OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 3 — Jan. 30, 2012
  • pp: 2858–2875

Coherence vortices in Mie scattered nonparaxial partially coherent beams

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

Optics Express, Vol. 20, Issue 3, pp. 2858-2875 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (2571 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We have previously demonstrated that Mie scattering of partially coherent plane waves can create coherence vortices, namely screw-type dislocations in the phase of the spectral degree of coherence. However, plane waves are an idealization and in practice, optical beams are often much closer to reality. Thus, in this paper, we consider coherence vortices created by Mie scattering of partially coherent focused beams. We demonstrate that Mie scattering of partially coherent complex focused beams can give rise to coherence vortices. As the scattered fields propagate coherence vortex-antivortex pairs are annihilated thus creating hair-pin structures in the coherence-vortex nodal lines. The evolution of correlation singularities in the scattered field with the variation of the complex focus point of the incident beam is also discussed. The variation of the degree of polarization of the scattered field is also studied.

© 2012 OSA

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
(290.5855) Scattering : Scattering, polarization
(260.6042) Physical optics : Singular optics

ToC Category:
Coherence and Statistical Optics

Original Manuscript: December 14, 2011
Revised Manuscript: January 9, 2012
Manuscript Accepted: January 11, 2012
Published: January 23, 2012

Madara L. Marasinghe, Malin Premaratne, David M. Paganin, and Miguel A. Alonso, "Coherence vortices in Mie scattered nonparaxial partially coherent beams," Opt. Express 20, 2858-2875 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica5, 785–795 (1938). [CrossRef]
  2. M. Born and E. Wolf, Principles of Optics, 7th (expanded) edition (Cambridge University Press, Cambridge, 1999).
  3. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
  4. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A336, 165–190 (1974). [CrossRef]
  5. I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun.119, 604–612 (1995). [CrossRef]
  6. G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun.222, 117–125 (2003). [CrossRef]
  7. M. Berry, “Making waves in physics,” Nature (London)403, 21 (2000). [CrossRef]
  8. M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt.42, 219–276 (2001). [CrossRef]
  9. W. Whewell, “Essay towards a first approximation to a map of cotidal lines,” Phil. Trans. R. Soc. Lond.123, 147–236 (1833). [CrossRef]
  10. M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature (London)394, 348–350 (1998). [CrossRef]
  11. M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett.97, 170406 (2006). [CrossRef] [PubMed]
  12. M. V. Berry and C. Upstill, “Catastrophe optics: morphologies of caustics and their diffraction patterns,” Prog. Opt.18, 257–346 (1980). [CrossRef]
  13. M. V. Berry, “Singularities in waves and rays,” in R. Balian, Kléman, and J-P Poirier eds., Les Houches Lecture Series, session XXXV, Physics of defects (North Holland, Amsterdam) 453–543 (1981).
  14. M. V. Berry, “Much ado about nothing: optical dislocation lines (phase singularities, zeros, vortices...,” Proc SPIE3487, 1–5 (1998). [CrossRef]
  15. G. Gouesbet, “Hypotheses on the a priori rational necessity of quantum mechanics,” Principia, an international journal of epistemology14, 393–404 (2010).
  16. M. V. Berry and M. R. Dennis, “Quantum cores of optical phase singularities,” J. Opt. A: Pure Appl. Opt.6, S178–S180 (2004). [CrossRef]
  17. S. M. Barnett, “On the quantum core of an optical vortex,” J. Mod. Opt.55, 2279–2292 (2008). [CrossRef]
  18. 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]
  19. I. D. Maleev, D. M. Palacios, A. S. Marathay, and G. A. Swartzlander, “Spatial correlation vortices in partially coherent light: theory,” J. Opt. Soc. Am. B21, 1895–1900 (2004). [CrossRef]
  20. 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]
  21. G. Gbur, T. D. Visser, and E. Wolf, “‘Hidden’ singularities in partially coherent wavefields,” J. Opt. A: Pure Appl. Opt.6, S239–S242 (2004). [CrossRef]
  22. G. Gbur and T. D. Visser, “Phase singularities and coherence vortices in linear optical systems,” Opt. Commun.259, 428–435 (2006). [CrossRef]
  23. G. Gbur, “Optical and coherence vortices and their relationships,” in Eighth International Conference on Correlation Optics, M. Kujawinska and O. V. Angelsky, eds. Proc. SPIE7008, 70080N-1–70080N-7 (2008).
  24. Y. Gu and G. Gbur, “Topological reactions of optical correlation vortices,” Opt. Commun.282, 709–716 (2009). [CrossRef]
  25. I. Maleev, “Partial coherence and optical vortices,” Ph.D. dissertation, Worcester Polytechnic Institute, 2004.
