Fractional second-harmonic Talbot effect

Perfect Talbot self-imaging effect of aperiodic gratings

We propose and investigate a class of aperiodic grating structure which can achieve perfect Talbot effect under certain conditions. The aperiodic grating structure is obtained by the superposition of two or more sine terms. In the case of two sine terms, the Talbot effect can be realized when the period ratio of two terms is arbitrary. While in the case of more than two sine terms, the period ratios of each term must meet certain extra conditions. The theory has been further verified by numerical simulations. It expands the field of Talbot effect and is of potential significance for subsequent research applications such as optical imaging and measurement.

Dynamic manipulation of nonlinear Talbot effect with structured light

The nonlinear Talbot effect has sparked considerable interest of researchers since it was proposed in recent years because it has many advantages compared with the Talbot effect in linear optics. In previous researches, such a nonlinear Talbot effect is only observed in nonlinear photonic crystals, which cannot dynamically manipulate in real time. Here, we report and experimentally demonstrate the high efficiency and dynamic manipulation of such a nonlinear Talbot effect with structured light. Different from the previous scheme, the nonlinear self-imaging effect observed in our experiment originates from the spatial phase structure of the incident fundamental frequency light. In our experiments, integer and fractional second-harmonic Talbot self-imaging is observed. Our results not only extend a novel technique for dynamic manipulation of the nonlinear Talbot effects, but also may have potential applications in parallel optical lithography, optical imaging, and optical computing.

Evolution of the nonlinear Raman-Nath diffraction from near field to far field

In this Letter, we studied the near-field effect of the nonlinear Raman-Nath diffraction experimentally in a 1D periodically poled LiTaO₃ crystal and established a theoretical relationship between the nonlinear effect in the near field and the corresponding effect in the far field. The interference of far-field spots in the near field constitutes the nonlinear Talbot self-imaging effect. Our results not only enhance our understanding of the nonlinear Talbot effect, but they also indicate potential applications of this effect in domain inspection and domain design.

Discrete Talbot effect in two-dimensional waveguide arrays

We theoretically study discrete Talbot self-imaging in hexagonal, square, and irregular two-dimensional waveguide arrays. Different from its counterpart in a continuous system, the periods of the input fields must belong to {1, 2, 3, 4, 6} for Talbot self-imaging. Also, the combinations of the input periods cannot be 3 & 4, or 4 & 6 along two different directions, which distinguishes itself from the one-dimensional discrete Talbot effect.

Diffraction interference induced superfocusing in nonlinear Talbot effect

We report a simple, novel subdiffraction method, i.e. diffraction interference induced superfocusing in second-harmonic (SH) Talbot effect, to achieve focusing size of less than λSH/4 (or λpump/8) without involving evanescent waves or subwavelength apertures. By tailoring point spread functions with Fresnel diffraction interference, we observe periodic SH subdiffracted spots over a hundred of micrometers away from the sample. Our demonstration is the first experimental realization of the Toraldo di Francia's proposal pioneered 62 years ago for superresolution imaging.

Quasi-phase-matched second-harmonic Talbot self-imaging in a 2D periodically-poled LiTaO3 crystal

We demonstrate the improved second-harmonic Talbot self-imaging through the quasi-phase-matching technique in a 2D periodically-poled LiTaO(3) crystal. The domain structure not only composes a nonlinear optical grating which is necessary to realize nonlinear Talbot self-imaging, but also provides reciprocal vectors to satisfy the phase-matching condition for second-harmonic generation. Our experimental results show that quasi-phase-matching can improve the intensity of the second-harmonic Talbot self-imaging by a factor of 21.