We report on first-order quasi-phase-matched frequency doubling of picosecond pulses to the green, using a sample of periodically poled lithium niobate. In cw mode-locked operation, 330 mW of average green power was generated with an average conversion efficiency of similar to 52%. With a quasi-cw mode-locked pulse train an average conversion efficiency of similar to 65% was achieved, and 1.3 W of green power (average power within the 10-mu s pulse envelope) was produced. At these powers there was no significant photorefractive damage, as confirmed by measured M(2) beam-quality factors of similar to 1.1 for both output fundamental and second-harmonic beams. (C) 1996 Optical Society of America