  26. M. L. Marasinghe, M. Premaratne, and D. M. Paganin, “Coherence vortices in Mie scattering of statistically stationary partially coherent fields,” Opt. Express18, 6628–6641 (2010). [CrossRef] [PubMed]
  27. M. L. Marasinghe, D. M. Paganin, and M. Premaratne, “Coherence-vortex lattice formed via Mie scattering of partially coherent light by several dielectric nanospheres,” Opt. Lett.36, 936–938 (2011). [CrossRef] [PubMed]
  28. D. G. Fischer and T. D. Visser, “Spatial correlation properties of focused partially coherent light,” J. Opt. Soc. Am. A21, 2097–2102 (2004). [CrossRef]
  29. G. Gouesbet and G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris)13, 97–103 (1982). [CrossRef]
  30. G. Gouesbet, G. Gréhan, and B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. (Paris)16, 83–93 (1985). [CrossRef]
  31. G. Gouesbet, G. Gréhan, and B. Maheu, “Computations of the gn coefficients in the generalized Lorenz-Mie theory using three different methods,” Appl. Opt.27, 4874–4883 (1988). [CrossRef] [PubMed]
  32. G. Gouesbet, B. Maheu, and G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A5, 1427–1443 (1988). [CrossRef]
  33. G. Gouesbet, “T-matrix formulation and generalized Lorenz-Mie theories in spherical coordinates,” Opt. Commun.283, 517–521 (2010). [CrossRef]
  34. G. Gouesbet and G. Gréhan, Generalized Lorenz-Mie theories, (Springer, Berlin, 2011). [CrossRef]
  35. J. A. Lock, “Improved Gaussian beam-scattering algorithm,” Appl. Opt.34, 559–571 (1995). [CrossRef] [PubMed]
  36. G. Gouesbet and G. Gréhan, Generalized Lorenz-Mie theories, (Springer, Berlin, 2011) 48–50. [CrossRef]
  37. R. Kant, “Generalized Lorenz-Mie scattering theory for focused radiation and finite solids of revolution: case I: symmetrically polarized beams,” J. Mod. Opt.52, 2067–2092 (2005). [CrossRef]
  38. A. S. van de Nes and P. Torok, “Rigorous analysis of spheres in Gauss-Laguerre beams,” Opt. Express15, 13360–13374 (2007). [CrossRef] [PubMed]
  39. Z. Cui, Y. Han, and H. Zhang, “Scattering of an arbitrarily incident focused Gaussian beam by arbitrarily shaped dielectric particles,” J. Opt. Soc. Am. B28, 2625–2632 (2011). [CrossRef]
  40. N. J. Moore and M. A. Alonso, “Closed form formula for Mie scattering of nonparaxial analogues of Gaussian beams,” Opt. Express16, 5926–5933 (2008). [CrossRef] [PubMed]
  41. M.V. Berry, “Evanescent and real waves in quantum billiards and Gaussian beams,” J. Phys. A: Math. Gen.27, L391–L398 (1994). [CrossRef]
  42. C. J. R. Sheppard and S. Saghafi, “Beam modes beyond the paraxial approximation: a scalar treatment,” Phys. Rev. A57, 2971–2979 (1998). [CrossRef]
  43. F. A. L. Cullen and P. K. Yu, “Complex source-point theory of the electromagnetic open resonator,” Proc. R. Soc. Lond. A366, 155–171 (1979). [CrossRef]
  44. C. J. R. Sheppard and S. Saghafi, “Electromagnetic Gaussian beams beyond the paraxial approximation,” J. Opt. Soc. Am. A16, 1381–1386 (1999). [CrossRef]
  45. C. J. R. Sheppard and S. Saghafi, “Transverse-electric and transverse-magnetic beam modes beyond the paraxial approximation,” Opt. Lett.24, 1543–1545 (1999). [CrossRef]
  46. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic Press, New York, 1969).
  47. E. Wolf, “New theory of partial coherence in the space-frequency domain. Part I: spectra and cross spectra of steady-state sources,” J. Opt. Soc. Am.72, 343–351 (1982). [CrossRef]
  48. L. Mandel and E. Wolf, “Spectral coherence and the concept of cross-spectral purity,” J. Opt. Soc. Am.66, 529–535 (1976). [CrossRef]
  49. J. Tervo, T. Setälä, and A. Friberg, “Degree of coherence for electromagnetic fields,” Opt. Express11, 1137–1143 (2003). [CrossRef] [PubMed]
  50. T. Setälä, J. Tervo, and A. T. Friberg, “Complete electromagnetic coherence in the space-frequency domain,” Opt. Lett.29, 328–330 (2004). [CrossRef] [PubMed]
  51. J. Tervo, T. Setälä, and A. T. Friberg, “Theory of partially coherent electromagnetic fields in the space-frequency domain,” J. Opt. Soc. Am. A21, 2205–2215 (2004). [CrossRef]
  52. E. Wolf, “Coherence properties of partially polarized electromagnetic radiation,” Il Nuovo Cimento13, 1165–1181 (1959). [CrossRef]
  53. J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, “Degree of polarization of statistically stationary electromagnetic fields,” Opt. Commun.248, 333–337 (2005). [CrossRef]
  54. T. Setälä, M. Kaivola, and A. T. Friberg, “Degree of polarization in near fields of thermal sources: effects of surface waves,” Phys. Rev. Lett.88, 123902 (2002). [CrossRef] [PubMed]
  55. W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: birth and evolution of phase singularities in the spatial coherence function,” in Fringe 2005, W. Osten, ed. (Springer BerlinHeidelberg, 2006), 46–53. [CrossRef]
  56. W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett.96, 073902 (2006). [CrossRef] [PubMed]

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