作为实现全固态激光器频率转换功能的关键材料, 紫外非线性光学晶体发挥着不可替代的作用。设计兼具大的非线性光学系数、合适的双折射和宽带隙的紫外非线性光学晶体仍然是该领域亟待攻克的一个难题。由于具有宽的带隙, 硫酸盐已成为紫外非线性光学晶体领域的一个重要研究方向。SO₄四面体基团具有接近非极性的Td对称性, 使其极化率各向异性和二阶极化率较小, 因而对晶体的非线性系数和双折射贡献很小。通常引入畸变程度高的阳离子多面体可以增加晶体的非线性效应和双折射。本工作将易于形成畸变多面体的Hg²⁺离子引入到硫酸盐体系中, 采用高温熔体法合成出新型非线性光学晶体材料Rb₃Hg₂(SO₄)₃Cl。该晶体属于单斜晶系, 空间群为P2₁, 晶胞参数为a=0.78653(2) nm, b=0.97901(2) nm, c=1.00104(3) nm, β=110.95(3), Z=2。其晶体结构由[SO₄]四面体、[HgO₅]和[HgO₄Cl]多面体以角共享的方式连接形成空间网状结构, 而Rb⁺填充在孔洞中。Rb₃Hg₂(SO₄)₃Cl晶体的粉末倍频效应为1.5倍KDP, 且能够在可见光区实现相位匹配。紫外漫反射光谱测试表明, 紫外截止边为251 nm, 对应光学带隙为4.94 eV。利用偏光显微镜确定该晶体在546.1 nm处的双折射为0.04。此外, 第一性原理计算表明, 晶体的非线性系数主要来源于扭曲的[HgO₅]、[HgO₄Cl]和[SO₄]多面体。上述结果表明, Rb₃Hg₂(SO₄)₃Cl是具有潜在应用前景的紫外非线性光学晶体材料。

Training an artificial neural network with backpropagation algorithms to perform advanced machine learning tasks requires an extensive computational process. This paper proposes to implement the backpropagation algorithm optically for in situ training of both linear and nonlinear diffractive optical neural networks, which enables the acceleration of training speed and improvement in energy efficiency on core computing modules. We demonstrate that the gradient of a loss function with respect to the weights of diffractive layers can be accurately calculated by measuring the forward and backward propagated optical fields based on light reciprocity and phase conjunction principles. The diffractive modulation weights are updated by programming a high-speed spatial light modulator to minimize the error between prediction and target output and perform inference tasks at the speed of light. We numerically validate the effectiveness of our approach on simulated networks for various applications. The proposed in situ optical learning architecture achieves accuracy comparable to in silico training with an electronic computer on the tasks of object classification and matrix-vector multiplication, which further allows the diffractive optical neural network to adapt to system imperfections. Also, the self-adaptive property of our approach facilitates the novel application of the network for all-optical imaging through scattering media. The proposed approach paves the way for robust implementation of large-scale diffractive neural networks to perform distinctive tasks all-optically.