Shaping light with nonlinear metasurfaces

This tutorial aims to provide an extensive overview of methods of generating and shaping light at new frequencies by using nonlinear metasurfaces. We first review methods of manipulating light by using linear metasurfaces, on the basis of local control of the amplitude and phase of transmitted and reflected light. To extend these principles to nonlinear metasurfaces, we first introduce the mechanisms and principles underlying nonlinear interactions in metasurfaces. We then show how to use these principles to control the phase, amplitude, and polarization of emitted nonlinear radiation and how, through careful spatial arrangement of single nonlinear elements on a metasurface, it is possible to tailor the shape of the light emitted through nonlinear interaction.