Abstract
We present analytic results on optical parametric amplifiers and generators where the pump pulse is short enough that its pulse shape dictates the dynamics of the energy transfer to signal and idler waves. We include the group velocity mismatches between the three waves as well as a phase mismatch. A Laplace transform-in-space and WKB-in-time asymptotic formalism is applied to co-propagating waves with a short pump pulse and any group velocity mismatch. Possible generalizations of this formalism to include the effects of nonuniform phase mismatch are indicated. An explicit evaluation of our results with Gaussian pulses is given.
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