Nonlinear beam shaping by non-collinear interactions

Nonlinear diffraction occurs when light encounters a periodicity in a nonlinear coefficient, for example, a periodically altered second order nonlinear coefficient impinged by a pump beam will result in a diffraction pattern in the second harmonic (SH). An interesting case of nonlinear diffraction is when the pump beam enters the crystal with an angle. This results with an asymmetrical diffraction pattern and enlarges the operational bandwidth [1]. In a perfectly periodic structure the result of diffraction for a Gaussian pump beam is a Gaussian beam in the SH. However, if the structure is modified using a computer generated hologram (CGH) [2] encoding technique, the obtained SH beam can have any arbitrary shape. This method enables 1D nonlinear beam shaping by a simple 1D modulation of the nonlinear coefficient. Moreover, it enables fully phase matched, and hence efficient scheme for 2D nonlinear beam shaping.