Abstract

We show that it is possible to find and characterise optical vortices in a speckle pattern using a multi-pinhole interferometer. This measurement does not require an additional flat wave front to interfere with the speckle, providing great experimental ease. In addition, a multi-pinhole interferometer can be made arbitrarily large and can therefore be adjusted to the expected speckle size. We present experimental results confirming our understanding.

© 2010 OSA

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References

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  1. J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145–1150 (1976).
    [CrossRef]
  2. J. W. Goodman, Speckle phenomena in optics (Roberts & Company, 2006).
  3. J. F. Nye, and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336, 165–190 (1974).
    [CrossRef]
  4. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [CrossRef] [PubMed]
  5. N. B. Baranova, V. I. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous fiel (theory and experiment),” JETP Lett. 33, 195–199 (1981).
  6. I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
    [CrossRef]
  7. D. Rozas, C. T. Law, and G. A. Swartzlander, Jr., “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997).
    [CrossRef]
  8. G. Molina-Terriza, E. M. Wright, and L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26, 163–165 (2001).
    [CrossRef]
  9. W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902 (2005).
    [CrossRef] [PubMed]
  10. K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, “Fractality of light’s darkness,” Phys. Rev. Lett. 100, 053902 (2008).
    [CrossRef] [PubMed]
  11. I. Freund, “Optical vortices in Gaussian random wave fields statistical probability densities,” J. Opt. Soc. Am. A 11, 1644–1652 (1994).
    [CrossRef]
  12. M. R. Dennis, “Local phase structure of wave dislocation lines: twist and twirl,” J. Opt. A 6, S202–S208 (2004).
  13. D. L. Fried, and J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992).
    [CrossRef] [PubMed]
  14. D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998).
    [CrossRef]
  15. M. Harwit, “Photon orbital angular momentum in astrophysics,” Astrophys. J. 597, 1266–1270 (2003).
    [CrossRef]
  16. N. M. Elias, “Photon orbital angular momentum in astronomy,” Astron. Astrophys. 492, 883–922 (2008).
    [CrossRef]
  17. G. C. G. Berkhout, and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
    [CrossRef] [PubMed]
  18. C.-S. Guo, S.-J. Yue, and G.-X. Wei, “Measuring the orbital angular momentum of optical vortices using a multipinhole plate,” Appl. Phys. Lett. 94, 231104 (2009).
    [CrossRef]
  19. R. W. Schoonover, and T. D. Visser, “Creating polarization singularities with an N-pinhole interferometer,” Phys. Rev. A 79, 043809 (2009).
    [CrossRef]
  20. G. C. G. Berkhout, and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A 11, 094021 (2009).

2009

C.-S. Guo, S.-J. Yue, and G.-X. Wei, “Measuring the orbital angular momentum of optical vortices using a multipinhole plate,” Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

R. W. Schoonover, and T. D. Visser, “Creating polarization singularities with an N-pinhole interferometer,” Phys. Rev. A 79, 043809 (2009).
[CrossRef]

G. C. G. Berkhout, and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A 11, 094021 (2009).

2008

K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, “Fractality of light’s darkness,” Phys. Rev. Lett. 100, 053902 (2008).
[CrossRef] [PubMed]

N. M. Elias, “Photon orbital angular momentum in astronomy,” Astron. Astrophys. 492, 883–922 (2008).
[CrossRef]

G. C. G. Berkhout, and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef] [PubMed]

2005

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

2004

M. R. Dennis, “Local phase structure of wave dislocation lines: twist and twirl,” J. Opt. A 6, S202–S208 (2004).

2003

M. Harwit, “Photon orbital angular momentum in astrophysics,” Astrophys. J. 597, 1266–1270 (2003).
[CrossRef]

2001

1998

1997

1994

1993

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
[CrossRef]

1992

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

D. L. Fried, and J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992).
[CrossRef] [PubMed]

1981

N. B. Baranova, V. I. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous fiel (theory and experiment),” JETP Lett. 33, 195–199 (1981).

1976

1974

J. F. Nye, and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336, 165–190 (1974).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Baranova, N. B.

N. B. Baranova, V. I. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous fiel (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Beijersbergen, M. W.

G. C. G. Berkhout, and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A 11, 094021 (2009).

G. C. G. Berkhout, and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Berkhout, G. C. G.

G. C. G. Berkhout, and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A 11, 094021 (2009).

G. C. G. Berkhout, and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef] [PubMed]

Berry, M. V.

J. F. Nye, and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336, 165–190 (1974).
[CrossRef]

Dennis, M. R.

K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, “Fractality of light’s darkness,” Phys. Rev. Lett. 100, 053902 (2008).
[CrossRef] [PubMed]

M. R. Dennis, “Local phase structure of wave dislocation lines: twist and twirl,” J. Opt. A 6, S202–S208 (2004).

Elias, N. M.

N. M. Elias, “Photon orbital angular momentum in astronomy,” Astron. Astrophys. 492, 883–922 (2008).
[CrossRef]

Flossmann, F.

K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, “Fractality of light’s darkness,” Phys. Rev. Lett. 100, 053902 (2008).
[CrossRef] [PubMed]

Freilikher, V.

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
[CrossRef]

Freund, I.

I. Freund, “Optical vortices in Gaussian random wave fields statistical probability densities,” J. Opt. Soc. Am. A 11, 1644–1652 (1994).
[CrossRef]

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
[CrossRef]

Fried, D. L.

Goodman, J. W.

Guo, C.-S.

C.-S. Guo, S.-J. Yue, and G.-X. Wei, “Measuring the orbital angular momentum of optical vortices using a multipinhole plate,” Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Hanson, S. G.

