Talbot effect is formed by the diffraction self-imaging of a periodic structure at certain propagation distance, where self-imaging of a structure is periodically repeated with the Talbot length d^2/λ in the direction of light propagation. Here, d is the structure period, λ is the wavelength of the illuminating light. As an important diffraction phenomenon, it has been widely applied in variety of fields, such as array illuminator, surface plasmon, information coding, and lithography. Compared with the traditional Talbot effect in linear optics, the nonlinear Talbot effect has shorter wavelength, which means it has lower diffraction limit and higher resolution. And the high coherence of the SH wave can be produced in nonlinear Talbot effect, which is a significant condition to generate and utilize higher quality diffraction. However, in previous researches, the nonlinear Talbot effect generated by NPC has an unchangeable SH intensity pattern and the low conversion efficiency owe to the inherent limitation of the NPCs. The methods by using the NPCs also greatly increase the cost and complexity of the experiment.

Here, we propose a new scheme to realize dynamic manipulation of the nonlinear Talbot effect with the structured light. The structure comes from the spatial phase distribution of the fundamental frequency (FF) light. The spatial phase distribution of the FF light can be modulated by a commercial rewritable spatial light modulator (SLM) , which is a more flexible method.

Firstly, we study the nonlinear Talbot effect of the 1D modulation. In our experiment, the modulated period equals to 98 μm. We periodically and sharply modulate the phase from 0 to π/4. we choose the cases with the duty cycles of the phase structure (DFF)=30% and DFF=50% to exhibit in the simulations and experiments. The simulations and experiments of the different planes are extended in Fig. 1.

To further reveal the flexibility, the 2D SH Talbot effect is investigated. The phase structure of the FW is also sharply modulated from 0 to π/4 and we simultaneously set DFFx=DFFy=30% and dx=dy=98 μm, as shown in Fig. 2(a). The simulations and experiments of the different imaging planes are extended in Fig. 2.

图 1 调控占空比为30%的不同成像平面下的仿真：(a) - (e) 和实验：(f) - (j)；调控占空比为50%的不同成像平面下的仿真：(k) - (o) 和实验：(p) - (t)

图 2 二维非线性Talbot效应; (a) FW调制模式；仿真：(b) - (e) 和实验：(f) - (i)

This research was published in “Lin Li, Haigang Liu, and Xianfeng Chen, Dynamic manipulation of nonlinear Talbot effect with structured light, Optics Letters, 46(6), 1281-1284 (2021)”

Link：https://doi.org/10.1364/OL.416988