Aim at High-Power ∼3.9 μm Lasing: Design of a Lightly-Ho3+-Doped InF$_{\text{3}}$ Fiber Laser via Cascaded Pumping and Transitions

Rare-earth-doped fluoride fiber provides a compact and robust platform for getting mid-infrared laser at 3∼5 μm that can find direct applications in the fields of spectroscopy, polymer processing, and infrared countermeasures. Based on this strategy, the longest wavelength has been experimentally pushed to ∼3.9 μm, from an 888 nm pumped 10 mol.% heavily-Ho ³⁺ -doped InF ₃ fiber laser [Optica, vol. 5, no. 7, pp. 761--764, 2018]. Its great heat load however, limits the output to ∼200 mW. To solve this problem, we theoretically propose a novel scheme, enabling high-power output with significantly reduced heat load, in which both the concepts of cascaded pumping and transitions have been simultaneously used. Specifically, the dual-wavelength pumping at 1950 nm and 1650 nm (i.e., ⁵ I ₈ → ⁵ I ₇ → ⁵ I ₅ ) is exploited to excite a 1 mol.% lightly-Ho ³⁺ - doped InF ₃ fiber, and the cascaded transitions at ∼3.9 μm and ∼2.9 μm (i.e., ⁵ I ₅ → ⁵ I ₆ → ⁵ I ₇ ) are activated. Consequently, >10 W ∼3.9 μm and >12 W ∼2.9 μm laser outputs have been predicted with the optical-to-optical efficiencies of 31.69% and 40.13%, respectively, indicating at least 50 times power enhancement at ∼3.9 μm. More importantly, the heat load of the pumped fiber end, which is most easily damaged, is only 12.6% of the aforementioned heavily-Ho ³⁺ -doped system. Further power scaling is mainly hampered by the potential optical damage of InF ₃ glass material. On the whole, our work has offered a promising scheme for significantly improving the performance of Ho ³⁺ -doped InF ₃ fiber laser at ∼3.9 μm, hence paving the way for developing high-power fiber laser technique in this band.