采用傅里叶频谱分析法, 将超短脉冲高斯光束展开为单色单角谱成分的线性叠加; 利用Kogelnik一维耦合波理论, 分析透射型体光栅对各单色单角谱成分的衍射特性; 再通过逆傅里叶变换得出衍射光波的时空分布与光栅各参量的对应关系。结果表明：衍射光束在时域以及在光栅波矢与光栅前表面法向所构成平面内的空域光强分布随光栅周期的减小而呈展宽趋势, 且在空域的展宽趋势较为迅速, 与入射光束在空域进行比较, 衍射光束空域分布发生非常明显的畸变; 衍射光束在时域以及在光栅波矢与光栅前表面法向所构成平面内的空域光强分布随光栅厚度的增大亦呈展宽趋势, 且展宽速度相当, 与入射光束在时域和空域比较, 均发生了较明显的畸变。

Based on Fourier transform, the ultra-short pulsed Gaussian laser beam is transformed into linear combinations of monochromatic plane waves. Depending on Kogelnik′s one-dimensional coupled-wave theory, the diffraction characteristics of monochromatic plane waves by transmitting volume grating are put forward, when the central wave vector satisfies the Bragg condition of the volume grating. With the inverse Fourier transform of diffraction of monochromatic plane waves, the law of spatial and temporal intensing distribution of diffractive beam with different parameters of volume grating is given. The results show that diffractive laser beam is broadened in the temporal and spatial domains, in the plane comprising of the grating vector and the normal vector of the grating front surface, with the decreasing period of the transmitting volume grating. Its broadening trend in the spatial domain is faster than that in the temporal domain. Compared with input ultra-short pulsed Gaussian laser beam, the diffractive laser beam is deteriorated obviously in the spatial domain. Diffractive laser beam is broadened in the temporal and spatial domains in the plane comprising of the grating vector and the normal vector of the grating front surface, with the increasing thickness of the grating. And its broadening trend is equal to each other in the spatial and in temporal domains. Compared with the input ultra-short pulsed Gaussian laser beam, the diffractive laser beam is deteriorated both in the temporal and spatial domains.