1：Experimental Design and Method Selection:

The study employed a three-step solid-state reaction method for synthesis, combined with X-ray diffraction (XRD) Rietveld refinement for structural analysis, density functional theory (DFT) calculations for electronic structure determination, and photoluminescence spectroscopy for optical property evaluation.

2：Sample Selection and Data Sources:

Samples of un-doped and Ce3+-doped Ba3Lu2B6O15 with varying Ce3+ concentrations (x = 0 to 0.20) were prepared using raw materials BaCO3, Lu2O3, H3BO3, and CeO2. Data were sourced from experimental measurements and computational simulations.

3：20) were prepared using raw materials BaCO3, Lu2O3, H3BO3, and CeOData were sourced from experimental measurements and computational simulations. List of Experimental Equipment and Materials:

3. List of Experimental Equipment and Materials: Equipment included a Rigaku XRD SmartLab diffractometer for XRD, FLS-980 spectrometer for diffuse reflectance and transient spectra, HITACHI F7000 spectrometer for quantum efficiency, and Materials Studio package with DMol3 module for DFT calculations. Materials were high-purity chemical reagents.

4：Experimental Procedures and Operational Workflow:

Raw materials were weighed, ground, and sintered in three steps (500°C in air, 850°C in air, 910°C in H2 atmosphere) with intermediate grinding. Phase purity was checked by XRD, optical properties were measured using spectrometers, and DFT calculations were performed with specific convergence thresholds and k-point sampling.

5：Data Analysis Methods:

XRD data were analyzed using TOPAS program for Rietveld refinement. Optical data were processed using equations for band gap calculation and quantum efficiency. DFT results were analyzed for band structure and density of states. Decay curves were fitted with bi-exponential equations for lifetime analysis.