Abstract

We have experimentally generated higher order optical vortices and scattered them through a ground glass plate that results in speckle formation. Intensity autocorrelation measurements of speckles show that their size decreases with an increase in the order of the vortex. It implies an increase in the angular diameter of the vortices with their order. The characterization of vortices in terms of their annular bright ring also helps us to understand these observations. The results may find applications in stellar intensity interferometry and thermal ghost imaging.

© 2014 Optical Society of America

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  1. J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 336, 165 (1974).
    [CrossRef]
  2. J. E. Curtis and D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
    [CrossRef]
  3. A. Kumar, P. Vaity, Y. Krishna, and R. P. Singh, Opt. Lasers Eng. 48, 276 (2010).
    [CrossRef]
  4. L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (IOP, 2003).
  5. B. Thide, H. Then, J. Sjoholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, Phys. Rev. Lett. 99, 087701 (2007).
    [CrossRef]
  6. G. M. Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
    [CrossRef]
  7. A. Kumar, J. Banerji, and R. P. Singh, Opt. Lett. 35, 3841 (2010).
    [CrossRef]
  8. A. Kumar, J. Banerji, and R. P. Singh, Phys. Rev. A 86, 013825 (2012).
    [CrossRef]
  9. S. G. Reddy, A. Kumar, S. Prabhakar, and R. P. Singh, Opt. Lett. 38, 4441 (2013).
    [CrossRef]
  10. J. D. Rigden and E. I. Gordan, Proc. IRE 50, 2367 (1962).
  11. J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).
  12. J. W. Goodman, Speckle Phenomena in Optics (Indian ed., 2008).
  13. R. Sirohi, Optical Methods of Measurements (Marcel Dekker, 1999).
  14. R. H. Brown and R. Q. Twiss, Nature 177, 27 (1956).
    [CrossRef]
  15. S. Crosby, S. Castelletto, C. Aruldoss, R. E. Scholten, and A. Roberts, New J. Phys. 9, 285 (2007).
    [CrossRef]
  16. M. N. O’Sullivan, K. W. C. Chan, and R. W. Boyd, Phys. Rev. A 82, 053803 (2010).
    [CrossRef]
  17. K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, Opt. Express 18, 5562 (2010).
    [CrossRef]

2013 (1)

2012 (1)

A. Kumar, J. Banerji, and R. P. Singh, Phys. Rev. A 86, 013825 (2012).
[CrossRef]

2010 (4)

A. Kumar, J. Banerji, and R. P. Singh, Opt. Lett. 35, 3841 (2010).
[CrossRef]

A. Kumar, P. Vaity, Y. Krishna, and R. P. Singh, Opt. Lasers Eng. 48, 276 (2010).
[CrossRef]

M. N. O’Sullivan, K. W. C. Chan, and R. W. Boyd, Phys. Rev. A 82, 053803 (2010).
[CrossRef]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, Opt. Express 18, 5562 (2010).
[CrossRef]

2007 (3)

S. Crosby, S. Castelletto, C. Aruldoss, R. E. Scholten, and A. Roberts, New J. Phys. 9, 285 (2007).
[CrossRef]

B. Thide, H. Then, J. Sjoholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

G. M. Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

2003 (1)

J. E. Curtis and D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 336, 165 (1974).
[CrossRef]

1962 (1)

J. D. Rigden and E. I. Gordan, Proc. IRE 50, 2367 (1962).

1956 (1)

R. H. Brown and R. Q. Twiss, Nature 177, 27 (1956).
[CrossRef]

Allen, L.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (IOP, 2003).

Aruldoss, C.

S. Crosby, S. Castelletto, C. Aruldoss, R. E. Scholten, and A. Roberts, New J. Phys. 9, 285 (2007).
[CrossRef]

Banerji, J.

A. Kumar, J. Banerji, and R. P. Singh, Phys. Rev. A 86, 013825 (2012).
[CrossRef]

A. Kumar, J. Banerji, and R. P. Singh, Opt. Lett. 35, 3841 (2010).
[CrossRef]

Barnett, S. M.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (IOP, 2003).

