3. Non-linear metamaterials

The vast majority of studies on metamaterials are limited to the linear regime, i.e. the regime in which the response of a structure is independent of the power of the incident signal. However, the appearance of non-linear phenomena in an artificial material characterized by singular dispersions of parameters could open up new perspectives. We could, for example, take advantage of an amplification phenomenon to compensate for losses that are currently holding back the development of optical components. Non-linearity can also be used to compensate for chromatic dispersion in focusing devices. To satisfy this type of application, the phenomena sought are harmonic generation and parametric amplification.

Harmonic generation is possible with conventional "right-handed" structures, where phase and group velocities are collinear and of the same sign. In the case of left-handed...