Npj Comput. Mater.: 光学二次谐波系的测量和分析：SHAARP.ml更简单

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来自美国宾夕法尼亚州立大学材料科学与工程系的Venkatraman Gopalan教授和陈龙庆教授领导的团队提出了一个全面综合的光学二次谐波理论框架和一个开源软件包♯SHAARP.ml，用于模拟任意单界面（与♯SHAARP.si相同(npj Comput Mater 8, 246 (2022).)）和复杂异质结构中的二次谐波响应。♯SHAARP.ml旨在为仿真和实验表征提供数值计算和半解析解，从而实现对复杂材料系统的快速、精确、灵活的非线性光学响应分析以满足用户不同的需求。

该研究团队所开发的♯SHAARP.ml软件具有如下特点：

（1）能够模拟具有均匀光学性质的任意层数的多层结构；

（2）允许模拟具有任意对称性 (从各向同性到三斜晶系)与取向的晶体，并且每层可以具有不同的吸收、双折射和色散；

（3）提供反射和透射解以满足试验设计需求；

（4）可以控制入射光的入射角和任意偏振状态（包括线偏振、圆偏振和椭圆偏振）；

（5）明确考虑线性和非线性波的多次反射所引入的干涉；

（6）提供用户友好的图形界面便于建模、计算与数据后处理。

该团队进一步使用两种主流实验方法验证和测试了模型的准确性，即Maker条纹（图2a）和二次谐波偏振测量（图2b，c），并研究了包括α-SiO₂单晶、α-SiO₂及金镀层、LiNbO₃和KTP单晶、ZnO//Pt//Al₂O₃薄膜，LiNbO₃和α-SiO₂双层，以及扭角双层MoS₂在内的七种非线性光学体系。♯SHAARP.ml在提取拟合计算二次谐波系数、数值计算预测各向异性SHG响应和Maker条纹图案、处理吸收、干涉和多次反射方面具有极高的准确性和灵活性。图3展示了♯SHAARP.ml软件的图形用户界面，为用户提供多样化的、需求导向的光学二次谐波分析（左侧和右侧分别对应参数区和结果区）。该研究为非线性光学材料的研究提供了更具普适性的模型、更完整而准确的分析框架、以及按照不同建模假设需求的解决方案，所开发的易于上手的开源软件可以助力不同背景科研人员对非线性光学材料进行分析与模拟。

所开发的♯SHAARP.ml开源软件源代码可以到以下链接下载：https://github.com/bzw133/SHAARP.ml

♯SHAARP.si开源软件源代码：

https://github.com/Rui-Zu/SHAARP

（原文链接：https://www.nature.com/articles/s41524-024-01229-2）

图1 光学二次谐波产生的基本原理示意图

图2 利用♯SHAARP.ml软件建模结合三种实验方法测量SHG系数

图3 ♯SHAARP.ml软件的图形用户界面

Optical second harmonic generation in anisotropic multilayers with complete multireflection of linear and nonlinear waves using ♯SHAARP.ml package 

Rui Zua, Bo Wanga, Jingyang He, Lincoln Weber, Akash Saha, Long-Qing Chen and Venkatraman Gopalan

Optical second harmonic generation (SHG) is a nonlinear optical effect widely used for nonlinear optical microscopy and laser frequency conversion. Closed-form analytical solution of the nonlinear optical responses is essential for evaluating materials whose optical properties are unknown a priori. A recent open-source code, ♯SHAARP.si, can provide such closed form solutions for crystals with arbitrary symmetries, orientations, and anisotropic properties at a single interface. However, optical components are often in the form of slabs, thin films on substrates, and multilayer heterostructures with multiple reflections of both the fundamental and up to ten different SHG waves at each interface, adding significant complexity. Many approximations have therefore been employed in the existing analytical approaches, such as slowly varying approximation, weak reflection of the nonlinear polarization, transparent medium, high crystallographic symmetry, Kleinman symmetry, easy crystal orientation along a high-symmetry direction, phase matching conditions and negligible interference among nonlinear waves, which may lead to large errors in the reported material properties. To avoid these approximations, we have developed an open-source package named Second Harmonic Analysis of Anisotropic Rotational Polarimetry in Multilayers (♯SHAARP.ml). The reliability and accuracy are established by experimentally benchmarking with both the SHG polarimetry and Maker fringes using standard and commonly used nonlinear optical materials as well as twisted 2-dimensional heterostructures.