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.

中文翻译：

---

使用非线性超曲面对光进行整形

本教程旨在通过使用非线性超颖表面全面概述在新频率下生成和整形光的方法。我们首先回顾在透射和反射光的振幅和相位的局部控制的基础上，通过使用线性超表面来操纵光的方法。为了将这些原理扩展到非线性超颖表面，我们首先介绍了超颖表面中非线性相互作用的机制和原理。然后，我们将展示如何使用这些原理来控制所发射的非线性辐射的相位，幅度和偏振，以及如何通过在超颖表面上精心设计单个非线性元素的空间布置，来调整通过非线性相互作用发射的光的形状。