We report passive mode-locking experiments with a novel self-doubling laser crystal Yb:YAl₃BO₃4 (Yb:YAB). The diode-pumped laser was mode locked by an ion-implanted semiconductor saturable absorber mirror. Far off phase matching, soliton mode locking produced pulse widths of 198 fs to 1.4 ps, with up to 660-mW output and optical efficiency of 24% at 1040 nm. The shortest pulses had a peak power of 28 kW with 440-mW average power and 16% efficiency. A few degrees off phase matching, a total of 60 mW of green femtosecond pulses was generated simultaneously. Close to phase matching, the laser produced picosecond pulses and, without infrared output, a total of 270 mW of green output, corresponding to 10% conversion efficiency (absorbed pump to green output).