Abstract

Speckle patterns produced by random optical fields with two (or more) widely different correlation lengths exhibit speckle spots that are themselves highly speckled. Using computer simulations and analytic theory we present results for the point singularities of speckled speckle fields, namely, optical vortices in scalar (one polarization component) fields and C points in vector (two polarization components) fields. In single correlation length fields both types of singularities tend to be more or less uniformly distributed. In contrast, the singularity structure of speckled speckle is anomalous; for some sets of source parameters vortices and C points tend to form widely separated giant clusters, for other parameter sets these singularities tend to form chains that surround large empty regions. The critical point statistics of speckled speckle is also anomalous. In scalar (vector) single correlation length fields phase (azimuthal) extrema are always outnumbered by vortices (C points). In contrast, in speckled speckle fields, phase extrema can outnumber vortices and azimuthal extrema can outnumber C points by factors that can easily exceed 104 for experimentally realistic source parameters.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. J. W. Goodman, Speckle Phenomen In Optics (Roberts & Co., 2007).
  2. M. Berry, J. Phys. A 11, 27 (1978).
    [CrossRef]
  3. B. I. Halperin, Physics of Defects, R.Balian, M.Kleman, and J.-P.Poirier, eds. (North-Holland, 1981), p. 814.
  4. N. B. Baranova, B. Ya Zel'dovich, A. V. Mamaev, N. Pilipetskii, and V. V. Shkukov, JETP Lett. 33, 195 (1981).
  5. F. Liu and G. F. Mazenko, Phys. Rev. B 46, 5963 (1992).
    [CrossRef]
  6. I. Freund, Phys. Rev. E 52, 2348 (1995).
    [CrossRef]
  7. B. W. Roberts, E. Bodenschatz, and J. P. Sethna, Physica D 99, 252 (1996).
    [CrossRef]
  8. I. Freund and D. A. Kesler, Opt. Commun. 124, 321 (1996).
    [CrossRef]
  9. I. Freund, Waves Random Media 8, 119 (1998).
  10. I. Freund and M. Wilkinson, J. Opt. Soc. Am. A 15, 2892 (1998).
    [CrossRef]
  11. M. V. Berry and M. R. Dennis, Proc. R. Soc. London, Ser. A 456, 2059 (2000).
    [CrossRef]
  12. M. V. Berry and M. R. Dennis, Proc. R. Soc. London, Ser. A 457, 141 (2001).
    [CrossRef]
  13. M. R. Dennis, Opt. Commun. 213, 201 (2002).
    [CrossRef]
  14. M. R. Dennis, J. Phys. A 34, L297 (2003).
    [CrossRef]
  15. M. S. Soskin, V. Denisenko, and I. Freund, Opt. Lett. 28, 1475 (2003).
    [CrossRef] [PubMed]
  16. G. Foltin, J. Phys. A 36, 1729 (2003).
    [CrossRef]
  17. M. R. Dennis, J. Phys. A 36, 6611 (2003).
    [CrossRef]
  18. M. Wilkinson, J. Phys. A 37, 6763 (2004).
    [CrossRef]
  19. M. Soskin, V. Denisenko, and R. Egorov, J. Opt. Soc. Am. A 6, S281 (2004).
  20. R. I. Egorov, V. G. Denisenko, and M. S. Soskin, JETP Lett. 81, 375 (2005).
    [CrossRef]
  21. For other applications of this term see , Section 3.6.
  22. J. F. Nye, Natural Focusing and Fine Structure of Light (IOP, 1999).
  23. A. I. Konukhov and L. A. Melnikov, J. Opt. Soc. Am. B 3, S139 (2001).
  24. I. Freund, Opt. Lett. 26, 1996 (2001).
    [CrossRef]
  25. H. T. Yura, S. G. Hanson, and M. L. Jakobsen, J. Opt. Soc. Am. A 25, 318 (2008), and references contained therein.
    [CrossRef]

2008 (1)

2005 (1)

R. I. Egorov, V. G. Denisenko, and M. S. Soskin, JETP Lett. 81, 375 (2005).
[CrossRef]

2004 (2)

M. Wilkinson, J. Phys. A 37, 6763 (2004).
[CrossRef]

M. Soskin, V. Denisenko, and R. Egorov, J. Opt. Soc. Am. A 6, S281 (2004).

2003 (4)

M. R. Dennis, J. Phys. A 34, L297 (2003).
[CrossRef]

G. Foltin, J. Phys. A 36, 1729 (2003).
[CrossRef]

M. R. Dennis, J. Phys. A 36, 6611 (2003).
[CrossRef]

M. S. Soskin, V. Denisenko, and I. Freund, Opt. Lett. 28, 1475 (2003).
[CrossRef] [PubMed]

2002 (1)

M. R. Dennis, Opt. Commun. 213, 201 (2002).
[CrossRef]

2001 (3)

I. Freund, Opt. Lett. 26, 1996 (2001).
[CrossRef]

M. V. Berry and M. R. Dennis, Proc. R. Soc. London, Ser. A 457, 141 (2001).
[CrossRef]

A. I. Konukhov and L. A. Melnikov, J. Opt. Soc. Am. B 3, S139 (2001).

2000 (1)

