In this Letter, we study the second-harmonic (SH) generation of temporally low-coherence light using the statistical optics method. By introducing the statistical characteristics of low-coherence light into the nonlinear coupled wave equation, we predict the self-convolution relationship between the power spectral density of the second-harmonic and that of the fundamental wave and demonstrate it in experiments. The effects of phase matching and group velocity matching on the second-harmonic bandwidth and conversion efficiency are analyzed, which is beneficial to improve the efficiency of low-coherent SH light. Combining the statistics optics and nonlinear optics, our research provides a suitable mathematical model for the study of nonlinear frequency conversion processes of temporally low-coherence light. Due to its statistical characteristics and temporal incoherence, low-coherence SH light would have further applications in uniform illumination, quantum optics, metrology, and so on.
