Abstract: The LiYF₄ single crystals singly doped Ho³⁺ and co-doped Ho³⁺, Pr³⁺ ions were grown by a modified Bridgman method. The Judd-Ofelt strength parameters (Ω₂, Ω₄, Ω₆) of Ho³⁺ were calculated according to the absorption spectra and the Judd-Ofelt theory, by which the radiative transition probabilities (A), fluorescence branching ratios (β) and radiative lifetime (τ_rad) were obtained. The radiative lifetimes of ⁵I₆ and ⁵I₇ levels in Ho³⁺ (1 mol%):LiYF₄ are 10.89 and 20.19 ms, respectively, while 9.77 and 18.50 ms in Ho³⁺/Pr³⁺ doped crystals. Hence, the τ_rad of ⁵I₇ level decreases significantly by introduction of Pr³⁺ into Ho³⁺:LiYF₄ crystal which is beneficial to the emission of 2.9 μm. The maximum emission cross section of Ho³⁺:LiYF₄ crystal located at 2.05 μm calculated by McCumber theory is 0.51 × 10^-20 cm² which is compared with other crystals. The maximum emission cross section at 2948 nm in Ho³⁺/Pr³⁺ co-doped LiYF₄ crystal obtained by Fuchtbauer-Ladenburg theory is 0.68 × 10^-20 cm², and is larger than the value of 0.53 × 10^-20 cm² in Ho³⁺ singly doped LiYF₄ crystal. Based on the absorption and emission cross section spectra, the gain cross section spectra were calculated. In the Ho³⁺ ions singly doped LiYF₄ crystal, the gain cross sections for 2.05 μm infrared emission becomes positive once the population inversion level reaches 30%. It means that the pump threshold for obtaining 2.05 μm laser is probably lower which is an advantage for Ho³⁺-doped LiYF₄ 2.05 μm infrared lasers. The calculated gain cross section for 2.9 μm mid-infrared emission does not become positive until the population inversion level reaches 40% in Ho³⁺/Pr³⁺:LiYF₄ crystal, but 50% in Ho³⁺ singly doped LiYF₄ crystal, indicating that a low pumping threshold is achieved for the Ho³⁺:⁵I₆ → ⁵I₇ laser operation with the introduction of Pr³⁺ ions. It was also demonstrated that Pr³⁺ ion can deplete rapidly the lower laser Ho³⁺:⁵I₇ level and has influence on the Ho³⁺:⁵I₆ level. The Ho³⁺/Pr³⁺:LiYF₄ crystal may be a potential media for 2.9 μm mid-infrared laser.

Key words: LiYF crystal, 2.9 #x003bcm, Ho/Pr, Optical spectra, Gain cross section