Overcoming the phase-mismatch by fundamental beam modulation

Providing the phase-matching condition is crucial to achieve efficient frequency conversion in a nonlinear crystal. Birefringence and periodically poled nonlinear crystals are widely used to establish the phase-matching condition. Here, a method is proposed to overcome the phase mismatching between interacting waves in a nonlinear crystal by modulation of the fundamental beam intensity and phase. Accordingly, the fundamental beam is focused by a multi-focal length diffractive optical element into a nonlinear crystal. Therefore, the fundamental beam suffers a specified number of foci along the propagation direction. The focus points of the fundamental beam are adjusted to coincide with locations that the interacting waves are in phase and for the length that the phases of the waves are opposite, the fundamental beam has a low intensity. Consequently, the back conversion is partially suppressed, and a net of conversion efficiency can be achieved. The method is validated by simulation of the second harmonic generation process. (paper)