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Here, we demonstrate the broadband spectra and efficient laser performance of a disordered Nd:Sr0.7La0.3Mg0.3Al11.7O19 (Nd:ASL) crystal. The polarized absorption and emission spectra were characterized and calculated with the Judd–Ofelt (J–O) theory, and the results show that this crystal has relatively large σ polarized absorption and emission cross sections, with peak emission cross sections of 4.5 × 10−20 cm2 at 1051 nm and an emission width of 30 nm at 1074 nm, which are favorable for pulsed lasers. The laser-diode-pumped continuous-wave (CW) and passively Q-switched lasers at 1051 nm were realized for the first time to our best knowledge. For CW laser, the maximum output power was 1.95 W with the slope efficiency of 42.6%, and for the passive Q-switching, the maximum output power was 0.73 W with the pulse width of 7.96 ns and peak power of 5.64 W. The results demonstrate that Nd:ASL crystal is a potential candidate for lasers, especially high-peak pulsed lasers such as Q-switching and mode-locking. [ABSTRACT FROM AUTHOR]