利用Kogelnik耦合波方程和传输矩阵法，推导了飞秒脉冲通过透射型多层体光栅(SVHG)衍射的耦合波方程，得到时、频域的衍射场和衍射光强表达式。时域衍射光强的数值模拟结果表明，每一个VHG层提供一个时域衍射脉冲，脉冲波形由该VHG参数决定，如厚度、折射率调制度等，与其他VHG和穿插层的参数无关。穿插层会对置于其左侧的VHG层衍射脉冲产生负时间轴方向的平移，对置于其右侧的VHG层衍射脉冲无影响，因此可以通过改变VHG层和穿插层参数实现可调控的飞秒脉冲串。最后，通过衍射效率和衍射谱表达式解释了产生脉冲串的原因。

Based on the Kogelnik′s coupled-wave theory and transfer matrix method, the expressions of temporal and spectral diffracted field and intensity are deduced, while a femtosecond pulse incidents on a transmitted stratified volume holographic grating (SVHG). Simulation results show that, each VHG layer diffracts out a sub-pulse and the waveform of which is modulated by corresponding VHG layer and and buffer layers parameters. The buffer layers placed on VHG′s right side will translate the diffracted sub-pulses along the negative time-axis, whereas the left side will not translate peak position, such property can be used to realize modulated femtosecond pulse train by controlling VHG and buffer layers parameters. At last, an explanation on these phenomena is given based on the diffraction efficiency and expressions of diffracted spectrum.Key words