A study of optical vortices with the Talbot effect

Abstract

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.

Two-dimensional Talbot effect of the optical vortices and their spatial evolution

“…As can be seen in Fig. 2 (top row), the measured intensity distributions (profiles) for the TC l = +1 consist of well-ordered 2D annular beamlet arrays with the ring-shaped maxima for all the Talbot planes, which differs from 1D case, where linear array of stripes is observed 31 . These maxima suffer from distortions caused by the weak intensity at the center of the incident annular beam.…”

“…This phenomenon is well-studied, both theoretically and experimentally, for plane waves 33 and theoretically investigated for the beams comprising phase singularities 20,34,35 . In the experiment, the Talbot effect of the OAM-carrying beams was observed in the 1D case 31 , as well as for the two-dimensional configuration at the THz radiation 35,36 and near-infrared single photons 37 . In the 1D case 31 , the experimental intensity patterns were in the form of a periodic set of stripes, while for two-dimensional configuration there is an array of beams with a topological charge.…”

“…In the experiment, the Talbot effect of the OAM-carrying beams was observed in the 1D case 31 , as well as for the two-dimensional configuration at the THz radiation 35,36 and near-infrared single photons 37 . In the 1D case 31 , the experimental intensity patterns were in the form of a periodic set of stripes, while for two-dimensional configuration there is an array of beams with a topological charge. The Talbot effect was explored using a superposition of two optical lattices generated by a superposition of two quasi-OAM states in 38 and exploited for generating optical vortex arrays by multiplexing metasurface design 22 .…”

“…In this connection, it is reasonable to examine the near-field diffraction of the OAM-carrying beams at a 2D amplitude diffraction grating. It should be noted that the diffraction of the OAM-carrying beams was studied for the cases of a single slit 28,29 , sector-shaped diaphragm 30 , and 1D gratings 31 . It is well-known that a plane wave incident onto a periodic grating is diffracted such that the Talbot effect occurs in the near-field 32 .…”

Experimental demonstration of twisted light’s diffraction theory based on digital spiral imaging

“…In addition, the rich relationship between light OAM and the far-field diffraction phenomena of single-slit [28][29][30][31] , double-slit [32] , triangular [33][34][35][36] , and multiple point-like apertures [37] has been exploited before. The Talbot effect has also been recently used to explore the topological charges of optical vortices in the near-field regime [38] . Sepcifically, in 2010, Hickmann et al [33] successfully demonstrated a very elegant way to directly reveal the magnitude and sign of the topological charge of light via observing the optical lattices diffracted by a triangular aperture.…”