Prospects of low-phonon energy Ho:MF₂ (M = Ca, Sr, Ba) crystals for 2-3 µm lasers

We report on a comparative spectroscopic study of Ho³⁺-doped fluorite-type crystals MF₂ (where M stands for Ca, Sr, and Ba), regarding their applications in lasers emitting at 2 to 3 µm. The transition intensities of Ho³⁺ ions are determined within a modified Judd-Ofelt analysis accounting for configuration interaction. The stimulated-emission cross-sections for the ⁵I₇ → ⁵I₈ (at 2.1 µm) and ⁵I₆ → ⁵I₇ (at 2.9 µm) are determined and compared with the reference Ho:LiYF₄ crystal. Effects related to electron-phonon interaction are studied: i) the multiphonon sidebands responsible for long-wave emission far beyond 2 µm are observed; ii) the rates of multiphonon non-radiative relaxation from the ⁵I₅, ⁵I₆ and ⁵I₇ Ho³⁺ manifolds are computed and linked to the phonon spectra of MF₂ crystals, and iii) the parameters of phonon-assisted energy-transfer upconversion from the ⁵I₇ level are quantified using the Burshtein model. Owing to their low phonon energy behavior and inhomogeneously broadened spectral bands, Ho:MF₂ crystals are promising for broadly tunable and mode-locked lasers.