Diffraction of Optical Vortices: The theory and some of applications
Saifollah Rasouli
Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
Abstract: In this work, the theory of diffraction of vortex beams from structured apertures, generation of elegant elliptical vortex Hermite–Gaussian beams, Talbot self-healing under vortex beams illumination, and creation of vortex beam arrays in the Cartesian coordinates are presented. First, with two different approaches, two general analytic studies on the diffraction of vortex beams from structured apertures are introduced. The near- and far-field diffraction of a vortex beam from an aperture having an arbitrary functionality are formulated in the Cartesian coordinates and two comprehensive and different approaches are presented. It is shown that, the form of resulting diffraction pattern from a given aperture under vortex beam illumination can be determined by a number of successive derivatives of 2D Fourier transform of the corresponding hypothetical aperture function or equally can be obtained by a summation of 2D Fourier transforms of the corresponding modified aperture function1. The both introduced analytic approaches are implemented in predicting of the diffraction of a vortex beam from an elliptic Gaussian aperture, an elliptic Gaussian phase mask, and a hyperbolic Gaussian phase mask in the far-field regime. It is shown that the diffraction of a vortex beam from an elliptic Gaussian aperture at the far- filed regime forms a light beam that belongs to a new family of light beams we call as “elegant elliptical vortex Hermite–Gaussian (vHG) beams” 1. The presented general analytic formula can be used for a large variety of apertures.
Using the presented general formulation, the diffraction of vortex beams from 2D periodic structures are investigated in the near-field regime, especially at the Talbot planes of the structures. It is shown that at the self-image planes vortex beam arrays may be created, and conditions of vortex beam arrays creation are derived2,3. In addition, it is shown that the modality of the Talbot self-healing effect depends to the profile of the aperture and illuminating beam structure3. We believe that the Talbot effect-based generation of vortex beam arrays might find more applications in optical tweezers, micromanipulations, and microfluidics.
Finally, it is shown that, the diffraction of vortex beams from radial gratings represents beautiful physical aspects, such as energy flow to the dark central region of the diffracting beam, which is similar to the effect of the Poisson-Arago spot.
The diffraction of a vortex beam from a radial grating also provides a simple, in situ, and two-level intensity-based method for determining the topological charge of the incident beam and provides a method for data transferring with the aid of radial carpet beams4,5.
Keywords: Optical vortices; Diffraction and gratings; Singular optics; Spatial light modulators; Laser beam shaping; Talbot and self-imaging effects; Optical tweezers or optical manipulation.
References:
1. D. Hebri and S. Rasouli, "Diffraction from two-dimensional orthogonal nonseparable periodic structures: Talbot distance dependence on the number theoretic properties of the structures," J. Opt. Soc. Am. A 36, 253-263, 2019.
2. D. Hebri, S. Rasouli, and A. M. Dezfouli, "Theory of diffraction of vortex beams from structured apertures and generation of elegant elliptical vortex Hermite–Gaussian beams," J. Opt. Soc. Am. A 36, 839-852, 2019.
3. S. Rasouli and D. Hebri, “Generation of two-dimensional arrays of optical vortices,” submitted 2019.
4. D. Hebri, S. Rasouli, and M. Yeganeh, “Intensity based measuring of the topological charge alteration by the diffraction of vortex beams from amplitude sinusoidal radial gratings,” J. Opt. Soc. Am. B 35, 724-730, 2018.
5. M. K. Karahroudi, M. K. Karahroudi, A. Mobashery, and B. Parmoon, "Information transmission using radial carpet beams," Appl. Opt. 58(8), 1886-1894 (2019).
