Nonlinear left-handed transmission line metamaterials

Metamaterials, exhibiting simultaneously negative permittivity e and permeability mu, more commonly referred to as left-handed metamaterials (LHMs) and also known as negative-index materials, have received substantial attention in the scientific and engineering communities [1]. Most studies of LHMs (and electromagnetic metamaterials in general) have been in the linear regime of wave propagation and have already inspired new types of microwave circuits and devices. The results of these studies have already been the subject of numerous reviews and books. This review covers a less explored but rapidly developing area of investigation involving media that combine nonlinearity (dependence of the permittivity and permeability on the magnitude of the propagating field) with the anomalous dispersion exhibited by LHM. The nonlinear phenomena in such media will be considered on the example of a model system: the nonlinear left-handed transmission line. These nonlinear phenomena include parametric generation and amplification, harmonic and subharmonic generation as well as modulational instabilities and envelope solitons.