All-solid-state lasers exhibit excellent laser beam quality, stable output wavelength, broad spectral range, and high-power narrow-pulse output characteristics, making them suitable for military, medical, surveying and mapping, communications and other fields. The gain medium serves as the core component of a solid-state laser. A laser gain medium with a wide gain bandwidth is essential for achieving narrow pulse widths in mode-locked pulsed lasers. In recent years, significant research has focused on Yb³⁺-doped disordered laser crystals for fs-level ultrashort pulse generation. Rare-earth ion-doped disordered mixed crystals are widely employed in ultrafast lasers due to their broad emission bandwidths. However, the relationship between fluorescence bandwidth and the structural disorder surrounding the luminescent ions has not been systematically investigated or verified. Therefore, addressing the application requirements for near-infrared ultrashort pulse lasers, this study investigates the local structural distortions around luminescent ions in mixed crystals with different crystal structures. It further correlates these structural characteristics with the luminescent properties of the crystals to analyze the relationship between local structure and the bandwidth of near-infrared fluorescence spectra. The ultimate goal is to broaden the emission spectrum through structural engineering modulation, thereby developing novel gain medium materials promising for ultrashort pulse lasers.

First-principles calculations were performed using the CASTEP code implementing the plane wave potential method based on density functional theory. The Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) was used to describe the exchange correlation potential between electrons. Based on convergence test, the 550 eV cut-off energy for all self-consistent field relaxation, and a k-grid with separation of 0.06/? was used in the first Brillouin zone integration to ensure the relaxation accuracy of 10^-5 eV and 0.01 eV/?. To account for quantum effects arising from strong electron correlation effects in the d- and f-electron systems of Yb³⁺ ions with the electronic structure of [Xe]4f¹³, the Hubbard (U) values of the non-full shell f orbitals is set to 1.0 eV for correction.

Yb³⁺-doped Y₂(Ca,Mg)₃(SiO₄)₃ (YCMS), Ca(Y,Gd)A1O₄ (CYGA), and (Gd,Y)AlO₃ (GYAP) crystals were grown using laser-heated pedestal growth (LHPG) method. The growth was conducted at a power of 39?43 W with a pull-rate ratio of 2.5?3. At the end of growth, the temperature was reduced to room temperature at a rate of 0.006?0.010 ℃/h to protect the crystals from large temperature variations. Single crystal X-ray diffraction and Raman spectra, fluorescence emission spectra were tested based on the optical polished samples. The spectroscopic properties (luminescent spectra of 950?1200 nm and fluorescence decays) were measured by the Edinburgh Instruments FLS920 and FSP920 spectrophotometers, under excitation of 922 nm. All measurements were performed at room temperature and other conditions were kept almost identical. The relationship between structural distortion and spectrum bandwidth broadening was analyzed based on structural changes such as cell parameters, cell volume, and distortion index.

Thermodynamically stable configurations derived from first-principles calculations are used to comprehensively characterize the local structure disorder around luminescent ions in mixed crystal systems. This characterization employed quantitative parameters including the structural distortion index, polyhedral volume difference, unit-cell parameters, and unit-cell volume. Focusing on the cubic garnet-structured Yb∶YCMS, the relationship between the degree of polyhedral distortion of Yb³⁺ and the full width at half maximum (FWHM) of the emission spectra (Fig. 4) was analyzed. The increase in both the distortion index of the [YbO₆]^9- polyhedron and the unit-cell volume enhances lattice disorder surrounding Yb³⁺. This heightened disorder strengthens crystal field splitting, ultimately leading to broadening of the emission spectra. As evidenced in Table 1, the emission spectral FWHM of Yb∶YCMS crystals (89.85?103.10 nm), incorporating the matrix-regulating ion Ca²⁺, exceeds that of Yb∶YMS (87.26 nm).This comparison confirms the efficacy of matrix regulation for spectral broadening and suggests a positive correlation between fluorescence spectral bandwidth and structural modifications. Further structural analysis was conducted on Yb∶CYGA and Yb∶GYAP crystals belonging to different crystal systems. These analyses also indicated that varying ion ratios within the host lattice induce not only changes in the local Yb³⁺ coordination environment but also a degree of distortion within the entire unit cell. The luminescent ions in locally symmetric environments exhibit relatively long decay time, as shown in Tables 1-3. This study provides a comprehensive explanation for the relationship between structural distortion (both local and global) and key optical properties: spectral FWHM (positively correlated) and lifetime (negatively correlated), providing valuable guidance for the future design of optically tunable laser gain media.

Based on the first-grown Yb∶YCMS, Yb∶CYGA and Yb∶GYAP mixed crystals with distinct crystal structures, the local geometric distortion around the luminescent ions was calculated using first-principles calculations. The structural distortion index and polyhedral volume difference are introduced as quantitative characterization parameters to describe the local structural disorder of the luminescent centers within these mixed crystal systems. It was found that as structural distortion increases, characterized by metrics such as the distortion index, ligand volume and unit cell parameters, the emission bandwidth undergoes inhomogeneous broadening. This finding verifies the effective broadening achieved through structural engineering in mixed crystal systems and provides valuable guidance for exploring novel gain materials for ultrashort pulse laser crystals.