Abstract

We previously demonstrated that Mie scattering of stationary partially coherent light by dielectric spheres generates coherence vortices. In this Letter, we demonstrate that a lattice of coherence vortices can be generated by Mie scattering of partially coherent electromagnetic waves by a system of three coplanar dielectric spheres. Spontaneous coherence-vortex creation and destruction is observed in our computer modeling of this system.

© 2011 Optical Society of America

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Errata

Madara L. Marasinghe, David M. Paganin, and Malin Premaratne, "Coherence-vortex lattice formed via Mie scattering of partially coherent light by several dielectric nanospheres: erratum," Opt. Lett. 36, 1926-1926 (2011)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-36-10-1926

References

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  1. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2006).
  2. A. Messiah, Quantum Mechanics (North-Holland, 1961), Vol.  1.
  3. G. Ruben, D. M. Paganin, and M. J. Morgan, Phys. Rev. A 78, 013631 (2008).
    [CrossRef]
  4. A. Boivin, J. Dow, and E. Wolf, J. Opt. Soc. Am. 57, 1171(1967).
    [CrossRef]
  5. M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 53, 293 (2009).
    [CrossRef]
  6. J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations (CRC Press, 1999).
  7. P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931).
    [CrossRef]
  8. M. S. Soskin and M. Vasnetsov, Prog. Opt. 42, 219 (2001).
    [CrossRef]
  9. A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
    [CrossRef]
  10. G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
    [CrossRef]
  11. H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, Opt. Lett. 28, 968 (2003).
    [CrossRef] [PubMed]
  12. G. Gbur, T. D. Visser, and E. Wolf, Opt. Commun. 239, 15 (2004).
    [CrossRef]
  13. M. L. Marasinghe, M. Premaratne, and D. M. Paganin, Opt. Express 18, 6628 (2010).
    [CrossRef] [PubMed]
  14. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  15. L. Mandel and E. Wolf, J. Opt. Soc. Am. 66, 529 (1976).
    [CrossRef]
  16. K. W. Nicholls and J. F. Nye, J. Phys. A 20, 4673 (1987).
    [CrossRef]
  17. J. Masajada and B. Dubik, Opt. Commun. 198, 21 (2001).
    [CrossRef]
  18. G. Ruben and D. M. Paganin, Phys. Rev. E 75, 066613(2007).
    [CrossRef]
  19. Y. Gu and G. Gbur, Opt. Commun. 282, 709 (2009).
    [CrossRef]
  20. M. V. Berry, J. F. Nye, and F. Wright, Phil. Trans. R. Soc. A 291, 453 (1979).
    [CrossRef]
  21. G. Ruben, M. J. Morgan, and D. M. Paganin, Phys. Rev. Lett. 105, 220402 (2010).
    [CrossRef]
  22. M. V. Berry, J. Phys. A: Math. Gen. 11, 27 (1978).
    [CrossRef]
  23. K. V. Larin, M. Motamedi, M. S. Eledrisi, and R. O. Esenaliev, Diabetes Care 25, 2263 (2002).
    [CrossRef] [PubMed]
  24. K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, Phys. Rev. Lett. 100, 053902 (2008).
    [CrossRef] [PubMed]

2010

M. L. Marasinghe, M. Premaratne, and D. M. Paganin, Opt. Express 18, 6628 (2010).
[CrossRef] [PubMed]

G. Ruben, M. J. Morgan, and D. M. Paganin, Phys. Rev. Lett. 105, 220402 (2010).
[CrossRef]

2009

Y. Gu and G. Gbur, Opt. Commun. 282, 709 (2009).
[CrossRef]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 53, 293 (2009).
[CrossRef]

2008

G. Ruben, D. M. Paganin, and M. J. Morgan, Phys. Rev. A 78, 013631 (2008).
[CrossRef]

K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, Phys. Rev. Lett. 100, 053902 (2008).
[CrossRef] [PubMed]

2007

G. Ruben and D. M. Paganin, Phys. Rev. E 75, 066613(2007).
[CrossRef]

2005

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

2004

G. Gbur, T. D. Visser, and E. Wolf, Opt. Commun. 239, 15 (2004).
[CrossRef]

2003

2002

K. V. Larin, M. Motamedi, M. S. Eledrisi, and R. O. Esenaliev, Diabetes Care 25, 2263 (2002).
[CrossRef] [PubMed]

2001

M. S. Soskin and M. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

J. Masajada and B. Dubik, Opt. Commun. 198, 21 (2001).
[CrossRef]

1987

K. W. Nicholls and J. F. Nye, J. Phys. A 20, 4673 (1987).
[CrossRef]

1979

M. V. Berry, J. F. Nye, and F. Wright, Phil. Trans. R. Soc. A 291, 453 (1979).
[CrossRef]

1978

M. V. Berry, J. Phys. A: Math. Gen. 11, 27 (1978).
[CrossRef]

1976

1967

1931

P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931).
[CrossRef]

Berry, M. V.

