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。 The coupled wave equation of femtosecond pulse diffracted by a transmissive multilayered grating (SVHG) is deduced using the Kogelnik coupling wave equation and the transfer matrix method, and the diffraction field and the expression of the diffracted light intensity in time and frequency domain are obtained. The numerical simulation of the time-domain diffracted light intensity shows that each VHG layer provides a time-domain diffraction pulse. The pulse waveform is determined by the VHG parameters, such as thickness, refractive index modulation, etc., and is independent of the parameters of other VHGs and interlayers. Interleaved layers shift the negative direction of the time axis of the VHG layer diffraction pulse placed on the left side of the diffraction pulse and have no effect on the diffraction pulses of the VHG layer placed on the right side of the layer. Therefore, the VHG layer and intercalation layer parameters can be adjusted to achieve the adjustable Femtosecond burst. Finally, the reason for generating the pulse train is explained by the diffraction efficiency and the diffraction spectrum expression.