在傍轴近似条件下建立了OPO的数学模型,通过引入三波混频中时间与空间关系,采用分步傅里叶算法模拟了纳秒级脉冲和连续光波在谐振腔内的三波混频过程。理论模型中考虑了不同频率光波之间的色散关系,可以在高转换效率情况下分析不同泵浦脉冲功率、脉冲时长、腔镜透反射比以及不同种子光输入等情况下的输出波形、功率以及OPO阈值等特性。实验中采用掺杂MgO的周期性极化铌酸锂晶体(MgO∶PPLN)为非线性介质,在输入1.06 μm泵浦激光脉冲能量为0.4 mJ时,产生3.8 μm闲频光超过0.07 mJ输出,与数值模拟结果0.08 mJ较为符合。

A mathematical model for optical parametric oscillator (OPO) by using paraxial approximation was proposed. It could simulate the wave mixing process of both nanosencond waves and contiunes waves. This model including the dispersion of different wavelengths of the three mixing waves used the split-Fourier method and the spatial and temporal relations between mixing waves to describe the process in OPO. The model could give output waveform, power and threshold in high efficiency OPO under the conditions of different pump pulse energies, pulse widths, transmissivities and reflectivities of cavity mirrors. In the experiment, a periodically poled lithium niobate crystal (PPLN) was used as the nonlinear medium. When the single pulse energy of input pump beam at 1.06 μm was 0.4 mJ, we could get the energy of idle wave at 3.8 μm more than 0.07 mJ, which was qualitatively fitted by the numerical result of 0.08 mJ.