Shaping light beams in nonlinear processes using structured light and patterned crystals

Shaping light in second order nonlinear interaction is a compact way of controlling both shape and frequency of the output, a desirable trait for many different applications such as optical communication, particle manipulation, microscopy, spectroscopy, and quantum information. The use of patterned nonlinear crystals, combining holographic methods with electric field poling, has proven a useful way to create arbitrary one- and two-dimensional shapes, as well as beams that follow curved trajectories. Using structured light as an input beam has also been shown to produce light with special properties, such as vortex beams carrying orbital angular momentum, curved Airy beams, and others. We review the latest advances in the field.