【摘要】 掺钕碱土氟化物晶体兼具宽光谱与高热导率特性，在重复频率超快激光领域中具备重要应用价值。同时，稀土掺杂碱土氟化物晶体的微观结构丰富、光谱性能多变，是研究晶体组成、结构与光谱性能之间构效关系的理想载体。本文以Nd,R∶MF₂（R为La、Ce、Gd、Y、Lu、Sc;M为Ca、Sr）晶体为研究对象，将光谱性能参数作为输出参量，以Nd、R离子掺杂浓度及CaF₂、SrF₂等晶体组分作为输入参量，构建了前馈反向传输（BP）神经网络模型，建立了掺钕氟化物激光晶体组分与光谱性能参数的关系模型。该模型突破了传统试错研发模式的局限，实现了基于晶体组成的光谱性能参数的直接预测，可面向前沿超快激光技术发展需求，为新型激光材料的定向设计与性能优化提供可靠的方法依据与理论参考。更多还原

【Abstract】 Objective Nd-doped alkaline-earth fluoride laser crystals（Nd, R∶MF₂, M=Ca, Sr; R=La, Ce, Gd, Y, Lu, Sc） exhibit broad emission bandwidths, long fluorescence lifetimes, and high thermal conductivity, making them promising candidates for highrepetition-rate ultrafast lasers. However, the complex correlation among crystal composition, local structure, and spectroscopic properties lacks quantitative modeling, and trial-and-error methods still dominate material screening processes. This study constructs a predictive model that directly correlates crystal composition with photoluminescence parameters, thereby providing a theoretical tool for the rational design and optimization of novel Nd-doped fluoride laser materials.Methods A dataset of approximately 110 reported photoluminescence parameters, including the absorption cross section（ACS at 796 nm）, peak emission cross section(PECS for the ⁴F_3/2→ ⁴I_11/2 transition), emission bandwidth(EB for the ⁴F_3/2→ ⁴I_11/2 transition), fluorescence quantum efficiency（FQE）, fluorescence branching ratio(FBR for the ⁴F_3/2→⁴I_11/2 transition), and fluorescence lifetime(FL of the ⁴F_3/2 energy level), is compiled for Nd,R∶CaF₂ and Nd,R∶SrF₂ crystals. The input features include Nd and R ion fractions, as well as the host matrix type（CaF₂ or SrF₂）. Following statistical correlation analysis, all features are standardized and transformed whenever necessary to enhance linear learnability. A multilayer feedforward back-propagation（BP） neural network is then constructed with two hidden layers containing 64 and 32 neurons using ReLU activation; the model is trained with the Adam optimizer adopting mean squared error as the loss function, while overfitting is mitigated through cross-validation and early stopping strategies. Model performance is evaluated using the coefficient of determination（R²） and mean absolute error（MAE） between predicted and experimental values.Results and Discussions The trained model accurately reproduces the experimental parameters, achieving R² values of 0.97（PECS）, 0.83（ACS）, 0.84（FBR）, 0.86（FQE）, 0.90（EB）, and 0.84（FL）, respectively. This demonstrates that the spectroscopic performance of Nd-doped fluoride crystals can be reliably predicted using only compositional information. Feature importance contribution analysis shows that all input parameters contribute comparably to most outputs; the host matrix dominates the determination of emission bandwidth with a contribution of approximately 0.30, while the influence of Y ion fraction remains relatively low at around 0.09. The predictive capability is further validated by exploring Nd,Y∶SrF₂ compositions with the Nd ion fraction ranging from 0.05% to 1% and Y ion fraction from 0.5% to 10%. The model predicts that the peak emission cross section increases as the Nd ion fraction decreases and Y ion fraction rises, reaching a maximum of approximately 6.3×10^-20 cm² at 0.05% Nd ion fraction and 10% Y ion fraction. The fluorescence lifetime increases with decreasing Nd ion fraction up to roughly 380 μs, whereas its dependence on Y exhibits a non-monotonic trend due to the competition between local symmetry effect and concentration-induced cross relaxation. The predicted emission bandwidth exceeds 28 nm at high Nd ion fractions and low Y ion fractions, satisfying the broad bandwidth requirements for ultrafast laser operation. Experimental measurements on synthesized Nd,Y∶SrF₂ crystals（0.6%-0.8% Nd ion fraction, 1%-9% Y ion fraction） verify the predicted trends, especially the monotonic decrease in fluorescence lifetime as the Y ion fraction increases from 1% to 4%.In addition, predictions for Nd,Y∶CaF₂ and Nd,Gd∶CaF₂ crystals show similar compositional dependencies yet distinct quantitative differences. For Nd,Y∶CaF₂, the emission cross section reaches 4.6×10^-20 cm², the lifetime extends to approximately 450 μs at low Nd ion fractions, and the maximum emission bandwidth exceeds 32 nm. For Nd, Gd∶CaF₂, lifetime up to 650 μs is predicted at low Nd and high Gd ion fractions, while the emission cross section saturates at around 2.8×10^-20 cm². These systematic predictions highlight the capability of the model to reveal composition-dependent trends and identify optimal doping regimes for different spectroscopic performance targets.Conclusions A feed-forward BP neural network model is successfully established to quantitatively correlate the compositions of Nd,R∶CaF₂ and Nd,R∶SrF₂ crystals with their spectroscopic parameters. The model achieves high prediction accuracy（R²≥0.83 for all outputs） and reveals clear trends regarding how dopant ion fraction and host matrix govern absorption and emission cross sections, fluorescence lifetime, quantum efficiencies, branching ratios, and emission bandwidths. Importantly, the model is experimentally validated on Nd,Y∶SrF₂ crystals, confirming its predictive reliability. This work demonstrates for the first time that the spectroscopic performance of Nd-doped fluoride crystals can be directly predicted from compositional information without requiring explicit structural or spectroscopic input data. The proposed approach not only accelerates the screening of laser gain materials but also provides a generalizable framework for the rational design of advanced crystals intended for ultrafast laser applications.更多还原