Energy is conserved, so the intensity drops, as the pulse stretches.
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This principle is used in radar techniques; it is also used in special high-peak power laser systems: amplifying a short pulse to moderate energies can cause damage to optical components, so instead the short pulse is stretched this way first, then amplified as a long, safer, pulse, then only reassembled as a short pulse after leaving the laser system. Reference: review article by Mourou et al. and one of the original papers describing the idea, by Strickland et al. This is also described a little in the easy-to-read review paper by Reid et al.
Last revised: 12 March 2003 - rsm