A deep understanding of the spectral gain characteristics of optical parametric oscillators (OPOs) and optical parametric amplifiers (OPAs) is important for a highly efficient optical parametric conversion. We numerically calculated the spectral gain characteristics of a quasi-phase-matching (QPM) parametric conversion process using the periodically poled 6% (mol/mol) MgO doped LiNbO3 (PPMgLN) as the nonlinear crystal. In the simulation we utilized the approach of a transformative matrix of the periodically poled nonlinear medium, which results from the small-signal approximation of three-wave mixed nonlinear equations. Numerical simulation results show that: (1) The full width at half maximum (FWHM) of the spectral gain of the parametric process becomes wider with the increase of parametric wavelength and reaches the maximum at degeneration; (2) The gain coefficient decreases gradually with the increase of parametric wavelength; (3) The spectral gain bandwidth decreases correspondingly with the increase of the nonlinear material length; (4) There exists an optimal parametric wavelength band, which is most suitable for the high gain parametric conversion when pumped by a laser source with a wide wavelength band, such as the high power fiber laser.
