Femtosecond laser pulse propagation in a uniaxial crystal

The wave equation describing the vector propagation of a femtosecond laser pulse of a few optical cycles in a uniaxial crystal is solved numerically by the method of unidirectional waves. Propagation of the pulse in the direction normal to the optical axis is studied, taking into account both second- and third-order nonlinearities of the crystal. Conversion efficiency as a function of crystal length, pump intensity and pulse duration is studied. As an example, the propagation of femtosecond laser pulse of tau=10 fs duration at lambda=810 nm in a LiNbO3 crystal 12 mum thick is studied numerically.