M. V. Berry, J. F. Nye, and F. Wright, Phil. Trans. R. Soc. A 291, 453 (1979).
[CrossRef]

M. V. Berry, J. Phys. A: Math. Gen. 11, 27 (1978).
[CrossRef]

Boivin, A.

Dennis, M. R.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 53, 293 (2009).
[CrossRef]

K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, Phys. Rev. Lett. 100, 053902 (2008).
[CrossRef] [PubMed]

Desyatnikov, A. S.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

Dirac, P. A. M.

P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931).
[CrossRef]

Dow, J.

Dubik, B.

J. Masajada and B. Dubik, Opt. Commun. 198, 21 (2001).
[CrossRef]

Eledrisi, M. S.

K. V. Larin, M. Motamedi, M. S. Eledrisi, and R. O. Esenaliev, Diabetes Care 25, 2263 (2002).
[CrossRef] [PubMed]

Esenaliev, R. O.

K. V. Larin, M. Motamedi, M. S. Eledrisi, and R. O. Esenaliev, Diabetes Care 25, 2263 (2002).
[CrossRef] [PubMed]

Flossmann, F.

K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, Phys. Rev. Lett. 100, 053902 (2008).
[CrossRef] [PubMed]

Gbur, G.

Y. Gu and G. Gbur, Opt. Commun. 282, 709 (2009).
[CrossRef]

G. Gbur, T. D. Visser, and E. Wolf, Opt. Commun. 239, 15 (2004).
[CrossRef]

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, Opt. Lett. 28, 968 (2003).
[CrossRef] [PubMed]

G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2006).

Gu, Y.

Y. Gu and G. Gbur, Opt. Commun. 282, 709 (2009).
[CrossRef]

Kivshar, Y. S.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

Larin, K. V.

K. V. Larin, M. Motamedi, M. S. Eledrisi, and R. O. Esenaliev, Diabetes Care 25, 2263 (2002).
[CrossRef] [PubMed]

Mandel, L.

Marasinghe, M. L.

Masajada, J.

J. Masajada and B. Dubik, Opt. Commun. 198, 21 (2001).
[CrossRef]

Messiah, A.

A. Messiah, Quantum Mechanics (North-Holland, 1961), Vol.  1.

Morgan, M. J.

G. Ruben, M. J. Morgan, and D. M. Paganin, Phys. Rev. Lett. 105, 220402 (2010).
[CrossRef]

G. Ruben, D. M. Paganin, and M. J. Morgan, Phys. Rev. A 78, 013631 (2008).
[CrossRef]

Motamedi, M.

K. V. Larin, M. Motamedi, M. S. Eledrisi, and R. O. Esenaliev, Diabetes Care 25, 2263 (2002).
[CrossRef] [PubMed]

Nicholls, K. W.

K. W. Nicholls and J. F. Nye, J. Phys. A 20, 4673 (1987).
[CrossRef]

Nye, J. F.

K. W. Nicholls and J. F. Nye, J. Phys. A 20, 4673 (1987).
[CrossRef]

M. V. Berry, J. F. Nye, and F. Wright, Phil. Trans. R. Soc. A 291, 453 (1979).
[CrossRef]

J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations (CRC Press, 1999).

O’Holleran, K.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 53, 293 (2009).
[CrossRef]

K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, Phys. Rev. Lett. 100, 053902 (2008).
[CrossRef] [PubMed]

Padgett, M. J.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 53, 293 (2009).
[CrossRef]

K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, Phys. Rev. Lett. 100, 053902 (2008).
[CrossRef] [PubMed]

Paganin, D. M.

G. Ruben, M. J. Morgan, and D. M. Paganin, Phys. Rev. Lett. 105, 220402 (2010).
[CrossRef]

M. L. Marasinghe, M. Premaratne, and D. M. Paganin, Opt. Express 18, 6628 (2010).
[CrossRef] [PubMed]

G. Ruben, D. M. Paganin, and M. J. Morgan, Phys. Rev. A 78, 013631 (2008).
[CrossRef]

G. Ruben and D. M. Paganin, Phys. Rev. E 75, 066613(2007).
[CrossRef]

Premaratne, M.

