Nonlinear Metamaterials

Metamaterials are engineered structures designed to exhibit exotic electromagnetic properties. Early on in the development of metamaterials, these properties were extended to exotic regimes of nonlinear behaviour, unknown in classical nonlinear optics. In this chapter, we give a historical overview of metamaterials, considering first their exotic linear properties, and show how these give rise to exotic nonlinear properties, at frequency ranges from RF to visible. We overview the main attractive features of metamaterials for nonlinear applications, namely their strong local field enhancement, their ability to achieve exotic phase matching conditions, and the possibility to create inclusions with the correct symmetry to enhance a chosen nonlinear process. We then summarise the two most important classes of nonlinear optical metamaterials, plasmonic and all-dielectric.