M. V. Berry and M. R. Dennis, Proc. R. Soc. London, Ser. A 456, 2059 (2000).
[CrossRef]

1998 (2)

1996 (2)

B. W. Roberts, E. Bodenschatz, and J. P. Sethna, Physica D 99, 252 (1996).
[CrossRef]

I. Freund and D. A. Kesler, Opt. Commun. 124, 321 (1996).
[CrossRef]

1995 (1)

I. Freund, Phys. Rev. E 52, 2348 (1995).
[CrossRef]

1992 (1)

F. Liu and G. F. Mazenko, Phys. Rev. B 46, 5963 (1992).
[CrossRef]

1981 (1)

N. B. Baranova, B. Ya Zel'dovich, A. V. Mamaev, N. Pilipetskii, and V. V. Shkukov, JETP Lett. 33, 195 (1981).

1978 (1)

M. Berry, J. Phys. A 11, 27 (1978).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

A. I. Konukhov and L. A. Melnikov, J. Opt. Soc. Am. B 3, S139 (2001).

J. Phys. A (5)

G. Foltin, J. Phys. A 36, 1729 (2003).
[CrossRef]

M. R. Dennis, J. Phys. A 36, 6611 (2003).
[CrossRef]

M. Wilkinson, J. Phys. A 37, 6763 (2004).
[CrossRef]

M. Berry, J. Phys. A 11, 27 (1978).
[CrossRef]

M. R. Dennis, J. Phys. A 34, L297 (2003).
[CrossRef]

JETP Lett. (2)

N. B. Baranova, B. Ya Zel'dovich, A. V. Mamaev, N. Pilipetskii, and V. V. Shkukov, JETP Lett. 33, 195 (1981).

R. I. Egorov, V. G. Denisenko, and M. S. Soskin, JETP Lett. 81, 375 (2005).
[CrossRef]

Opt. Commun. (2)

I. Freund and D. A. Kesler, Opt. Commun. 124, 321 (1996).
[CrossRef]

M. R. Dennis, Opt. Commun. 213, 201 (2002).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (1)

F. Liu and G. F. Mazenko, Phys. Rev. B 46, 5963 (1992).
[CrossRef]

Phys. Rev. E (1)

I. Freund, Phys. Rev. E 52, 2348 (1995).
[CrossRef]

Physica D (1)

B. W. Roberts, E. Bodenschatz, and J. P. Sethna, Physica D 99, 252 (1996).
[CrossRef]

Proc. R. Soc. London, Ser. A (2)

M. V. Berry and M. R. Dennis, Proc. R. Soc. London, Ser. A 456, 2059 (2000).
[CrossRef]

M. V. Berry and M. R. Dennis, Proc. R. Soc. London, Ser. A 457, 141 (2001).
[CrossRef]

Waves Random Media (1)

I. Freund, Waves Random Media 8, 119 (1998).

Other (4)

B. I. Halperin, Physics of Defects, R.Balian, M.Kleman, and J.-P.Poirier, eds. (North-Holland, 1981), p. 814.

For other applications of this term see , Section 3.6.

J. F. Nye, Natural Focusing and Fine Structure of Light (IOP, 1999).

J. W. Goodman, Speckle Phenomen In Optics (Roberts & Co., 2007).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Scalar speckle. Shown are simulations for disks with a = 1 and b = 100 . In (a) and (b) I b = 0 , which yields familiar single Λ speckle with Λ 1 . In (c)–(g) I b I a = 2 10 6 ( K = 0.02 ) , which yields speckled speckle with Λ a 1 and Λ b 0.01 . (a) Intensity of single Λ speckle, (b) phase map corresponding to (a), (c) intensity of speckled speckle, (d) phase map corresponding to (c), (e)–(f) forty-fold enlargements of the regions in (d) pointed to by the arrows labeled e, f, and g. Here and throughout the intensity (phase) is coded increasing (0 to 2 π ) black to white, and positive (negative) vortices are shown by white circles with black rims and black circles with white rims.

Fig. 2
Fig. 2

Vector field speckled speckle. Shown are simulations for disks with a = 1 , b = 10 , I b I a = 3 10 3 ( K = 0.3 ) . (a) Intensity, (b) phase Φ 12 of complex Stokes field S 12 , (c) enlargement of the black–white band on the horizontal centerline in (b), (d)–(f) enlargement of the region beneath the black–white band in (b), (d) phase Φ 12 of S 12 , (e) phase Φ R of E R , and (f) phase Φ L of E L .

Equations (6)

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

S a b ( r ) = I a S a ( r ) + I b S b ( r ) ,
W a b ( r ) = [ W a ( r ) + K W b ( r ) ] ( 1 + K ) ,
S 1 = E x 2 E y 2 = 2 Re ( E R * E L ) ,
S 2 = 2 R e ( E x * E y ) = 2 Im ( E R * E L ) .
E R = ( E x i E y ) 2 1 2 , E L = ( E x + i E y ) 2 1 2 .
( E V ) max = g [ ( 3 ) 1 2 ρ 2 ] 1 ,

Metrics