Nonlinear photonic crystals (NPCs), in which the second-order susceptibilityis spatially modulated, open a door in the field of nonlinear wave mixing. Both one-dimensional (1D) and two-dimensional (2D) structures, including square, hexagonal lattices, annular periodical, or even random structures, have widely been fabricated to realize optical parametric processes. Various nonlinear processes, such as nonlinear Cherenkov radiation, nonlinear Raman-Nath and nonlinear Bragg diffraction have been intensively studied in NPCs. Especially, with holography concept introduced to nonlinear optics, arbitrary two-dimensional nonlinear beam shaping, such as vortex and airy beams, could be realized. However, all these methods, which manipulate the structure of the NPCs, have several drawbacks, including complex fabrication and unchangeable second harmonic (SH) pattern.

We proposed and experimentally demonstrated that nonlinear Raman-Nath second harmonic can be achieved in real time when a fundamental wave with the phase periodically modulated, termed as structured fundamental wave, incident in a homogeneous nonlinear medium. The diffraction of second harmonic originates from the structured fundamental wave, rather than the grating of a nonlinear photonic crystal. Nonlinear second harmonic generation, in forms of both one- and two-dimensional, was investigated in our experiment. This method circumvents the limitation of nonlinear photonic crystals in some extend and has potential applications in nonlinear frequency conversion, optical signal processing and beam shaping, etc.

the research was published on Haigang Liu, Jun Li,Xiaohui Zhao, YuanlinZheng, and XianfengChen, Nonlinear Raman-Nath second harmonic generation with structured fundamental wave, Optics Express, 24(12), 15666-15671(2016)