Fourier relationship between angular position and optical orbital angular momentum

Eric Yao, Sonja Franke-Arnold, Johannes Courtial, Stephen M. Barnett, Miles Padgett

Research output: Contribution to journalArticle

76 Citations (Scopus)

Abstract

We demonstrate the Fourier relationship between angular position and angular momentum for a light mode. In particular we measure the distribution of orbital angular momentum states of light that has passed through an aperture and verify that the orbital angular momentum distribution is given by the complex Fourier-transform of the aperture function. We use spatial light modulators, configured as diffractive optical components, to define the initial orbital angular momentum state of the beam, set the defining aperture, and measure the angular momentum spread of the resulting beam. These measurements clearly confirm the Fourier relationship between angular momentum and angular position, even at light intensities corresponding to the single photon level.
LanguageEnglish
Pages9071-9076
Number of pages5
JournalOptics Express
Volume14
Issue number20
DOIs
Publication statusPublished - 2 Oct 2006

Fingerprint

angular momentum
orbitals
apertures
light modulators
luminous intensity
momentum
photons

Keywords

  • physics
  • optics
  • fourier relationship
  • light
  • photons
  • angular momentum
  • beam
  • aperture

Cite this

Yao, E., Franke-Arnold, S., Courtial, J., Barnett, S. M., & Padgett, M. (2006). Fourier relationship between angular position and optical orbital angular momentum. Optics Express, 14(20), 9071-9076. https://doi.org/10.1364/OE.14.009071
Yao, Eric ; Franke-Arnold, Sonja ; Courtial, Johannes ; Barnett, Stephen M. ; Padgett, Miles. / Fourier relationship between angular position and optical orbital angular momentum. In: Optics Express. 2006 ; Vol. 14, No. 20. pp. 9071-9076.
@article{0dd0882afdf04baf86b66ce85e5c5023,
title = "Fourier relationship between angular position and optical orbital angular momentum",
abstract = "We demonstrate the Fourier relationship between angular position and angular momentum for a light mode. In particular we measure the distribution of orbital angular momentum states of light that has passed through an aperture and verify that the orbital angular momentum distribution is given by the complex Fourier-transform of the aperture function. We use spatial light modulators, configured as diffractive optical components, to define the initial orbital angular momentum state of the beam, set the defining aperture, and measure the angular momentum spread of the resulting beam. These measurements clearly confirm the Fourier relationship between angular momentum and angular position, even at light intensities corresponding to the single photon level.",
keywords = "physics, optics, fourier relationship, light, photons, angular momentum, beam, aperture",
author = "Eric Yao and Sonja Franke-Arnold and Johannes Courtial and Barnett, {Stephen M.} and Miles Padgett",
year = "2006",
month = "10",
day = "2",
doi = "10.1364/OE.14.009071",
language = "English",
volume = "14",
pages = "9071--9076",
journal = "Optics Express",
issn = "1094-4087",
publisher = "Optical Society of America",
number = "20",

}

Yao, E, Franke-Arnold, S, Courtial, J, Barnett, SM & Padgett, M 2006, 'Fourier relationship between angular position and optical orbital angular momentum' Optics Express, vol. 14, no. 20, pp. 9071-9076. https://doi.org/10.1364/OE.14.009071

Fourier relationship between angular position and optical orbital angular momentum. / Yao, Eric; Franke-Arnold, Sonja; Courtial, Johannes; Barnett, Stephen M.; Padgett, Miles.

In: Optics Express, Vol. 14, No. 20, 02.10.2006, p. 9071-9076.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Fourier relationship between angular position and optical orbital angular momentum

AU - Yao, Eric

AU - Franke-Arnold, Sonja

AU - Courtial, Johannes

AU - Barnett, Stephen M.

AU - Padgett, Miles

PY - 2006/10/2

Y1 - 2006/10/2

N2 - We demonstrate the Fourier relationship between angular position and angular momentum for a light mode. In particular we measure the distribution of orbital angular momentum states of light that has passed through an aperture and verify that the orbital angular momentum distribution is given by the complex Fourier-transform of the aperture function. We use spatial light modulators, configured as diffractive optical components, to define the initial orbital angular momentum state of the beam, set the defining aperture, and measure the angular momentum spread of the resulting beam. These measurements clearly confirm the Fourier relationship between angular momentum and angular position, even at light intensities corresponding to the single photon level.

AB - We demonstrate the Fourier relationship between angular position and angular momentum for a light mode. In particular we measure the distribution of orbital angular momentum states of light that has passed through an aperture and verify that the orbital angular momentum distribution is given by the complex Fourier-transform of the aperture function. We use spatial light modulators, configured as diffractive optical components, to define the initial orbital angular momentum state of the beam, set the defining aperture, and measure the angular momentum spread of the resulting beam. These measurements clearly confirm the Fourier relationship between angular momentum and angular position, even at light intensities corresponding to the single photon level.

KW - physics

KW - optics

KW - fourier relationship

KW - light

KW - photons

KW - angular momentum

KW - beam

KW - aperture

UR - http://arxiv.org/PS_cache/physics/pdf/0606/0606142v1.pdf

U2 - 10.1364/OE.14.009071

DO - 10.1364/OE.14.009071

M3 - Article

VL - 14

SP - 9071

EP - 9076

JO - Optics Express

T2 - Optics Express

JF - Optics Express

SN - 1094-4087

IS - 20

ER -

Yao E, Franke-Arnold S, Courtial J, Barnett SM, Padgett M. Fourier relationship between angular position and optical orbital angular momentum. Optics Express. 2006 Oct 2;14(20):9071-9076. https://doi.org/10.1364/OE.14.009071