  The nonlinear frequency conversion of low-temporal-coherent light holds a
variety of applications and has attracted considerable interest. However, its
physical mechanism remains relatively unexplored, and the conversion efficiency
and bandwidth are extremely insufficient. Here, considering the instantaneous
broadband characteristic, we establish a model of second harmonic generation
(SHG) of low-temporal-coherent pulse, and reveal its differences from the
coherent conditions. It is found that the second harmonic (SH) of
low-temporal-coherent light is produced by not only the degenerate SH processes
but also crossed sum-frequency processes. On the basis of this, we propose a
method for realizing low-temporal-coherent SHG with high efficiency and broad
bandwidth, and experimentally demonstrate a conversion efficiency up to 70%
with a bandwidth of 3.1 THz (2.9 nm centered at 528 nm). To the best of our
knowledge, this is the highest efficiency and broadest bandwidth of
low-temporal-coherent SHG, and its efficiency is almost the same with that of
the narrowband coherent condition. Furthermore, the spectral evolution
characteristics of the broadband low-temporal-coherent pulse in SHG process are
revealed in experiments, that the SH power spectral density (PSD) is
proportional to the self-convolution of the fundamental wave PSD, which is
greatly different from that of the coherent process. Our research opens a door
for the study of the low-coherent nonlinear optical processes.
