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Femtosecond optical parametric oscillators (OPOs) are widely used inultrafast nonlinear frequency conversion and quantum information. However,conventional OPOs based on quasi-phase-matching (QPM) crystals have manyparasitic non-phase-matched processes which decreases the conversionefficiency. Here, we propose nine-wave coupled equations (NWCEs) to simulateall phase-matched and non-phase-matched interactions in QPM crystals to improveconventional three-wave coupled equations (TWCEs), especially for the situationof high intensity ultrashort pulses and complexly structured crystals. Wediscuss how to design the poling period of QPM crystal to maximize theconversion efficiency of signal light for a given OPO system. The simulationreveals that the OPO based on chirped periodically poled lithium niobate(CPPLN) with certain chirp rate has higher signal wave conversion efficiencythan that of a PPLN, and demonstrates that NWCEs illustrates more details ofthe pulse evolution in the OPO cavity. Starting from a CPPLN, an aperiodicallypoled lithium niobate (APPLN) design is available by modifying the domainlengths of the crystal and optimizing the OPO output power via dynamicaloptimization algorithm. The results show that by using a properly designedAPPLN crystal, a 1600nm OPO, when pumped by a femtosecond laser with 1030nmcentral wavelength, 150 femtosecond pulse duration and 5 GW/cm2 power intensityat the focus, can achieve very efficient output with a signal light conversionefficiency of 50.6%, which is higher than that of PPLN (25.2%) and CPPLN(40.2%). The scheme in this paper will provide a reference for the design ofnonlinear QPM crystals of OPOs and will help to understand the complexnonlinear dynamical behavior in OPO cavities.

Consideration of non-phase-matched nonlinear effects in the design of quasi-phase-matching crystals for optical parametric oscillators