The optical Talbot effect has been used to explore the topological charges of optical vortices. We recorded the self-imaging of a diffraction grating in the near-field regime with the optical vortex of several topological charges. Our twisted light was generated by a spatial light modulator (SLM). Previous studies showed that interferometric methods can determine the particular orbital angular momentum (OAM) states, but a large number of OAM eigenvalues are difficult to distinguish from the interference patterns. Here, we show that the Talbot patterns can distinguish the charges as well as the OAM of the vortices with high orders. Owing to the high sensitivity and self-imaging of the Talbot effect, several OAM eigenvalues can be distinguished by direct measurement. We check the experimental results with our theory. The present results are useful for classical and quantum metrology as well as future implementations of quantum communications.

We apply the near-field Talbot effect to distinguish, characterize, and detect optical vortices. We perform experiments with single-, double-, multiple-slit, and grating diffraction. High-contrast image detection is achieved with the Talbot effect of a grating, even for higher than l=±1 orbital angular momentum states. Furthermore, we manipulate the vortex beam with different vortex states and use the Talbot effect for detecting. The experimental results are supported by theoretical simulations and demonstrate that the Talbot effect provides an excellent tool for optical vortex detection.

We demonstrate the quantum Talbot effect using a beam of single photons produced by parametric down conversion. In contrast to the previous works, we use a programmable spatial light modulator to behave as a diffraction grating. Thus, the investigation of the Talbot diffraction patterns under the variation of grating structure can be easily performed. The influence of spectral bandwidth of the down-converted photons on the diffraction pattern is also investigated. A theoretical model based on the wave nature of photons is presented to explain the Talbot diffraction patterns under varying conditions. The measured diffraction patterns are in good agreement with the theoretical prediction. We are convinced that our study improves the understanding of the quantum Talbot effect.

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