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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 4 — Apr. 1, 2013
  • pp: 582–588

Topological reactions of correlation functions in partially coherent electromagnetic beams

Shreyas B. Raghunathan, Hugo F. Schouten, and Taco D. Visser  »View Author Affiliations

JOSA A, Vol. 30, Issue 4, pp. 582-588 (2013)

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It was recently shown that so-called coherence vortices, singularities of the two-point correlation function, generally occur in partially coherent electromagnetic beams. We study the three-dimensional structure of these singularities and show that in successive cross sections of a beam a rich variety of topological reactions takes place. These reactions involve, apart from vortices, the creation or annihilation of dipoles, saddles, maxima and minima of the phase of the correlation function. Since these reactions happen generically, i.e., under quite general conditions, these observations have implications for interference experiments with partially coherent, electromagnetic beams.

© 2013 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(050.1940) Diffraction and gratings : Diffraction
(260.1960) Physical optics : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics
(260.6042) Physical optics : Singular optics

ToC Category:
Coherence and Statistical Optics

Original Manuscript: January 11, 2013
Manuscript Accepted: February 5, 2013
Published: March 6, 2013

Shreyas B. Raghunathan, Hugo F. Schouten, and Taco D. Visser, "Topological reactions of correlation functions in partially coherent electromagnetic beams," J. Opt. Soc. Am. A 30, 582-588 (2013)

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  1. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. A 336, 165–190 (1974). [CrossRef]
  2. I. Freund, “Critical foliations,” Opt. Lett. 26, 545–547 (2001). [CrossRef]
  3. I. Freund, “Optical vortex trajectories,” Opt. Commun. 181, 19–33 (2000). [CrossRef]
  4. I. Freund and D. A. Kessler, “Critical point trajectory bundles in singular wave fields,” Opt. Commun. 187, 71–90 (2001). [CrossRef]
  5. G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 87, 023902 (2001). [CrossRef]
  6. A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241, 237–247 (2004). [CrossRef]
  7. A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, “Observation of topological transformations of optical vortices in two-dimensional photonic lattices,” Opt. Express 14, 8317–8327 (2006). [CrossRef]
  8. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th (expanded) ed. (Cambridge University, 1999).
  9. G. P. Karman, A. van Duijl, and J. P. Woerdman, “Creation and annihilation of phase singularities in a focal field,” Opt. Lett. 22, 1503–1505 (1997). [CrossRef]
  10. A. Boivin, J. Dow, and E. Wolf, “Energy flow in the neighborhood of the focus of a coherent beam,” J. Opt. Soc. Am. 57, 1171–1175 (1967). [CrossRef]
  11. H. F. Schouten, G. Gbur, T. D. Visser, D. Lenstra, and H. Blok, “Creation and annihilation of phase singularities near a sub-wavelength slit,” Opt. Express 11, 371–380 (2003). [CrossRef]
  12. H. F. Schouten, T. D. Visser, and D. Lenstra, “Optical vortices near sub-wavelength structures,” J. Opt. B 6, S404–S409 (2004). [CrossRef]
  13. D. W. Diehl and T. D. Visser, “Phase singularities of the longitudinal field components in high-aperture systems,” J. Opt. Soc. Am. A 21, 2103–2108 (2004). [CrossRef]
  14. J. F. Nye, Natural Focusing and Fine Structure of Light (IOP Publishing, 1999).
  15. M. S. Soskin and M. V. Vasnetsov, “Singular optics,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2001), Vol. 42, pp. 83–110.
  16. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  17. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  18. G. Gbur and T. D. Visser, “The structure of partially coherent fields,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2010), Vol. 55, pp. 285–341.
  19. 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]
  20. G. V. Bogatyryova, C. V. Fel’de, 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]
  21. G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222, 117–125 (2003). [CrossRef]
  22. 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]
  23. G. A. Swartzlander and J. Schmit, “Temporal correlation vortices and topological dispersion,” Phys. Rev. Lett. 93, 093901 (2004). [CrossRef]
  24. 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. A 21, 1895–1900 (2004). [CrossRef]
  25. 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]
  26. G. A. Swartzlander and R. I. Hernandez-Aranda, “Optical Rankine vortex and anomalous circulation of light,” Phys. Rev. Lett. 99, 163901 (2007). [CrossRef]
  27. T. van Dijk and T. D. Visser, “Evolution of singularities in a partially coherent vortex beam,” J. Opt. Soc. Am. A 26, 741–744 (2009). [CrossRef]
  28. D. G. Fischer and T. D. Visser, “Spatial correlation properties of focused partially coherent light,” J. Opt. Soc. Am. A 21, 2097–2102 (2004). [CrossRef]
  29. T. van Dijk, H. F. Schouten, and T. D. Visser, “Coherence singularities in the field generated by partially coherent sources,” Phys. Rev. A 79, 033805 (2009). [CrossRef]
  30. M. L. Marasinghe, M. Premaratne, and D. M. Paganin, “Coherence vortices in Mie scattering of statistically stationary partially coherent fields,” Opt. Express 18, 6628–6641 (2010). [CrossRef]
  31. M. L. Marasinghe, M. Premaratne, D. M. Paganin, and M. A. Alonso, “Coherence vortices in Mie scattered nonparaxial partially coherent beams,” Opt. Express 20, 2858–2875 (2012). [CrossRef]
  32. W. Wang and M. Takeda, “Coherence current, coherence vortex, and the conservation law of coherence,” Phys. Rev. Lett. 96, 223904 (2006). [CrossRef]
  33. Y. Gu and G. Gbur, “Topological reactions of optical correlation vortices,” Opt. Commun. 282, 709–716 (2009). [CrossRef]
  34. 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]
  35. S. B. Raghunathan, H. F. Schouten, and T. D. Visser, “Correlation singularities in partially coherent electromagnetic beams,” Opt. Lett. 37, 4179–4181 (2012). [CrossRef]
  36. S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, 1994), pp. 174–180.
  37. T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, “Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere,” Phys. Rev. Lett. 104, 173902 (2010). [CrossRef]
  38. R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956). [CrossRef]
  39. S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, “Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams,” J. Opt. A 10, 055001 (2008). [CrossRef]
  40. T. Hassinen, J. Tervo, T. Setälä, and A. T. Friberg, “Hanbury Brown-Twiss effect with electromagnetic waves,” Opt. Express 19, 15188–15195 (2011). [CrossRef]
  41. G. Gbur and G. A. Swartzlander, “Complete transverse representation of a correlation singularity of a partially coherent field,” J. Opt. Soc. Am. B 25, 1422–1429 (2008). [CrossRef]
  42. G. Gbur, T. D. Visser, and E. Wolf, “Hidden singularities in partially coherent wavefields,” J. Opt. A 6, S239–S242 (2004). [CrossRef]
  43. G. Gbur and T. D. Visser, “Phase singularities and coherence vortices in linear optical systems,” Opt. Commun. 259, 428–435 (2006). [CrossRef]
  44. T. D. Visser and R. W. Schoonover, “A cascade of singular field patterns in Young’s interference experiment,” Opt. Commun. 281, 1–6 (2008). [CrossRef]
  45. J. F. Nye, “Unfolding of higher-order wave dislocations,” J. Opt. Soc. Am. A 15, 1132–1138 (1998). [CrossRef]
  46. C. Hsiung, A First Course in Differential Geometry (International, 1997), p. 266.

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