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

Harwit, M.

M. Harwit, “Photon orbital angular momentum in astrophysics,” Astrophys. J. 597, 1266–1270 (2003).
[CrossRef]

Law, C. T.

Mamaev, A. V.

N. B. Baranova, V. I. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous fiel (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Miyamoto, Y.

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

Molina-Terriza, G.

Nye, J. F.

J. F. Nye, and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336, 165–190 (1974).
[CrossRef]

O’Holleran, K.

K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, “Fractality of light’s darkness,” Phys. Rev. Lett. 100, 053902 (2008).
[CrossRef] [PubMed]

Padgett, M. J.

K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, “Fractality of light’s darkness,” Phys. Rev. Lett. 100, 053902 (2008).
[CrossRef] [PubMed]

Pilipetskii, N. F.

N. B. Baranova, V. I. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous fiel (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Rozas, D.

Schoonover, R. W.

R. W. Schoonover, and T. D. Visser, “Creating polarization singularities with an N-pinhole interferometer,” Phys. Rev. A 79, 043809 (2009).
[CrossRef]

Shkunov, V. V.

N. B. Baranova, V. I. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous fiel (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Shvartsman, N.

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Swartzlander, G. A.

Takeda, M.

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

Torner, L.

Vaughn, J. L.

Visser, T. D.

R. W. Schoonover, and T. D. Visser, “Creating polarization singularities with an N-pinhole interferometer,” Phys. Rev. A 79, 043809 (2009).
[CrossRef]

Wang, W.

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

Wei, G.-X.

C.-S. Guo, S.-J. Yue, and G.-X. Wei, “Measuring the orbital angular momentum of optical vortices using a multipinhole plate,” Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Wright, E. M.

Yue, S.-J.

C.-S. Guo, S.-J. Yue, and G.-X. Wei, “Measuring the orbital angular momentum of optical vortices using a multipinhole plate,” Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Zel’dovich, V. I.

N. B. Baranova, V. I. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous fiel (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Appl. Opt.

Appl. Phys. Lett.

C.-S. Guo, S.-J. Yue, and G.-X. Wei, “Measuring the orbital angular momentum of optical vortices using a multipinhole plate,” Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Astron. Astrophys.

N. M. Elias, “Photon orbital angular momentum in astronomy,” Astron. Astrophys. 492, 883–922 (2008).
[CrossRef]

Astrophys. J.

M. Harwit, “Photon orbital angular momentum in astrophysics,” Astrophys. J. 597, 1266–1270 (2003).
[CrossRef]

J. Opt. A

G. C. G. Berkhout, and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A 11, 094021 (2009).

M. R. Dennis, “Local phase structure of wave dislocation lines: twist and twirl,” J. Opt. A 6, S202–S208 (2004).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

JETP Lett.

N. B. Baranova, V. I. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous fiel (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Opt. Commun.

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
[CrossRef]

Opt. Lett.

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

R. W. Schoonover, and T. D. Visser, “Creating polarization singularities with an N-pinhole interferometer,” Phys. Rev. A 79, 043809 (2009).
[CrossRef]

Phys. Rev. Lett.

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, “Fractality of light’s darkness,” Phys. Rev. Lett. 100, 053902 (2008).
[CrossRef] [PubMed]

G. C. G. Berkhout, and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci.

J. F. Nye, and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336, 165–190 (1974).
[CrossRef]

Other

J. W. Goodman, Speckle phenomena in optics (Roberts & Company, 2006).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic drawing of the setup that is used to measure optical vortices in a speckle pattern. A helium-neon laser (HeNe), appropriately attenuated with a neutral density filter wheel (FW), and two mirrors (M1 and M2) are used to illuminate a small part of a light shaping diffusor (LSD) which creates the speckle pattern. At a sufficiently large distance to guarantee fully developed speckle, a multi-pinhole interferometer (MPI), a lens (L) and a CCD camera (CCD) are placed on a translation stage (TS) that can be moved in the x and y-direction. Several multi-pinhole interferometers with different number of pinholes, pinhole separation and pinhole diameter are combined on a single optical component and a diaphragm (D) is used to select one.

Fig. 2.
Fig. 2.

Interference patterns behind the multi-pinhole interferometer recorded at two different positions in the speckle pattern. (a) shows the interference pattern at relative position x = 0mm, a region of high field intensity. (b) shows the interference pattern at relative position x = 1mm, a region of low field intensity. The changing pattern is explained by an optical vortex impinging the multi-pinhole interferometer in (b). The size of each pixel in the CCD image is 6.5µm and both images contain 1392 × 1040 pixels. Both images are recorded using the same settings of the CCD-camera and are normalised to the peak intensity of image (a), allowing a direct comparison of the total intensities in the images.

Fig. 3.
Fig. 3.

(a) Phase of the Fourier transform of the interference pattern in Fig. 2 (b). As a guide to the eye the positions where the relative phase is read off are shown as the vertices of the white pentagon. The same pentagon can be drawn in ten different orientations. (b) shows the average phase at the individual pinholes ψ calculated from the ten different orientations as a function of the azimuthal angle ϕ. The dotted lines are drawn as a guide to the eye and indicate the relative phases for optical vortices of topological charge l = 2, 1, 0, −1, −2 from top to bottom.

Fig. 4.
Fig. 4.

(a) Normalised total intensity in the recorded interference patterns as a function of multi-pinhole interferometer position x. Since this intensity is proportional to the intensity in a small ring around the vortices, it is expected not to go to zero. (b) Vorticity of the field impinging the multi-pinhole interferometer as calculated using the Fourier transform analysis. The two minima in (a) clearly correspond to optical vortices of opposite sign.

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