We present a soliton modelocked Yb:YAG laser, which produces 1 ps pulses at 45 MHz repetition rate and 1.5 W average output power at a center wavelength of 1030 nm. The Yb:YAG crystal is pumped with a 40-W, 1-cm, high-power, low-brightness diode bar at 940 nm. Passive modelocking is initiated by a semiconductor saturable absorber mirror. We suppressed Q-switching instabilities by choosing the cavity and absorber parameters according to a previously developed theory.

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