Incoherence effect of single-mode pump on second-harmonic generation

A single-mode laser beam has a partially incoherent nature. By expressing such a single-mode beam as an array of square-root damping waves, we have derived a factor that describes the influence of the incoherence of a single-mode pump on second-harmonic generation. This factor is analytically formulated as a function of the ratio of crystal length to laser coherence length. When this ratio is smaller than 1.1, the value of the factor is above unity with a maximum of 1.253, indicating that a single-mode pump leads to enhanced second-harmonic intensity.