Metamaterials (MMs) are artificial structures that display properties beyond those available in naturally occurring materials.
The most notable MM is the negative-index material with simultaneously negative electric and magnetic responses. Recently,
MMs exhibiting negative electric and magnetic properties in the infrared and optical frequencies have been realized, which
will affect substantially the conventional optics and their applications in devices of compact cavities, adaptive lenses, tunable
mirrors, isolators, converters, and so on. Moreover, MMs with nonlinear electric and/or magnetic response have also been
demonstrated. This will further stimulate intense investigation in MM-based nonlinear optics due to the richness and the
potential applications of the nonlinear property of MMs. In this paper, we report on our recent progress on investigation of
some typical third-order nonlinear optical phenomena in MMs, such as modulation instability, soliton propagation, self-focusing,
and so on. The controllability and the novel properties of the nonlinear phenomena in MMs are demonstrated.