Partial spectral and temporal coherence of plane-wave pulse trains in second-harmonic generation

We study the spectral and temporal coherence effects in the passage of a Gaussian Schell-model (GSM) scalar, plane-wave pulse train through a slab of nonlinear optical crystal exhibiting second-harmonic generation. We show that due to the nonlinear interaction the temporal and spectral degrees of coherence of the fundamental (F) and second-harmonic (SH) pulse trains at the exit facet may deviate markedly from the GSM and the global degree of coherence of the SH wave generally decreases with increasing incident F beam intensity. In addition, we find that due to the partial coherence of the incident GSM field the transmitted SH wave may show a double-peaked intensity distribution.