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A rigorous analysis of ultrashort pulse shaping by the spectral filtering of dispersed frequency components is presented. Particular attention is directed toward the case of two liquid-crystal spatial light modulators used to provide programmable manipulation of both the phase and the amplitude profiles of the shaped waveform in the time domain. Different optical configurations are evaluated and their theoretical and practical effects determined. An important result is that, even with optimal alignment and components, the diffraction arising from spectral filtering necessarily produces a transverse spatial shift that varies linearly along the temporal profile of the shaped waveform. Despite this effect it is shown that the technique can generate arbitrary phase and amplitude temporal profiles (subject to limitations in temporal extent and temporal resolution) for the Gaussian spatial component of the shaped output waveform.
Wefers et al. (1995) studied this question.