We present a theoretical model to deal with second harmonic generation (SHG) of ultrashort pulses in refractive-index-linear-modulating (RILM) nonlinear crystals. New coupled-wave equations were derived based on plane wave propagation. Under the undepleted-pump approximation, the analytic solutions for SHG of ultrashort pulses were obtained. The second harmonic (SH) pulse width and the efficiency were optimized in terms of the RILM parameter and the chirp coefficient of fundamental pulses. The results show that modulation of the refractive index (RI) in nonlinear crystals leads to a spectral localization of SHG that compensates the group velocity mismatch (GVM) and therefore compresses SH pulses. The modulation complicates the SHG process, which determines the pulse width, and the conversion efficiency varies with length and bandwidth. Especially, an overshooting compression phenomenon was found, which arose mainly from internal interference of the carrier frequency component in a SH pulse.
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