OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 7 — Mar. 29, 2010
  • pp: 6628–6641

Coherence vortices in Mie scattering of statistically stationary partially coherent fields

Madara L. Marasinghe, Malin Premaratne, and David M. Paganin  »View Author Affiliations

Optics Express, Vol. 18, Issue 7, pp. 6628-6641 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (1163 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Points within a fully coherent complex scalar optical field, where the amplitude is identically zero but the optical phase has a jump discontinuity, have been widely investigated by the singular-optics community. More recent researches have extended the domain of singular optics to include partially coherent fields. For example, in coherence vortices the phase of the two-point spectral degree of coherence of a partially coherent field exhibits vortex structure around a point where the magnitude of the spectral degree of coherence vanishes. We show that the spectral degree of coherence of Mie scattered partially coherent statistically stationary electromagnetic fields exhibits a rich set of coherence vortices in both the internal and external fields. Specifically, we look at Mie scattering of a stationary beam from a dielectric sphere and study the formation of coherence vortices and their evolution with both the properties of the scattering sphere, and of the incident partially coherent beam.

© 2010 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(290.4020) Scattering : Mie theory
(290.5850) Scattering : Scattering, particles
(050.4865) Diffraction and gratings : Optical vortices
(260.6042) Physical optics : Singular optics

ToC Category:
Coherence and Statistical Optics

Original Manuscript: December 15, 2009
Revised Manuscript: February 19, 2010
Manuscript Accepted: March 8, 2010
Published: March 16, 2010

Madara L. Marasinghe, Malin Premaratne, and David M. Paganin, "Coherence vortices in Mie scattering of statistically stationary partially coherent fields," Opt. Express 18, 6628-6641 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Born and E. Wolf, Principles of Optics, 7th (expanded) edition (Cambridge University Press, Cambridge, 1999).
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
  3. H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, "Phase singularities of the coherence functions in Young’s interference pattern," Opt. Lett. 28, 968-970 (2003). [CrossRef] [PubMed]
  4. G. Gbur and T. D. Visser, "Coherence vortices in partially coherent beams," Opt. Commun. 222, 117-125 (2003). [CrossRef]
  5. M. V. Berry, "Making waves in physics: three wave singularities from the miraculous 1830s," Nature 403, 21 (2000). [CrossRef] [PubMed]
  6. J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. Roy. Soc. Lond. A 336, 165-190 (1974). [CrossRef]
  7. M. Soskin and M. Vasnetsov, "Singular optics," in Progress in Optics, E.Wolf, ed., (North-Holland, Amsterdam, 2001) Vol. 42, pp. 219-276. [CrossRef]
  8. 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: Pure Appl. Opt. 11, 094021 (2009). [CrossRef]
  9. G. A. Swartzlander, "The optical vortex coronagraph," J. Opt. A: Pure Appl. Opt. 11, 094022 (2009). [CrossRef]
  10. C. Maurer and S. Bernet and M. Ritsch-Marte, "Refining common path interferometry with a spiral-phase Fourier filter," J. Opt. A: Pure Appl. Opt. 11, 094023 (2009). [CrossRef]
  11. W. A. Wozniak and M. Banach, "Measurements of linearly birefringent media parameters using the optical vortex interferometer with the Wollaston compensator," J. Opt. A: Pure Appl. Opt. 11, 094024 (2009). [CrossRef]
  12. P. A. M. Dirac, "Quantised singularities in the electromagnetic field," Proc. Roy. Soc. Lond. A 133, 60-72 (1931). [CrossRef]
  13. G. Gbur, T. Visser and E. Wolf, "‘Hidden’ singularities in partially coherent wavefields," J. Opt. A: Pure Appl. Opt. 6, S239-S242 (2004). [CrossRef]
  14. G. Gbur and T. D. Visser, "Phase singularities and coherence vortices in linear optical systems," Opt. Commun. 259, 428-435 (2006). [CrossRef]
  15. G. V. Bogatyryova, C. V. Felde, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, "Partially coherent vortex beams with a separable phase," Opt. Lett. 28, 878-880 (2003). [CrossRef] [PubMed]
  16. G. Gbur, "Optical and coherence vortices and their relationships," in Eighth International Conference on Correlation Optics, M. Kujawinska and O. V. Angelsky, eds. Proc. SPIE 7008, 70080N-1-70080N-7 (2008).
  17. Y. Gu and G. Gbur, "Topological reactions of optical correlation vortices," Opt. Commun. 282, 709-716 (2009). [CrossRef]
  18. D. M. Palacios, I. D. Maleev, A. S. Marathay and G. A. Swartzlander, "Spatial correlation singularity of a vortex field," Phys. Rev. Lett. 92, 143905 (2004). [CrossRef] [PubMed]
  19. D. G. Fischer and T. D. Visser, "Spatial correlation properties of focused partially coherent fields," J. Opt. Soc. Am. A 21, 2097-2102 (2004). [CrossRef]
  20. D. M. Paganin, Coherent X-ray Optics (Oxford University Press, New York, 2006).
  21. G. Mie, "Beitrage zur Optik Truber Medien speziell kolloidaler Metallosungen," Ann. Phys. 25, 377-442 (1908). [CrossRef]
  22. M. Mishchenko, L. Travis and A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles, 3rd electronic release (Cambridge University Press, United Kingdom, 2002).
  23. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  24. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, Cambridge, 2007).
  25. L. J. Allen, H. M. L. Faulkner, M. P. Oxley, and D. Paganin, "Phase retrieval and aberration correction in the presence of vortices in high-resolution transmission electron microscopy," Ultramicroscopy 88, 85-97 (2001). [CrossRef] [PubMed]
  26. M. Morin, P. Bernard and P. Galarneau, "Moment definition of the pointing stability of a laser beam," Opt. Lett. 19, 1379-1381 (1994). [CrossRef] [PubMed]
  27. M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux and M. Tiedtke, "Laser pointing stability measurements," Proc. SPIE 2870, 216-224 (1996). [CrossRef]
  28. P. Kwee, F. Seifert, B. Willke and K. Danzmann, "Laser beam quality and pointing measurement with an optical resonator," Rev. Sci. Instrum. 78, 073103 (2007). [CrossRef] [PubMed]
  29. C. Matlzer, "MATLAB functions for Mie scattering and absorption," IAP Res. Rep. No. 02-08, June (2002).
  30. M. R. Dennis, K. O’Holleran and M. J. Padgett, "Singular optics: optical vortices and polarization singularities" in Progress in Optics, E. Wolf, ed., (North-Holland, Amsterdam, 2009) 53, 293-363.
  31. J. F. Nye, Natural Focusing and Fine Structure of Light (Institute of Physics Publishing, 1999).
  32. W. Gardner, A. Napolitano, and L. Paura, "Cyclostationarity: Half a Century of Research," Signal Process. 86, 639-697 (2006). [CrossRef]
  33. B. J. Davis, "Observable coherence theory for statistically periodic fields," Phys. Rev. A 76, 043843 (2007). [CrossRef]
  34. V. Manea, "General interference law for nonstationary, separable optical fields," J. Opt. Soc. Am. A 26, 1907-1914 (2009). [CrossRef]
  35. R. W. Schoonover, B. J. Davis, and P. S. Carney, "The generalized Wolf shift for cyclostationary fields," Opt. Express 17, 4705-4711 (2009). [CrossRef] [PubMed]
  36. C. R. Fernandez-Pousa, "Intensity spectra after first-order dispersion of composite models of scalar cyclostationary light," J. Opt. Soc. Am. A 26, 993-1007 (2009). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited