Fluoride crystals, due to their low phonon energies, are attractive hosts of trivalent lanthanide ions for applications in upconverting phosphors, quantum information science, and solid-state laser refrigeration. In this article, we report the rapid, low-cost hydrothermal synthesis of potassium lutetium fluoride (KLF) microcrystals for applications in solid-state laser refrigeration. Four crystalline phases were synthesized, namely orthorhombic K<sub>2</sub>LuF<sub>5</sub> (Pnma), trigonal KLuF<sub>4</sub> (P3<sub>1</sub>21), orthorhombic KLu<sub>2</sub>F<sub>7</sub> (Pna2<sub>1</sub>), and cubic KLu<sub>3</sub>F<sub>10</sub> (Fm3m), with each phase exhibiting unique microcrystalline morphologies. Luminescence spectra and emission lifetimes of the four crystalline phases were characterized based on the point-group symmetry of trivalent cations. Laser refrigeration was measured by observing both the optomechanical eigenfrequencies of microcrystals on cantilevers in vacuum, and also the Brownian dynamics of optically trapped microcrystals in water. Among all four crystalline phases, the most significant cooling was observed for 10%Yb:KLuF<sub>4</sub> with cooling of 8.6 $\pm$ 2.1 K below room temperature. Reduced heating was observed with 10%Yb:K<sub>2</sub>LuF<sub>5</sub>
Adaptive Gradient Estimation Stochastic Parallel Gradient Descent Algorithm for Laser Beam Cleanup