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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 16 — Jul. 30, 2012
  • pp: 18209–18223

Analytical light scattering and orbital angular momentum spectra of arbitrary Vogel spirals

Luca Dal Negro, Nate Lawrence, and Jacob Trevino  »View Author Affiliations

Optics Express, Vol. 20, Issue 16, pp. 18209-18223 (2012)

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In this paper, we present a general analytical model for light scattering by arbitrary Vogel spiral arrays of circular apertures illuminated at normal incidence. This model suffices to unveil the fundamental mathematical structure of their complex Fraunhofer diffraction patterns and enables the engineering of optical beams carrying multiple values of orbital angular momentum (OAM). By performing analytical Fourier-Hankel decomposition of spiral arrays and far field patterns, we rigorously demonstrate the ability to encode specific numerical sequences onto the OAM values of diffracted optical beams. In particular, we show that these OAM values are determined by the rational approximations (i.e., the convergents) of the continued fraction expansions of the irrational angles utilized to generate Vogel spirals. These findings open novel and exciting opportunities for the manipulation of complex OAM spectra using dielectric and plasmonic aperiodic spiral arrays for a number of emerging engineering applications in singular optics, secure communication, optical cryptography, and optical sensing.

© 2012 OSA

OCIS Codes
(350.4600) Other areas of optics : Optical engineering
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Diffraction and Gratings

Original Manuscript: June 4, 2012
Revised Manuscript: July 18, 2012
Manuscript Accepted: July 20, 2012
Published: July 24, 2012

Luca Dal Negro, Nate Lawrence, and Jacob Trevino, "Analytical light scattering and orbital angular momentum spectra of arbitrary Vogel spirals," Opt. Express 20, 18209-18223 (2012)

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