Parametric gain of the generation and the amplification of ultrashort optical pulses

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Abstract
A theoretical model for calculating the effective gain of parametric generation and amplification of ultrashort optical pulses is presented. This model takes into account both spatial and temporal effects, including spatial beam broadening, temporal pulse broadening, spatial walk-off of the pulse beams, and temporal walk-off of the parametrically interacting pulses. An analytical formulation for the parametric efficiency coefficient and the effective gain in terms of six spatial and temporal characteristic lengths is obtained. This formulation allows for an easy evaluation of the threshold and the efficiency of a synchronously pumped optical parametric oscillator generating ultrashort pulses without requiring the solution of a differential equation. It can also be used to calculate the amplification factor and the output pulse energy in parametric amplification and difference-frequency generation of ultrashort pulses. Numerical results for picosecond and femtosecond optical parametric generation and amplification in the KTP crystal are presented for many different experimental conditions.

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