Tunable nonlinear beam shaping by non-collinear interactions

A method is proposed for nonlinear beam shaping, employing a non-collinear quasi phase-matched interaction in a crystal whose nonlinear coefficient is encoded by a computer generated hologram pattern. In this method the same axis is used for both satisfying the phase-matching requirements and encoding the holographic information, the result is a single shaped beam in the generated frequency. This allows to shape beams in one-dimension using a very simple method to fabricate patterned nonlinear crystals and to shape beams in two-dimensions with high conversion efficiency. The one-dimensional case is experimentally demonstrated by converting a fundamental Gaussian beam into Hermite-Gaussian beams at the second harmonic in a KTiOPO4 crystal. The two-dimensional case is demonstrated by generating Hermite-Gaussian and Laguerre-Gaussian beams in a stoichiometric lithium tantalate crystal. The suggested scheme enables broad wavelength tuning by simply tilting the crystal.