Bergman, J.

B. Thide, H. Then, J. Sjoholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Berry, M. V.

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 336, 165 (1974).
[CrossRef]

Boyd, R. W.

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, Opt. Express 18, 5562 (2010).
[CrossRef]

M. N. O’Sullivan, K. W. C. Chan, and R. W. Boyd, Phys. Rev. A 82, 053803 (2010).
[CrossRef]

Brown, R. H.

R. H. Brown and R. Q. Twiss, Nature 177, 27 (1956).
[CrossRef]

Carozzi, T. D.

B. Thide, H. Then, J. Sjoholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Castelletto, S.

S. Crosby, S. Castelletto, C. Aruldoss, R. E. Scholten, and A. Roberts, New J. Phys. 9, 285 (2007).
[CrossRef]

Chan, K. W. C.

M. N. O’Sullivan, K. W. C. Chan, and R. W. Boyd, Phys. Rev. A 82, 053803 (2010).
[CrossRef]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, Opt. Express 18, 5562 (2010).
[CrossRef]

Crosby, S.

S. Crosby, S. Castelletto, C. Aruldoss, R. E. Scholten, and A. Roberts, New J. Phys. 9, 285 (2007).
[CrossRef]

Curtis, J. E.

J. E. Curtis and D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef]

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics (Indian ed., 2008).

Gordan, E. I.

J. D. Rigden and E. I. Gordan, Proc. IRE 50, 2367 (1962).

Grier, D. G.

J. E. Curtis and D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef]

Ibragimov, N. H.

B. Thide, H. Then, J. Sjoholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Istomin, Y. N.

B. Thide, H. Then, J. Sjoholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Khamitova, R.

B. Thide, H. Then, J. Sjoholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Krishna, Y.

A. Kumar, P. Vaity, Y. Krishna, and R. P. Singh, Opt. Lasers Eng. 48, 276 (2010).
[CrossRef]

Kumar, A.

S. G. Reddy, A. Kumar, S. Prabhakar, and R. P. Singh, Opt. Lett. 38, 4441 (2013).
[CrossRef]

A. Kumar, J. Banerji, and R. P. Singh, Phys. Rev. A 86, 013825 (2012).
[CrossRef]

A. Kumar, J. Banerji, and R. P. Singh, Opt. Lett. 35, 3841 (2010).
[CrossRef]

A. Kumar, P. Vaity, Y. Krishna, and R. P. Singh, Opt. Lasers Eng. 48, 276 (2010).
[CrossRef]

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 336, 165 (1974).
[CrossRef]

O’Sullivan, M. N.

M. N. O’Sullivan, K. W. C. Chan, and R. W. Boyd, Phys. Rev. A 82, 053803 (2010).
[CrossRef]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, Opt. Express 18, 5562 (2010).
[CrossRef]

Padgett, M. J.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (IOP, 2003).

Palmer, K.

B. Thide, H. Then, J. Sjoholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Prabhakar, S.

Reddy, S. G.

Rigden, J. D.

J. D. Rigden and E. I. Gordan, Proc. IRE 50, 2367 (1962).

Roberts, A.

S. Crosby, S. Castelletto, C. Aruldoss, R. E. Scholten, and A. Roberts, New J. Phys. 9, 285 (2007).
[CrossRef]

Scholten, R. E.

S. Crosby, S. Castelletto, C. Aruldoss, R. E. Scholten, and A. Roberts, New J. Phys. 9, 285 (2007).
[CrossRef]

Singh, R. P.

S. G. Reddy, A. Kumar, S. Prabhakar, and R. P. Singh, Opt. Lett. 38, 4441 (2013).
[CrossRef]

A. Kumar, J. Banerji, and R. P. Singh, Phys. Rev. A 86, 013825 (2012).
[CrossRef]

A. Kumar, J. Banerji, and R. P. Singh, Opt. Lett. 35, 3841 (2010).
[CrossRef]

A. Kumar, P. Vaity, Y. Krishna, and R. P. Singh, Opt. Lasers Eng. 48, 276 (2010).
[CrossRef]

Sirohi, R.

