequencies are in the LHM region. Finally, we show that the cell’s size turns out to be critical in designing the filter, and as an example we present here four metamaterial cells.