## 2 Experiments Details  
### Preparation of NaYF\({}_{4}\)/NaLuF\({}_{4}\): Yb, Er NPs-PMMA  
The performance of medium gain material is an important factor affecting EDWA gain, particularly the Yb-Er ion doping concentration and the luminescence intensity. However, these two factors are often incompatible. On the one hand, small-sized nanoparticles tend to disperse easily in polymer matrix materials, but they have a large specific surface area and a significant surface luminescence quenching phenomenon, which in turn affects the luminescence intensity of nanoparticles. Larger-sized nanoparticles cause light scattering in the device, which leads to additional losses. On the other hand, nanoparticles are usually incorporated into polymer materials in a physically doped manner. Er\({}^{3+}\) exists as inorganic salts and is poorly compatible with organic polymers, resulting in a low concentration of Er\({}^{3+}\) optical activity in polymer matrix materials, in addition, the stability of the material also needs to be improved. Therefore, we carried out shell coating on the surface of rare-earth doped nanoparticles to improve the luminescence intensity of the nanoparticles and used the modification of unsaturated groups on the surface of nanoparticles to bond nanoparticles to polymer monomers through chemical bonds, which can greatly improve the incorporation of nanoparticles into polymers while solving the problems of easy agglomeration, low solubility, and poor stability of nanoparticles in polymers. The core-shell nanoparticles were synthesized using a mild hydrothermal method. In this condition, the unsaturated perssad on the surface of nanoparticles was protectedby reacting at a relatively low temperature. The heterogeneous induction procedure was explored, as shown in Figure 1. The process is mainly divided into two major steps: first, was the preparation of the pure cubic phase of nuclear nanomaterial \(\alpha\)-NaYF\({}_{4}\). A total of 0.6 g of NaOH powder was dissolved in a solution of 20 mL oleic acid, 10 mL ethanol, and 10 mL deionized water and mixed by stirring to dissolve fully as a clear solution. A total of 0.5 mmol of YCl\({}_{3}\)-6H\({}_{2}\)O powder was weighed and dissolved in 4 mL of deionized water and stirred thoroughly to form a solution, and this solution was added dropwise to the above solution and stirred continuously until it was a homogeneous dissolution. A total of 2 mmol of KF-2H\({}_{2}\)O solid was dissolved in 4 mL of deionized water. It was stirred continuously until the solution was slowly dripped into the above-mixed solution and then stirred well to obtain a semi-white solution. This well-mixed solution was divided equally into two polytetrafluoroethylene-lined high-pressure reactors, heated at 160 \({}^{\circ}\)C for 240 min, and cooled to room temperature to obtain a mixed solution containing \(\alpha\)-NaYF4 nanoparticles. Then, the shell growth link was performed. A total of 0.3 g NaOH powder was weighed and dissolved in 10 mL oleic acid, 5 mL ethanol, and 1 mL deionized water to prepare a solution. A 20 mL solution containing \(\alpha\)-NaYF\({}_{4}\) nuclear nanoparticles was mixed with the above solution and stirred. A total of 0.195 mmol of LuCl\({}_{3}\)\(\cdot\)6H\({}_{2}\)O powder, 0.05 mmol of YbCl\({}_{3}\)-6H\({}_{2}\)O powder, and 0.005 mmol of ErCl\({}_{3}\)\(\cdot\)6H\({}_{2}\)O solid were weighted and dissolved in 2 mL of deionized water. A mixture of nuclear nanoparticles was slowly dropped and stirred continuously to form a homogeneous solution. A total of 2 mmol of KF-2H\({}_{2}\)O was dissolved in 2 mL of deionized water and stirred vigorously and continuously to obtain the mixture. Then it was dispensed into two polytetrafluoroethylene-lined high-pressure reactors and heated at 160 \({}^{\circ}\)C for 480 min for the second-step crystal-growth process, during which cation exchange occurred between the newly added Lu\({}^{3+}\) and Y\({}^{3+}\). A NaY\({}_{\chi}\)Lu(\({}_{1-3}\))F\({}_{4}\) heterointerface was formed on the nuclear surface.