A 3-D thermal model applicable to arbitrary sample geometries was developed in COMSOL to analyze laser cooling of 1% Yb3+:KYW crystals. The model includes the effects of thermal conduction, black-body radiation, and background impurities. The simulation results showed that the largest limitation to cooling was the thermal conduction between the crystal and its glass capillary tube supports. Although glass has a low thermal conductivity, it absorbs a significant amount of heat through black body radiation because of its high emissivity (~0.9). The absorbed heat is transferred to the crystal sample through the thermal contact, causing an observable dip in the curve of temperature versus time thereby reducing the net, steady-state cooling power. This limitation was overcome using silicon aerogel, whose conductivity and emissivity are 3 orders and 1 order smaller than glass, respectively. The aerogel maintains the temperature gradient and the heat transported to the crystal is negligible, resulting in a much lower minimum achievable temperature and removing the dip in the temperature evolution curve. By changing the sample support from glass to aerogel, the minimum achievable temperature under ambient conditions was lowered from 0.2 K to 1.5 K in a 1% Yb:KYW crystal with 1W pump at 1023 nm. These results, together with analysis of radiation balance in a 10 mm long crystal of 1% Yb:KYW, were used for a preliminary investigation of self-cooled lasing in this tungstate host.
Long Cheng, Laura B. Andre, and Stephen C. Rand, "3D thermal transport analysis and experiments on a self-cooled tungstate laser (Conference Presentation)," Proc. SPIE 10936, Photonic Heat Engines: Science and Applications, 109360R (Presented at SPIE OPTO: February 05, 2019; Published: 4 March 2019); https://doi.org/10.1117/12.2507900.6009800801001.
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