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The Yb:YAG is an excellent high-average power and ultra-short pulse laser crystal.Transition intensity parameters Aktp and Huang-Rhys factors are fitted to its emission spectrum by the full-profile fitting method.Calculated results indicate that the emission spectrum of Yb∶YAG at cryogenic temperature consists of three pure electron state transitions and two phononassisted transitions,one vibronic transition releases one-phonon of 3 cm-1,and the other vibronic transition absorbs onephonon of 22 cm-1.At 300 K,the phonon assisted transition of 3 cm-1 tus into two-or more-phonon assisted transitions.The procedure absorbing phonon can reduce the thermal load of Yb∶YAG and improve the laser efficiency,which may be one of the reasons why Yb∶YAG has excellent performance.The emission bands of Yb:YAG are broadened thermally,and the peak values decrease by several times.The emission cross sections of Yb:YAG determined by Fuchtbauer-Ladenburg (F-L) formula are remarkably different from those calculated with Aktp,which indicates that it is necessary for a laser material to determine its transition intensity parameters Aktp in order to reasonably evaluate the laser performance.