The holography technique, which records the amplitude and phase of a wave from an illuminated object, has been developed for decades since it was proposed. It has blossomed and yielded fruit in many other fields as a powerful tool of wave shaping, such as acoustics, microwaves, electron beams, and surface-plasmon-polariton waves. The holography concept has also been introduced to the nonlinear field by shaping the nonlinear light wave in one-dimensional (1D) or 2D manners. However, in previous works, such holography technique is realized by designing of the nonlinear photonic crystals, which lacks flexibility owning to complex fabrication and the unchangeable spatial structure of the media. The disadvantage can be mitigated by introducing a technique capable of manipulating the light wave front in a dynamical way to the nonlinear holography.

We propose and experimentally demonstrate dynamic nonlinear optical holograms by introducing the concept of computer-generated holograms for second-harmonic generation of a structured fundamental wave with a specially designed wave front. The generation of Laguerre-Gaussian second-harmonic beams is investigated in our experiment. Such a method, which only dynamically controls the wave front of the fundamental wave by a spatial light modulator, does not need domain inversion in nonlinear crystals and hence is a more flexible way to achieve the off-axis nonlinear second-harmonic beams. It can also be adopted in other schemes and has potential applications in nonlinear frequency conversion, optical signal processing, and real-time hologram, etc.