Focusing Optimization for High-Power Continuous-Wave Second-Harmonic Generation in the Presence of Thermal Effects

We study thermal effects in high-power single-pass second-harmonic generation (SP-SHG) of continuous-wave (cw) green radiation in MgO:sPPLT and describe optimization of critical factors including the fundamental beam waist, position, and focusing parameter, for attainment of maximum SP-SHG efficiency. By developing a numerical model combining split-step Fourier and finite-element methods, we compute the relevant parameters for optimization of SP-SHG of a cw Yb-fiber laser at 1064 nm in a 30-mm-long crystal. Real experimental parameters and boundary conditions are used to simulate nonuniform heat distribution in the crystal under high-power operation and study its effects on SP-SHG optimization. The results indicate that for input powers exceeding a certain limit, the Boyd and Kleinman (BK) criteria for optimum focusing are no longer valid. By increasing the fundamental power to 50 W, we find that the optimum focusing parameter decreases by a factor of 4, from ξ =2.8 to 0.7. We also find that the maximum SP-SHG output power is always obtained for fundamental waist at the center of the crystal, and we present a general strategy for the choice of ξ at different fundamental powers. Using a top-sinked oven design, the BK focusing condition can be established even at high fundamental powers.