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This investigation examines in detail the rates of energy transfer relevant to the ⁵I₅ → ⁵I₆ transition (at 3930 nm) in Ho³⁺-doped InF₃ glass as a function of the Ho³+ concentration. The decay times, branching ratios and rate parameters for energy transfer were measured in this investigation for Ho³⁺ (x)-doped InF₃ glass with x = 2, 4 and 10 mol.% and they were used as the input parameters for a rate equation analysis. Excited state absorption (ESA) initiating from the lower laser level is included in the study. Numerical simulation of CW laser emission at 3.9 μm was performed using two pump wavelengths, one for upper laser level excitation (i.e., ⁵I₈ → ⁵I₅ = λP₁) and the other for lower laser level de-excitation (i.e., ⁵I₆ → ⁵S₂ = λp₂). The pump wavelength λP₂ = 962 nm was chosen based on the measurements of ESA and the application of the McCumber method. Critically, the estimated ESA cross section at λp₂ = 962 nm (σESA = 7.1 × 10⁻²¹ cm²) is approximately sixteen times larger than ground state (⁵I₈) absorption cross section (σGSA = 4.3 × 10⁻²² cm²) and ESA does not overlap with any ground state absorption process. Our calculations suggest that even for high Ho³⁺ concentration in which cross relaxation has been shown in a previous study to quench the ⁵I₅ level, ESA is nevertheless strong enough to allow a sufficient population inversion required for practical CW emission.
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