The interference contrast in a near-field diffraction pattern can be improved using an asymmetric grating with a small grating window. However, commercial asymmetrically shaped gratings are not available. Here, we report a method that overlaps two gratings to produce an arbitrary open fraction in the combination grating. Both theoretical simulation and experimental observations of the near-field Talbot effect are provided to validate this concept. A characterization of optical vortices is also used as a demonstration of potential applications. This method is simple and can improve the resolution in metrology with optical sensors.

In a prior report the optical vortex was characterized using the near-field Talbot effect [1, 2]. This near-field technique can resolve both order and charge of the orbital angular momentum state of the vortex beam. We have proposed before that a small open fraction of the grating in the Talbot configuration can improve the image contrast [3]. In this study, we combine these previously reported techniques, i.e. the Talbot effect for probing an optical vortex and overlapping gratings to manipulate the open fraction. Both theoretical simulation and experimental demonstration are presented here. We believe that our technique can be an alternative method for optical vortex imaging, and could be useful in optical applications.

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Higher orders of orbital angular momentum states (OAMs) of light have been produced with a double-pass configuration through a zero-order vortex half-wave retarder (VHWR). This double-pass technique can reduce the number of VHWR plates used, thus reducing costs. The OAM states of the vortex beams are identified by the near-field Talbot effect. Polarization dependence of the vortex states can also be demonstrated with this VHWR using Talbot effect. Without using the Talbot patterns, this effect of the polarization on the vortex beam can not be recognized. A theoretical validation has also been provided to complement the experimental results. Our study gives an improved understanding of this approach to use a VHWR plate.

A simplified explanation of near-field and far-field diffraction with matter-wave is described using the path integral formulation. Our approach is demonstrated with cold Rb atoms in single-, double-, and multiple-slit configurations. With the use of an initial wave for the particle beam that corresponds to the slit opening and the number of slits, the transition from near-field to far-field diffraction can also be explored. Identifying the boundary between near-field and far-field diffraction is the first priority for implementing matter-wave diffraction experiments.