A new theory for the treatment of a pulsed beam propagating through a grating pair

A new theoretical model, without the first-order approximation of grating diffraction, has been developed for studying the propagation of a pulsed beam through a grating pair. By using our model, the astigmatic aberration of the grating pair has been analyzed in detail. It was shown that the grating pair may be a good optical element for astigmatic compensation of monochromatic optical beams. But for grating pulse compression, the astigmatic aberration affects the pulse fronts and the effects of finite beam size (FBS). These effects on the compression of ultra-broadband pulses have been studied. It was found that, due to these effects, the space-time shapes of the compressed pulse are severely distorted. The magnitude of this distortion depends not only on the astigmatic aberration, but also on the spectral bandwidth and spatial divergence of the pulse. When the input pulsed beam is collimated, the waveform distortion due to the effects of FBS can be eliminated, but the pulse front distortion remains. In addition, the spatial and temporal properties of the compressed pulse for a single-pass compressor have been studied. An analytical expression without the well-collimated condition was obtained to describe the effect of lateral frequency shift. Also, the effect of third-order dispersion on a single-pass compressor is discussed