轴对称超短强激光在空气中的传输可以用2D+1维非线性薛定谔方程来描述，该方程一般可用FCN方法进行求解，即在时间上应用快速傅里叶变换方法、在空间横截面上采用Crank-Nicholson差分法。但由于计算非常耗时，传统串行的FCN方法只能计算强激光在百m量级距离上传输。基于OpenMP设计了求解2D+1维非线性薛定谔方程的并行方法及其程序。数值模拟结果证明了程序的正确性和较高的并行效率。当线程数为15时并行加速比为12。此并行方法可应用于模拟长距离的超短超强激光的传输。

The propagation of axis-symmetric ultra-short high-intensity laser pulse in air can be described by the 2D+1 non-linear Schrdinger equation, which is often solved by the FCN method (split-step Fourier method with Crank-Nicholson scheme in the transverse direction). However, since the FCN method is very time-consuming, the series FCN code can only deal with the simulations of the propagation of laser pulse up to hundreds meters. We develop a parallel algorithm for the FCN method basing on OpenMP. Numerical simulations demonstrate the correctness and high parallel-efficiency of the parallel FCN code. The speed-up ratio is about 12 for 15 threads. The parallel FCN code can be used to simulate the long-distance propagation of the ultra-short high-intensity laser pulses.