R. Sirohi, Optical Methods of Measurements (Marcel Dekker, 1999).

Sjoholm, J.

B. Thide, H. Then, J. Sjoholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Terriza, G. M.

G. M. Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Then, H.

B. Thide, H. Then, J. Sjoholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Thide, B.

B. Thide, H. Then, J. Sjoholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Torner, L.

G. M. Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Torres, J. P.

G. M. Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Twiss, R. Q.

R. H. Brown and R. Q. Twiss, Nature 177, 27 (1956).
[CrossRef]

Vaity, P.

A. Kumar, P. Vaity, Y. Krishna, and R. P. Singh, Opt. Lasers Eng. 48, 276 (2010).
[CrossRef]

Nat. Phys. (1)

G. M. Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Nature (1)

R. H. Brown and R. Q. Twiss, Nature 177, 27 (1956).
[CrossRef]

New J. Phys. (1)

S. Crosby, S. Castelletto, C. Aruldoss, R. E. Scholten, and A. Roberts, New J. Phys. 9, 285 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

A. Kumar, P. Vaity, Y. Krishna, and R. P. Singh, Opt. Lasers Eng. 48, 276 (2010).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (2)

A. Kumar, J. Banerji, and R. P. Singh, Phys. Rev. A 86, 013825 (2012).
[CrossRef]

M. N. O’Sullivan, K. W. C. Chan, and R. W. Boyd, Phys. Rev. A 82, 053803 (2010).
[CrossRef]

Phys. Rev. Lett. (2)

B. Thide, H. Then, J. Sjoholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

J. E. Curtis and D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef]

Proc. IRE (1)

J. D. Rigden and E. I. Gordan, Proc. IRE 50, 2367 (1962).

Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 336, 165 (1974).
[CrossRef]

Other (4)

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (IOP, 2003).

J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).

J. W. Goodman, Speckle Phenomena in Optics (Indian ed., 2008).

R. Sirohi, Optical Methods of Measurements (Marcel Dekker, 1999).

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Figures (9)

Fig. 1.
Fig. 1.

Experimental setup for the generation and recording of speckles from optical vortices.

Fig. 2.
Fig. 2.

(a) Obtained speckle pattern of first order optical vortex, (b) the distribution of auto correlation function, (c) and (d) are the variations in autocorrelation function in both transverse directions X and Y, respectively.

Fig. 3.
Fig. 3.

Speckle patterns formed by the vortices with orders m=05 at a given plane.

Fig. 4.
Fig. 4.

Plot of lnS versus lnAm, where S and Am are the experimentally obtained speckle size and area of the bright region of the optical vortices, respectively. (The inset shows the same plot for a Gaussian beam with different areas.) The solid line is the best fit for our experimental data.

Fig. 5.
Fig. 5.

Plot of divergence of the speckle fields versus order of vortices.

Fig. 6.
Fig. 6.

Transverse intensity distribution of an optical vortex of order 1 and its line profile.

Fig. 7.
Fig. 7.

Numerically obtained values of χ2+χ1 (filled squares) and the line y=m+1.3 as a function of m.

Fig. 8.
Fig. 8.

Line profiles along the vortex centres of optical vortices for orders 0 to 5 that are produced in the laboratory.

Fig. 9.
Fig. 9.

Experimental and theoretical results showing the variation of (a) inner and outer radii and (b) area of bright annular region with the order of a vortex.

Tables (1)

Tables Icon

Table 1. Numerical Solutions of Eqs. (3a) and (3b)

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

Em(r)=(x+iy)mexp(x2+y2w02)
Im(r)=r2mexp(2r2w02),r2=x2+y2.
χ1mexp(2χ1)=χ0mexp(2χ02),
χ2mexp(2χ2)=χ0mexp(2χ02).
χ2+χ1=m+1.3.
χ2χ1=qm,qm=(m+1.3)2m2exp(1.4/m).
r1=(m+1.3qm)1/2/2,
r2=(m+1.3+qm)1/2/2.
Am=π(χ2χ1)=πqm,

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