Fig. 1. (a) SH diffraction from a nonlinear χ⁽²⁾ grating. The grating has a periodic variation of the sign of the second-order nonlinear coefficient χ⁽²⁾, which can generate SH waves with uniform amplitude but periodic phase difference of π. (b) Illustrating Talbot self-healing, where the initially missing point (#3) is restored in the first Talbot image plane.

Fig. 2. Experimental setup for nonlinear Talbot self-healing. HW, half-wave plate; P, polarizer; L, lens; S, nonlinear photonic sample; F, short-band-pass filter; G, Glan prism; CMOS, CMOS camera.

Fig. 3. (a) Čerenkov SH microscopic image of the fabricated NPCs with a square lattice. Several lattice points are missing on purpose to serve as the structural defects (marked by the yellow squares). (b) The ferroelectric domain structure imaged on the output surface of the NPC. (c) The SH self-image at the first nonlinear Talbot plane. The missing lattice points are all restored, indicating the nonlinear Talbot self-healing.

Fig. 4. (a) Čerenkov SH microscopic image of the hexagonally poled LiNbO₃ NPCs. The designed defects are several missing lattice points located randomly throughout the sample (marked by the yellow hexagons). (b) The ferroelectric domain structure imaged on the output surface of the NPC. (c) The SH self-image at the first nonlinear Talbot plane, with the missing points being restored.

Fig. 5. (a) Čerenkov SH microscopic image of the LiNbO₃ NPC with sunflower seed pattern. (b) The ferroelectric domain structure imaged on the output surface of the crystal. (c), (d) The SH near-field diffraction patterns imaged at distances of 20 µm and 50 µm from the sunflower pattern.