Dynamic control of light beams in second harmonic generation

In this Letter, we report the dynamic control of the spatial shape of the second harmonic (SH) beam generated in a nonlinear crystal, by controlling the phase of the input fundamental beam before entering the crystal. This method enables 2D beam shaping and does not require any special fabrication beforehand. We have shown in simulation and experiment that this is possible for both short and long crystals: for short crystals, we assume the transverse phase of the SH beam is doubled relative to the input phase of the fundamental beam; for longer crystals, genetic algorithms were used in order to solve the inverse phase problem, which generally does not have an analytical solution. The method we present enables us to dynamically shape a beam in a nonlinear process, using standard crystals and optical equipment, and without the need to use any optical element after the nonlinear crystal.