## 2 Experiments Details
### Characterization of NaYF\({}_{4}\)/NaLuF\({}_{4}\): Yb, Er NPs-PMMA  
A spot of the nanoparticles powder was dissolved in cyclohexane to form a transparent solution and dropped onto a carbon film copper mesh. The morphology and size of the nanoparticles were observed with Hitachi H-600 transmission electron microscopy. The TEM images of the nuclear \(\alpha\)-NaYF\({}_{4}\) material are presented in Figure 2a. The nanoparticles with a regular square shape were dispersed uniformly. The particle size we measured was within the range of 10-15 nm, as shown in Figure 2c. The average particle size of nuclear NaYF\({}_{4}\) nanoparticles was around 13 nm, according to [PERSON]'s formula. TEM images of the nanoparticles coated shell are shown in Figure 2b. The morphology of the nanoparticles appeared spherical, which was because the size of the hexagon tended to be spherical when it was small. They were dispersed uniformly without agglomeration. Compared with  
Figure 1: Schematic image of the heterogeneous induction procedure. (**a**) synthesis of cubic core; (**b**) Cation exchange; (**c**) Hexogonal shell coating. uncoated particles, the size of the particle was increased; as shown in Figure 2d, the size of the nanoparticles after shell coating was approximately 21 nm. The nanoparticles we synthesized were coated with oleic acid. The C=C, C=O double bonds from oleic acid ligands were protected well using the solvothermal method. Nanoparticles were chemically bonded to the polymer monomer using unsaturated ligand double bonds, and a schematic image of the covalent linking nanocomposites is shown in Figure 3. We dissolved 0.1 mmol nanoparticles in 4 mL butyl acetate. A total of 10 g methyl methacrylate (MMA) was weighed and dissolved in 2 mL butyl acetate. Then, polymerization initiator azobisisobutyronitrile (ABIN) was added together in a single-port flask. We put the flask in an oil bath followed by heating (65 \({}^{\circ}\)C) and stirring for 60 min to complete the prepolymerization reaction. The solution containing nanoparticles was added dropwise into the flask. We increased the temperature of the oil bath (80 \({}^{\circ}\)C) and continuously stirred it to achieve the copolymerization reaction. The NPs-PMMA covalent linking nanocomposites were obtained by free-radical polymerization, ionic polymerization, and the polymerization of nanoparticles with organic polymer monomers under the catalyzation of free-radical initiators and ionic-type initiators. The doped Er\({}^{3+}\) concentration was enhanced to 2.8 \(\times\) 10\({}^{26}\) m\({}^{-3}\), which was increased compared to traditional physical doping. The critical properties of film forming, emission spectra, and absorption spectra of the gain medium were characterized and were found to impact the gain performances of EDWA. The NPs-PMMA was spin-coated on Si and heated by 120 \({}^{\circ}\)C for 2 h in the oven to form a 7 \(\upmu\)m-thick film. Atomic force microscopy (AFM) was used to characterize the film-forming properties of the material shown in Figure 4a,b. As shown, the film surface was flat and smooth without nanoparticle precipitation. The surface roughness of the film was measured to be only 0.349 nm (scan area 20 \(\upmu\)m \(\times\) 20 \(\upmu\)m), which was an order of magnitude lower than traditional physical doping. This suggests that it is an ideal material for preparing waveguide devices. The infrared emission spectrums pumped by 980 nm of the \(\alpha\)-Na\(\mathrm{Y}\)F\({}_{4}\)/\(\beta\)-Na\(\mathrm{Lu}\)F\({}_{4}\): Er\({}^{3+}\), Yb\({}^{3+}\) NPs, and \(\alpha\)-Na\(\mathrm{Lu}\)F\({}_{4}\) NPs with the same doping concentration were measured. As illustrated in Figure 4c, the main emission peak of both  
Figure 2: (**a**) TEM images of NaYF\({}_{4}\) core; (**b**) TEM images of core-shell NaYF\({}_{4}\)/NaLuF\({}_{4}\): Yb\({}^{3+}\), Er\({}^{3+}\); (**c**) Size distribution of NaYF\({}_{4}\) core; (**d**) Size distribution of core-shell NaYF\({}_{4}\)/NaLuF\({}_{4}\): Yb\({}^{3+}\), Er\({}^{3+}\).