1：Experimental Design and Method Selection:

The study used a quantum cutting model with rate equations to predict and analyze the energy transfer process. Samples were synthesized via a high-temperature solid-state method and characterized using fluorescence spectroscopy and laser excitation.

2：Sample Selection and Data Sources:

b-NaGd1-xF4:x%Yb3+ samples with x = 0, 0.2, 0.5, 3, 5, 7 were prepared. Data were collected from emission spectra, excitation spectra, and lifetime measurements at room temperature.

3：2, 5, 3, 5, 7 were prepared. Data were collected from emission spectra, excitation spectra, and lifetime measurements at room temperature. List of Experimental Equipment and Materials:

3. List of Experimental Equipment and Materials: Equipment includes a Q-Series laser system (266 nm excitation), silicon detector (200-700 nm), InGaAs detector (900-1600 nm), fluorescence spectrometer (FLS920, Edinburgh Instruments), Hamamatsu R928 photomultiplier tube, and a standard mercury lamp for calibration. Materials include NaF (98%), GdF3 (99.5%), and YbF3 (99.999%).

4：5%), and YbF3 (999%). Experimental Procedures and Operational Workflow:

4. Experimental Procedures and Operational Workflow: Samples were synthesized by grinding and heating mixtures at 680°C for 6 hours. Emission spectra were measured under 266 nm laser excitation. Fluorescence lifetime and excitation spectra were recorded using the FLS920 spectrometer. Data analysis involved fitting decay curves and calculating efficiencies.

5：Data Analysis Methods:

Data were analyzed using rate equations for quantum cutting, single exponential fitting for lifetimes, and calculations of energy transfer efficiency and quantum efficiency based on fluorescence intensities and lifetimes.