SPACE-TIME PROFILES OF SHAPED ULTRAFAST OPTICAL WAVE-FORMS

A derivation of the space-time profiles of ultrafast optical waveforms shaped by filtering of spatially separated frequency components Is pr esented, Closed form expressions for the space-time impulse response f unctions are given for the cases of single and double passes through a pulse shaping apparatus, For a single pass and a short unshaped pulse , diffraction by the mask filter gives rise to a translational spatial shift in the desired electric field profile that varies linearly with time along the shaped waveform. This result is completely general, an d applies to frequency-domain pulse shaping with either continuous or discrete mask filters, It is also shown that double passing the appara tus does not generally reverse this effect but rather introduces furth er space-time coupling such as a time-varying spotsize, Examples of sp ecific mask patterns are presented and implications for the generation of high-fidelity shaped optical waveforms are discussed.