We present simple formulas for the diffraction efficiencies of a binary phase grating that performs array illumination with ultrashort pulse beams. Using scalar diffraction theory, we formulated the efficiencies as a function of pulse spectral width by Fourier-transforming the complex-modulated frequency spectra of diffracted pulses in the far-field region. From the analytical simulations, we found that pulse array uniformity departs from unity as the spectral width increases, or the pulse duration decreases, thereby limiting the attainable split counts. This finding can be considered in the design of gratings for delivering controlled amounts of pulse energies to diffraction orders of interest.

中文翻译：

---

用于超短脉冲光束阵列照明的二元相位光栅衍射效率的公式

我们提出了用超短脉冲光束进行阵列照明的二元相位光栅的衍射效率的简单公式。使用标量衍射理论，我们通过对远场区域中衍射脉冲的复调制频谱进行傅立叶变换，将效率公式化为脉冲频谱宽度的函数。从分析模拟中，我们发现随着频谱宽度的增加或脉冲持续时间的减少，脉冲阵列均匀性偏离了统一性，从而限制了可达到的分裂计数。可以在光栅设计中考虑这一发现，以将受控量的脉冲能量传递到感兴趣的衍射级。