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.

中文翻译：

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时间低相干光的二次谐波生成

在这封信中，我们使用统计光学方法研究了时间上低相干光的二次谐波（SH）生成。通过将低相干光的统计特性引入非线性耦合波方程，我们预测了二次谐波和基波的功率谱密度之间的自卷积关系，并在实验中进行了证明。分析了相位匹配和群速度匹配对二次谐波带宽和转换效率的影响，有利于提高低相干SH光的效率。结合统计光学和非线性光学，我们的研究为研究时间低相干光的非线性频率转换过程提供了合适的数学模型。