In 2018, research groups from Nanjing University and University of Science and Technology of China successfully prepared the three-dimensional(3D) nonlinear photonic crystal ( NPC ) for the first time in the LiNbO3 crystal using femtosecond -laser-processing technique. They also verified the 3D quasi-phase match (QPM) and broke through the bottleneck of preparing 3D NPC. Recently, they applied 3D NPC to high-efficiency nonlinear beam shaping for the first time, which improved the conversion efficiency of the generated second-harmonic ( SH ) beam up two orders of magnitude compared to conventional 2D nonlinear beam shaping. The manuscript titled as Efficient Nonlinear Beam Shaping in Three-dimensional Lithium Niobate Nonlinear Photonic Crystals is published on Nature Communications 10, 4193 (2019).
The nonlinear beam shaping technique in the nonlinear photonic crystal can perform frequency conversion and wavefront manipulation at the same time. Nonlinear focal spots, nonlinear vortex beams and nonlinear non-diffracting beams can be generated as well. Previously, limited by the modulation dimensions of one-dimensional ( 1D ) and two-dimensional ( 2D ) nonlinear photonic crystals, phase matching usually is difficult to be realized in nonlinear beam shaping, as a result of which the nonlinear conversion efficiency is low. In 3D nonlinear photonic crystals, full 3D nonlinear coefficient modulation makes high-efficiency nonlinear beam shaping possible.
Utilizing the three degrees of freedom of the three-dimensional NPC and through the design scheme of nonlinear holography and periodic array, high-efficiency nonlinear beam shaping can be achieved. Take LiNbO3 crystal as an example, the conventional fullwavefront modulation is realized by 2D binary phase modulation in the x-y plane of the crystal through polarization and other methods (Fig. 1a). When the fundamental light passes through the crystal in the z direction, the SH light after shaping can be obtained. However, due to the phase mismatch and the smaller d22value, the conversion efficiency of 1mm crystals is usually lower than 1 × 10-6. In this research, researchers employed thefemtosecond-laser-processing technique to prepare three-dimensional nonlinear photonic crystals in LiNbO3 (Fig. 1b). In order to utilize the maximum nonlinear coefficient d33 of LiNbO3, the phase modulation was performed in the x-z plane and the periodic distribution along y direction provided additional reciprocal vectors to compensate for the reciprocal lattice mismatch of fundamental light and SH light, thereby achieving QPM and obtaining high conversion efficiency.
Figure 1 Design principle of 3D NPCs.
a Nonlinear Raman-Nath diffraction orders generated when a fundamental beam is incident on a 2D nonlinear fork-grating NPC and vector mismatches for various diffraction orders.
b Schematic diagram of the second-order Raman-Nath diffraction after the fundamental wave passes through the 3D nonlinear fork-grating NPC and the wave vector match on the second order
To verify this theory, the researchers designed a 3D NPC in a 5% MgO-doped LiNbO3 single crystal, which was used to generate SH vortex beams and Hermite Gaussian (HG) beams respectively. Fig. 2 shows a 3D nonlinear fork-grating and efficient generation of SH vortex beams carrying different topological charges (TCs). Fig. 2a shows the SH confocal microscopic diagram of structure, the structure size is 45μm (x) × 45μm (y) × 45μm (z), where the modulation period of the x direction and y direction both are 3μm. The provided reciprocal vector Gx = Gy = 2π / 3μm-1. When the fundamental light is incident in the y direction of the crystal and the polarization direction is in the z direction, the corresponding theoretical values of QPM wavelengths of ± 1, ± 2, and ± 3 diffraction orders are 819 nm, 801 nm, and 776 nm respectively. Fig. 3a shows the dependence of the SH wave intensity of different orders with the changing wavelength of the fundamental wave when the intensity of the fundamental wave is unchanged. It can be observed different diffraction orders of SH vortex beams are phase matched at 820 nm, 802 nm, and 781 nm, which agree well with the theoretical values. At the same time, it could be seen that vortex lights with TCs of ± 1, ± 2, and ± 3 are obtained on the ± 1, ± 2, and ± 3 orders, respectively (Fig. 2b-2d). Fig. 3b shows the dependence of the intensity of SH wave with the intensity of the fundamental wave at the phased matched wavelengths of different orders. When the fundamental power is 1.2W, the SH conversion efficiency of ± 1, ± 2, and ± 3 diffraction orders can reach 2.8 × 10-5, 2.7 × 10-5, and 0.44 × 10-5 respectively.
Figure 2 Far-field diffraction patterns of the 3D nonlinear fork-grating array.
a The 3D NPC structures in the x–z and x–y planes through a confocal SH microscopic system b–d Raman-Nath diffraction patterns at 820nm, 802nm, and 781nm fundamental waves corresponding to ± 1, ± 2, ± 3 diffraction orders enhancements.
Figure 3 SH conversion efficiency of 3D fork-grating.
a Dependence of SHwave intensity with the fundamental wavelength.
b Dependence of SH wave intensity with fundamental wave intensity
In addition to the 3D fork-grating, the researchers also designed a NPC structure that can convert the fundamental Gaussian beams to the HG beams. Fig. 4a shows the 3D schematic diagram of the structure and the x-z cross-sectional view obtained by the SH confocal microscope. The structure size is 32μm (x) × 90μm (y) × 32μm (z), where there are 30 cycles in the y direction with a period of 3μm. The theoretical value of the first diffraction order match wavelength is 819 nm. The dependence of the intensity of the SH wave with the wavelength of the fundamental wave is shown in Fig. 4c. The actual match wavelength of the first diffraction order is 818 nm, which is in good agreement with the theoretical value. The fundamental wave of 818nm is incident in the y direction of the crystal, and the far-field diffraction shows that the HG (1,1) mode appears on the ± 1 diffraction order (Fig. 4b). Fig. 4d shows the relationship between the intensity of the SH wave and the intensity of the fundamental wave. When the fundamental wave power is 1.2W, the SH conversion efficiency of the +1 (or -1) diffraction order can reach 3.97 × 10-4.The conversion efficiency is improved up to two orders of magnitude compared to the 2D NPC prepared by electrodeposition.
Figure 4 Generation of HG mode
3D structure diagram and x-z cross-sectional view obtained by the SH confocal microscope;
b. SH diffraction pattern when the fundamental wavelength is 818nm;
c.Dependence of SHwave intensity with the fundamental wavelength.
d. Dependence of SH wave intensity with fundamental wave intensity.
3D NPC’s highly efficient nonlinear beam shaping exhibits its precise 3D manipulation of nonlinear light waves, which can be further extended to 3D nonlinear holography and the generation of high-dimensional photon entangled states. Moreover, the 3D NPC with a size of 100 microns is capable of both frequency conversion and light field manipulation, and it will also be one of the potential choice for integrating light sources on photonic chips.
Nanjing University is the first author affiliation. Dr. Dunzhao Wei, Dr. Chaowei, Wang and Xiaoyi Xu are co-first authors. The corresponding authors are Prof. Yong Zhang, Prof. Dong Wu, and Prof. Min Xiao. This work also received Academician Shining Zhu’s instruction. This research was supported by the National Key R & D Program of China, the National Natural Science Foundation of China, National Laboratory of Solid State Microstructures and the Collaborative Innovation Center of Advanced Microstructures.
(Submitted by Xiaoyi Xu )