Ruben, G.

G. Ruben, M. J. Morgan, and D. M. Paganin, Phys. Rev. Lett. 105, 220402 (2010).
[CrossRef]

G. Ruben, D. M. Paganin, and M. J. Morgan, Phys. Rev. A 78, 013631 (2008).
[CrossRef]

G. Ruben and D. M. Paganin, Phys. Rev. E 75, 066613(2007).
[CrossRef]

Schouten, H. F.

Soskin, M. S.

M. S. Soskin and M. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

Torner, L.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

Vasnetsov, M.

M. S. Soskin and M. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

Visser, T. D.

G. Gbur, T. D. Visser, and E. Wolf, Opt. Commun. 239, 15 (2004).
[CrossRef]

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, Opt. Lett. 28, 968 (2003).
[CrossRef] [PubMed]

G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
[CrossRef]

Wolf, E.

G. Gbur, T. D. Visser, and E. Wolf, Opt. Commun. 239, 15 (2004).
[CrossRef]

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, Opt. Lett. 28, 968 (2003).
[CrossRef] [PubMed]

L. Mandel and E. Wolf, J. Opt. Soc. Am. 66, 529 (1976).
[CrossRef]

A. Boivin, J. Dow, and E. Wolf, J. Opt. Soc. Am. 57, 1171(1967).
[CrossRef]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

Wright, F.

M. V. Berry, J. F. Nye, and F. Wright, Phil. Trans. R. Soc. A 291, 453 (1979).
[CrossRef]

Diabetes Care

K. V. Larin, M. Motamedi, M. S. Eledrisi, and R. O. Esenaliev, Diabetes Care 25, 2263 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Phys. A

K. W. Nicholls and J. F. Nye, J. Phys. A 20, 4673 (1987).
[CrossRef]

J. Phys. A: Math. Gen.

M. V. Berry, J. Phys. A: Math. Gen. 11, 27 (1978).
[CrossRef]

Opt. Commun.

J. Masajada and B. Dubik, Opt. Commun. 198, 21 (2001).
[CrossRef]

G. Gbur, T. D. Visser, and E. Wolf, Opt. Commun. 239, 15 (2004).
[CrossRef]

Y. Gu and G. Gbur, Opt. Commun. 282, 709 (2009).
[CrossRef]

G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Phil. Trans. R. Soc. A

M. V. Berry, J. F. Nye, and F. Wright, Phil. Trans. R. Soc. A 291, 453 (1979).
[CrossRef]

Phys. Rev. A

G. Ruben, D. M. Paganin, and M. J. Morgan, Phys. Rev. A 78, 013631 (2008).
[CrossRef]

Phys. Rev. E

G. Ruben and D. M. Paganin, Phys. Rev. E 75, 066613(2007).
[CrossRef]

Phys. Rev. Lett.

G. Ruben, M. J. Morgan, and D. M. Paganin, Phys. Rev. Lett. 105, 220402 (2010).
[CrossRef]

K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, Phys. Rev. Lett. 100, 053902 (2008).
[CrossRef] [PubMed]

Proc. R. Soc. A

P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931).
[CrossRef]

Prog. Opt.

M. S. Soskin and M. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 53, 293 (2009).
[CrossRef]

Other

J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations (CRC Press, 1999).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2006).

A. Messiah, Quantum Mechanics (North-Holland, 1961), Vol.  1.

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for generation of coherence-vortex lattice via Mie scattering of partially coherent plane waves from an assembly of three coplanar spherical particles.

Fig. 2
Fig. 2

Coherence-vortex lattice in spectral degree of coherence of scattered field. All dimensions are in mm. (a) Magnitude of the spectral degree of coherence of the scattered field at the plane z = R. (b) Phase of the spectral degree of coherence of the scattered field at the plane z = R. (c) Magnitude variation of the spectral degree of coherence of the scattered field in a rectangular volume. (d) Phase variation of the spectral degree of coherence of the scattered field in a rectangular volume.

Fig. 3
Fig. 3

Evolution of nodal lines of the coherence vortices. All dimensions are in mm.

Equations (3)

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

m = 1 2 π Γ r 1 arg [ ψ ( r 1 ) ] · d t 1 ,
μ ( r 1 , r 2 ; ω ) = Tr [ W i j ( r 1 , r 2 ; ω ) ] S ( r 1 , ω ) S ( r 2 , ω ) ,
m = 1 2 π Γ r 1 arg [ μ ( r 1 , r 2 ; ω ) ] · d t 1 ,

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