Temporal optical rogue waves in high power short-cavity Yb-doped random fiber laser

•The stochastic pulses and temporal optical rogue waves (RWs) behavior are observed and investigated in the high power short-cavity Yb-doped random fiber laser (YDRFL) for the first time.•The record output power without the stimulated Raman scattering (SRS) is promoted to 26.6 W in the YDRFL with the Ge-doped fiber (GDF) length of 120 m.•The experimental results manifest that the proportion of RWs depends on the GDF length and can also affect the stability of output lasing and the M2 factor distribution.•The experimental phenomenons display that the multiple high order SRS stokes lights and the visible light radiations are generated in the YDRFL with shorter GDF length.•The research results reveal that achieving the relative stable output power requires the greater pump power for the shorter GDF length.