Parametric amplification of chirped optical pulses under pump depletion

We present simple analytical solutions of coupled wave equations describing chirped pulse parametric amplification under pump depletion. The evolution of the duration and spectrum of amplified pulses in OPA pumped by Gaussian and supergaussian pulses has been investigated both numerically and analytically. Also, the dependence of the energy conversion efficiency from pump to signal was determined for a range of parameter values, and an optimum ratio of signal and pump pulse durations was evaluated.