Coherent phonon excitation in multiphonon-coupled lasing beyond the fluorescence spectrum

Electronic transitions in crystalline solids are typically accompanied by the generation or annihilation of phonons, the quantized modes of lattice vibrations. As the number of involved phonons increases, multiphonon-assisted photoluminescence diminishes and eventually becomes undetectable in the fluorescence spectrum, making it unsuitable for conventional lasing prediction based on fluorescence analysis. This study introduces a theoretical model for a multiphonon-coupled (MPC) laser that operates beyond the fluorescence spectral range by incorporating coherent phonon excitations. By considering the spectral overlap between the lasing transition and phonon modes, a quantitative expression for the stimulated emission cross-section is derived, demonstrating an enhancement of up to ten orders of magnitude compared to cases without coherent phonon involvement. The proposed framework enables significant wavelength extension, with tunable emission around 1100 nm and a maximum emission wavelength of 1311 nm observed in three Yb³⁺-doped crystals. This approach offers a robust theoretical basis for describing and realizing MPC laser action in conventional crystalline materials beyond their intrinsic fluorescence limits.