Nd∶phosphate laser glass has been studied as a gain medium in high-power laser systems at the National Ignition Facility (USA), Laser Mégajoule (France), and SG-Ⅱ and SG-Ⅲ facilities (China). To meet the growing demand for higher gain in high-power laser systems, the performance of Nd∶glass must be improved to a new level (spectroscopic, thermal, chemical, and mechanical properties). The responses of many properties, as well as the network structure, to changes in glass composition are often highly nonlinear. Traditional empirical design methods can no longer satisfy the requirements of new developments in a timely manner. The objective of this study is to establish an accurate glass modeling system that can be used as a platform for the designs and property predictions of Nd∶phosphate laser glass; the modeling system is called glass structure gene modeling (GSgM) or statistical composition-structure-property (C-S-P) modeling.

Using information of the glass network structure as a “bridge”, C-S-P methodology transforms the need of solving a complex or unknown nonlinear relationship of C-P to solving two linear relationships of C-S and S-P, and the structure component (S) bridges the two linear parts into one. Separate linear C-S and S-P models were established using the Cornell first-order linear mixture formula. In this study, the glass design was based on 60P₂O₅-24K₂O-9MgO-5Al₂O₃-2R₂O₃ (R=Y, La, and Sb) with 1% (mole fraction) Nd₂O₃ by introducing extra Li₂O or Na₂O, targeting the glass property responses to Li₂O and Na₂O, covering mole fraction of 2%, 4%, 6%, and 8%. The series of Li₂O and Na₂O samples were called as PL1?4 and PN1?4, respectively (Table 1). This study focused on the effects of Li₂O and Na₂O on glass spectroscopic properties (Table 2), including emission cross section (σ_emi), effective linewidth (Δλ_eff), fluorescence lifetime (τ_f), and Judd-Ofelt parameters (Ω₂, Ω₄, and Ω₆). Structural information of the glass network was derived from Fourier transform infrared (FTIR) spectroscopic analysis (Fig.2). Each FTIR spectrum was decomposed into 15 Gaussian bands according to the IR network structural units of the phosphate glass using commercial software from Thermo Scientific (GRAMS Suite) (Table 3). The structural information of the glass, represented by the IR band areas (A_i), composition, and properties, was used to build the S-P and C-S models. Using the commercial software JMP, the glass structural units that significantly affected a given glass property were selected using a stepwise statistical screening method. The S-P model was used independently to simulate glass properties, whereas the C-S model was used to predict the structural responses of the glass network to compositional changes. With the establishment of the modeling database, the glass properties were estimated through the C→S→P route and the design glass composition through the P→S→C route. Model validation was also conducted by comparing the model-predicted properties with the measured properties.

Figure 4 shows the original S-P modeling results for the glass spectroscopic properties. Compared with the S-P(Δλ_eff) model with R²=0.98 and Radj2=0.97, the models for σ_emi, τ_f, Ω₂, Ω₄, and Ω₆ exhibit relatively lower accuracies (i.e., higher P-values). It implies that, except for Δλ_eff, which is derived directly from the fluorescence spectra, Ω₂, Ω₄, Ω₆, and σ_emi have relatively larger errors from computations. τ_f also exhibits larger measurement error. One data point of each property apparently deviates from the “95% confidence zone” of each corresponding model, and is subsequently excluded from the model (Fig. 5). Consequently, remarkable improvement is achieved by S-P models for Ω₂, Ω₄, Ω₆, and σ_emi. Using the modeling parameters listed in Table 5, a structural prediction formula for each property is obtained. It is worth noting that, similar to C-P models, the S-P models can also be used directly for property simulation using glass structural information (such as the FTIR integrated area A_i in this study). The C-S models for Li₂O and Na₂O are built in the same manner (Fig. 6). The combined model of S-P and C-S models completes the C-S-P platform. By reversing the C→S→P direction, that is, P→S→C, a new glass can be designed. The final C-S-P platform is constructed as shown in Fig.7. A mixed-alkali glass PLN (mole fraction of Li₂O is 2.1% and mole fraction of Na₂O is 3.2%) is used to validate the C-S-P model. Results show that the measured values (numerators) are in good agreement with the predicted values (denominators) for all the properties: σ_emi=4.13/4.14 pm², τ_f=331/333 μs, Δλ_eff=24.49/24.5 nm, Ω₂=4.62/4.62 pm², Ω₄=4.84/4.83 pm², and Ω₆=5.73/5.72 pm²; the relative errors are within 0.6% (Table 6).

The development of the GSgM platform (C-S-P) enables accurate prediction of a combined property set for the first time, which is often difficult to achieve using the conventional approach, C-P. The spectroscopic properties (Δλ_eff, σ_emi, τ_f, Ω₂, Ω₄, and Ω₆) of an Nd∶phosphate glass series are simulated with satisfactory accuracies. GSgM offers a new dimension in designing the performance of glass through the manipulation of genes of the glass network and simultaneously avoids solving unknown nonlinear responses of the glass properties to composition changes. Finally, the model validation process is successfully demonstrated by C→S→P modeling. Therefore, GSgM is a powerful tool for glass design that moves away from the conventional C-P approach to offer insight into how the glass network structure or structural units (genes) are critical for tailoring the required glass performance.