Left-handed metamaterials with saturable nonlinearity

The left-handed properties of metamaterials with saturable nonlinearity are analyzed with respect to their electromagnetic response as a function of externally varying parameters. We demonstrate that the response of the medium is strongly affected by the saturation of the nonlinear effects. The last can be exploited to modulate the amplitude or tune the frequency of the response. Moreover, the existence of bistability regions in large parts of the external parameter space allows for switching between different magnetization states, with either positive or negative response. The stability issue of multiple possible states is addressed through modulational instability analysis of plane wave envelopes in each of those states.