Induced Diffraction in Phase-Mismatched Second-Harmonic Generation

We show analytically that in phase-mismatched second-harmonic generation, an effective diffraction is induced at the second-harmonic (SH) frequency. Numerical simulation results agree with the analytical predictions. Compared to the case of linear propagation, the effect of the overall diffraction at the SH frequency becomes doubled due to the induced diffraction, which causes an interesting result that the SH beam width will be larger than that of the fundamental field.