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

Femtosecond optical parametric oscillators (OPOs) are widely used in ultrafast nonlinear frequency conversion and quantum information. However, conventional OPOs based on quasi-phase-matching (QPM) crystals have many parasitic non-phase-matched processes which decrease the conversion efficiency. Here, we propose nine-wave coupled equations (NWCEs) to simulate all phase-matched and non-phase-matched interactions in QPM crystals to improve conventional three-wave coupled equations (TWCEs), especially for the situation of high intensity ultrashort pulses and complexly structured crystals. We discuss how to design the poling period of QPM crystal to maximize the conversion efficiency of signal light for a given OPO system. The simulation reveals that the OPO based on chirped periodically poled lithium niobate (CPPLN) with a certain chirp rate has higher signal wave conversion efficiency than that of a PPLN, and demonstrates that NWCEs illustrate more details of the pulse evolution in the OPO cavity. Starting from a CPPLN, an aperiodically poled lithium niobate (APPLN) design is available by modifying the domain lengths of the crystal and optimizing the OPO output power via dynamical optimization algorithm. The results show that by using a properly designed APPLN crystal, a 1600 nm OPO, when pumped by a femtosecond laser with 1030 nm central wavelength, 150 femtosecond pulse duration and 5 GW/cm2 power intensity at the focus, can achieve very efficient output with a signal light conversion efficiency 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 of nonlinear QPM crystals of OPOs and will help to understand the complex nonlinear dynamical behavior in OPO cavities.