To optimise the transformation rate (efficiency) in the optical frequency conversion of laser beams of ultra-short light pulses in optically non-linear media such as a crystal (56), a double refracting crystal (54) is arranged in the beam path before the optically non-linear medium (56). The length of the double refracting crystal (54) is selected and the orientation of its optical crystal axis in relation to the propagation direction of the laser beams involved in the frequency conversion is set such that the change caused by the double refracting crystal (54) in the location, time and direction of incidence of the laser pulses (14) and (16) on the optically non-linear medium (56) and the resulting change in the spatial and temporal overlap of the laser pulses in the optically non-linear medium (56) for optical frequency conversion in the crystal (56) give a conversion efficiency which is higher than the conversion efficiency which would be achieved without the double refracting crystal (54).