Nonlinear frequency conversion in the quadratic nonlinear crystals is an important method to generate coherent radiation in wavelengths when compact and efficient sources are not available. It is worth noting that, beam shaping of a nonlinear harmonic wave has attracted intense interest in recent years and has been studied in various applications, including optical micro-manipulation, optical micro-fabrication, optical imaging, quantum optics, and optical communication. However, the usual way to realize the nonlinear beam shaping by the electric-field poling technique is challenging to achieve efficient nonlinear harmonic frequency along with the shaping of the beam in two transverse dimensions, since the longitudinal part of the vectorial phase-matching condition is not fulfilled. In this letter, we demonstrated efficient two-dimensional (2D) arbitrary harmonic beam shaping in amplitude-type nonlinear photonic crystals (A-NPCs) by femtosecond laser micromachining, where the phase-matching condition is fulfilled through the birefringence and nonlinear Raman-Nath effect in longitudinal and transverse phase matching.

Fig 1. (a) Schematic illustration of the A-NPCs fabricated by femtosecond laser micromachining. (b) A comparison between simulation, fabricated, and SH image of the CGH patterns in the HG10, HG11, and HG12 structures, respectively.

In experiments, we fabricated computer-generated holograms (CGHs) in lithium niobate crystal with specific cutting angle by femtosecond laser micromachining, as shown in Fig 1(a). The quadratic nonlinear susceptibility χ^((2) ) of the crystal was erased, since the crystallinity is reduced through laser irradiation domain, while the unirradiated domain remained unchanged. Then the crystal with the geometric specific pattern of 0 or +1 binary modulation of the quadratic nonlinear susceptibility χ^((2) ) has been fabricated. To demonstrate the nonlinear beam shaping with A-NPCs, we chose to fabricate a crystal aimed to generate three modes from the Hermite-Gaussian (HG) family, HG10, HG11, and HG12, as shown in Fig 1(b).

The A-NPCs were pumped by a Nd: YAG laser with the wavelength of 1064nm, as shown in Fig 2(a). The beam shaping patterns can be achieved in the first diffraction order in the far-field, as shown in Fig 2(b). Since the phase-matching condition is fulfilled through the birefringence and nonlinear Raman-Nath effect in longitudinal and transverse phase matching, The normalized conversion efficiency in the +1 first diffraction order we calculated is
8.4%W-1cm-2. We also had demonstrated the generating of nonlinear vortex beams with the fork grating structure in Fig 2(c). This work provides an efficient second harmonic beam shaping method by femtosecond laser micromachining, which will be useful for all-optical shaping, routing, and switching of beams.

Fig 2. (a) Schematic illustration of the nonlinear wavefront shaping setup in A-NPCs. (b) Comparison between theoretical and measured beam profiles at the first diffraction order in the HG10, HG11, and HG12 structures, respectively. (c) The calculated, fabricated, and the far-field experiment result of the fork grating structure for generating the nonlinear vortex beams.

The research was published in“Bing Zhu, Haigang Liu, Yuping Chen*, and Xianfeng Chen, "High conversion efficiency second-harmonic beam shaping via amplitude-type nonlinear photonic crystals," Opt. Lett. 45, 220-223 (2020).”

Link：https://doi.org/10.1364/OL.45.000220