Spatially engineered nonlinearity in resonant metasurfaces

Metasurfaces—structured arrays of nanoresonators—are becoming more and more essential in our every-day life. They are already employed in smartphone cameras, are being developed for LiDAR and 3D sensing, and will constitute even more devices in the near future.

One of the most intriguing applications of metasurfaces is nonlinear frequency conversion, in particular second-harmonic generation: two photons of incoming light are converted into a single photon with twice the frequency (half the wavelength). Metasurfaces can enhance and control this process despite being very thin. Their performance in nonlinear frequency conversion mainly depends on two parameters: geometry, i.e., the shape of nanoresonators and their arrangement, and the material. After fabrication metasurface properties can still be tuned, e.g., by changing its environment with added liquid crystals, by applying voltage, or by heating. However, these methods will not only affect nonlinear frequency conversion, but also linear properties like transmittance or reflectance. A method to independently control the linear and nonlinear response of metasurfaces did not exist so far.

In the work done by a research team from the Institute of Applied Physics and the Institute of Solid State Physics at Friedrich Schiller University Jena, Germany. Researchers harvest this effect and modify second-harmonic generation while keeping the linear properties of metasurfaces constant. They realize metasurfaces from lithium niobate with periodically inverted nonlinearity. This inversion creates a diffraction grating affecting only the second harmonic. The relevant research results were published in Photonics Research, Volume 11, No. 2, 2023 (Anna Fedotova, Mohammadreza Younesi, Maximilian Weissflog, Dennis Arslan, Thomas Pertsch, Isabelle Staude, Frank Setzpfandt. Spatially engineered nonlinearity in resonant metasurfaces[J]. Photonics Research, 2023, 11(2): 252).

Researchers explore metasurfaces from lithium niobate, a dielectric widely used in integrated optics and photonics. Besides having many other advantageous properties, lithium niobate is ferroelectric: in its crystal structure, negative and positive charges are separated creating a spontaneous polarization. When applying a strong electric field, the ion positions in the crystal lattice can be switched. This correspondingly changes the sign of the nonlinearity, e.g. the second-order nonlinear susceptibility χ⁽²⁾ of the material as schematically shown by the blue and red columns in Fig. 1a. This switching process is called electric-field poling. Interestingly, linear properties of a poled metasurface such as transmittance or reflectance remain unchanged, as shown in Fig. 1b, while the second-harmonic response based on the second-order nonlinear susceptibility is altered.

When exciting these metasurfaces with a pulsed femtosecond laser, second harmonic generated in them is diffracted by two diffraction gratings: one formed by the metasurface periodic geometry itself and one in the nonlinearity induced by poling.

By varying the size of domains where the nonlinearity is inverted from 0.5 µm to 2 µm (poling period from 1 µm to 4 µm) but keeping the other geometry parameters of the metasurface the same, researchers show how the diffraction pattern changes. An example for this is depicted in Figs. 1c and d. The poled metasurface in Fig. 1c has six additional diffraction orders compared to a non-poled one.

In this work, researchers demonstrated that electric-field poling adds another degree of freedom for designing nonlinear metasurfaces and enhances their capabilities. The next step in this journey can be poling metasurfaces aperiodically and creating patterns to shape the second-harmonic emission, which opens up another route to manipulate its directionality and can be used for nonlinear holograms.

非线性超构表面的探索：用铌酸锂实现非线性独立控制

微纳光学是当前光学学科发展最活跃的研究之一，而纳米谐振器结构阵列——超构表面，是微纳光学中具有前瞻话题性的研究方向，旨在实现亚波长尺度下对电磁波超越衍射极限的操纵。超构表面在人们的日常生活中变得越来越重要，有望颠覆智能手机摄像头产业，并且赋予激光雷达、3D传感器、AR/VR等设备极具想象力的未来。

超构表面最有趣的应用之一是非线性频率转换，如二次谐波生成：入射光的两个光子倍频（波长减半）转换为单个光子。超构表面可以在极薄的厚度内实现对非线性频率转换过程的增强和控制，其主要取决于两个因素：纳米谐振器的几何结构（纳米谐振器的形状和排列）以及材料。在制造成型后，超构表面的性能仍然可以通过多种方式进行调整，比如添加液晶、施加电压或加热等。然而，这些方法不仅会影响非线性频率转换，而且还会影响线性特性，比如透射率或反射率。目前尚无能够分别独立控制超构表面的线性和非线性响应的方法。

为解决上述问题，德国耶拿大学应用物理和固体物理研究所Frank Setzpfandt团队基于铌酸锂材料开展了超构表面设计的探索。研究人员设计了具有周期性反转非线性的铌酸锂超构表面，这种反转可以形成只影响二次谐波的衍射光栅，从而在保持超构表面线性特性不变的同时实现对二次谐波的生成的调控。相关研究成果发表于Photonics Research 2023年第2期（Anna Fedotova, Mohammadreza Younesi, Maximilian Weissflog, Dennis Arslan, Thomas Pertsch, Isabelle Staude, Frank Setzpfandt. Spatially engineered nonlinearity in resonant metasurfaces[J]. Photonics Research, 2023, 11(2): 252）。

铌酸锂是一种被广泛应用于集成光学和光子学的电介质材料，因其电光效应而闻名。能够制备纳米尺度铌酸锂微纳结构，并实现对光行为的操纵，是实现高密度集成光电器件的关键所在。此外，铌酸锂还是一种铁电晶体：其正负离子不重合而产生的自发极化方向可被外加电场改变。因而对其施加强电场时，离子在晶格中的位置可以切换，进而导致相关非线性系数符号的改变。

如图1(a)所示，蓝色和红色列表示材料被电场极化的正和负二阶非线性极化率。有趣的是极化超构表面的线性性质(如透射率或反射率)保持不变，而基于二阶非线性极化率的二次谐波响应发生了变化，如图1(b)所示。当用飞秒脉冲激光激励该超构表面时，生成的二次谐波被两个光栅衍射：一个由超构表面几何结构本身形成，另一个由极化引起的非线性区域形成。

研究人员将非线性转换域的大小由0.5 μm改变为2 μm（极化周期从1 μm改变为4 μm），同时保持超构表面的其他几何参数不变，其二次谐波衍射图展示了衍射模式的变化。如图1(c)和(d)所示，前者的极性超构表面与后者的非极性超构表面相比，二次谐波衍射图具有6个附加的衍射级。

Frank Setzpfandt博士表示：“这项研究表明电场极化为设计非线性超构表面增加了自由度。下一步研究可能是对超构表面进行非周期性的极化，调控二次谐波发射，并可应用于非线性全息领域。总之，作为三维超构材料的衍生物，具有亚波长厚度的人工超构表面结构能够在紧凑的平台上灵活操纵光与物质的相互作用，有利于多功能、超紧凑光子器件的研发，对于微纳光子学和集成光子学具有重要意义。”