Metasurfaces are artificial two-dimensional (2D) planar surfaces that consist of subwavelength 'meta-atoms' (i.e. metallic or dielectric nanostructures). They are known for their capability to achieve better and more efficient light control in comparison to their traditional optical counterparts. Abrupt and sharp changes in the electromagnetic properties can be induced by the metasurfaces rather than the conventional gradual accumulation that requires greater propagation distances. Based on this feature, planar optical components like mirrors, lenses, waveplates, isolators and even holograms with ultrasmall thicknesses have been developed. Most of the current metasurface studies have focused on tailoring the linear optical effects for applications such as cloaking, lens imaging and 3D holography. Recently, the use of metasurfaces to enhance nonlinear optical effects has attracted significant attention from the research community. Benefiting from the resulting efficient nonlinear optical processes, the fabrication of integrated all-optical nano-devices with peculiar functionalities including broadband frequency conversions and ultrafast optical switching will become achievable. Plasmonic excitation is one of the most effective approaches to increase nonlinear optical responses due to its induced strong local electromagnetic field enhancement. For instance, continuous phase control on the effective nonlinear polarizability of plasmonic metasurfaces has been demonstrated through spin-rotation light coupling. The phase of the nonlinear polarization can be continuously tuned by spatially changing the meta-atoms' orientations during second and third harmonic generation processes, while the nonlinear metasurfaces also exhibit homogeneous linear properties. In addition, an ultrahigh second-order nonlinear susceptibility of up to 104 pm V-1 has recently been reported by coupling the plasmonic modes of patterned metallic arrays with intersubband transition of multi-quantum-well layered substrate. In order to develop ultra-planar nonlinear plasmonic metasurfaces, 2D materials such as graphene and transition metal dichalcogenides (TMDCs) have been extensively studied based on their unique nonlinear optical properties. The third-order nonlinear coefficient of graphene is five times that of gold substrate, while TMDC materials also exhibit a strong second-order magnetic susceptibility. In this review, we first focus on the main principles of planar nonlinear plasmonics based on metasurfaces and 2D nonlinear materials. The advantages and challenges of incorporating 2D nonlinear materials into metasurfaces are discussed, followed by their potential applications including orbital angular momentum manipulating and quantum optics.

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平面非线性光学及其应用

超表面是由亚波长“超原子”（即金属或介电纳米结构）组成的人造二维（2D）平面表面。与传统的光学同类产品相比，它们以能够实现更好、更高效的光控制而闻名。超表面可以引起电磁特性的突然和急剧变化，而不是需要更大传播距离的传统逐渐积累。基于这一特点，已经开发出具有超薄厚度的平面光学元件，如反射镜、透镜、波片、隔离器甚至全息图。当前大多数超表面研究都集中在为隐形、透镜成像和 3D 全息术等应用定制线性光学效应。最近，使用超表面来增强非线性光学效应已经引起了研究界的极大关注。受益于由此产生的高效非线性光学过程，具有特殊功能（包括宽带频率转换和超快光开关）的集成全光纳米器件的制造将成为可能。等离子体激发是增加非线性光学响应的​​最有效方法之一，因为它诱导了强的局部电磁场增强。例如，已经通过自旋旋转光耦合证明了对等离子体超表面的有效非线性极化率的连续相位控制。非线性极化的相位可以通过空间改变元原子来连续调整 在二次和三次谐波产生过程中的方向，而非线性超表面也表现出均匀的线性特性。此外，通过将图案化金属阵列的等离子体模式与多量子阱层状衬底的子带间跃迁耦合，最近报道了高达 104 pm V-1 的超高二阶非线性磁化率。为了开发超平面非线性等离子体超表面，基于其独特的非线性光学特性，已经广泛研究了诸如石墨烯和过渡金属二硫属化物（TMDC）等二维材料。石墨烯的三阶非线性系数是金基板的五倍，而TMDC材料也表现出很强的二阶磁化率。在本次审查中，我们首先关注基于超表面和二维非线性材料的平面非线性等离子体的主要原理。讨论了将二维非线性材料结合到超表面中的优势和挑战，然后是它们的潜在应用，包括轨道角动量操纵和量子光学。