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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 6 — Mar. 24, 2014
  • pp: 6495–6510

Argand-plane vorticity singularities in complex scalar optical fields: An experimental study using optical speckle

Freda Rothschild, Alexis I. Bishop, Marcus J. Kitchen, and David M. Paganin  »View Author Affiliations

Optics Express, Vol. 22, Issue 6, pp. 6495-6510 (2014)

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The Cornu spiral is, in essence, the image resulting from an Argand-plane map associated with monochromatic complex scalar plane waves diffracting from an infinite edge. Argand-plane maps can be useful in the analysis of more general optical fields. We experimentally study particular features of Argand-plane mappings known as “vorticity singularities” that are associated with mapping continuous single-valued complex scalar speckle fields to the Argand plane. Vorticity singularities possess a hierarchy of Argand-plane catastrophes including the fold, cusp and elliptic umbilic. We also confirm their connection to vortices in two-dimensional complex scalar waves. The study of vorticity singularities may also have implications for higher-dimensional fields such as coherence functions and multi-component fields such as vector and spinor fields.

© 2014 Optical Society of America

OCIS Codes
(030.6140) Coherence and statistical optics : Speckle
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(350.6980) Other areas of optics : Transforms
(110.3175) Imaging systems : Interferometric imaging
(110.4153) Imaging systems : Motion estimation and optical flow
(050.4865) Diffraction and gratings : Optical vortices
(260.6042) Physical optics : Singular optics

ToC Category:
Physical Optics

Original Manuscript: February 3, 2014
Revised Manuscript: March 2, 2014
Manuscript Accepted: March 3, 2014
Published: March 12, 2014

Freda Rothschild, Alexis I. Bishop, Marcus J. Kitchen, and David M. Paganin, "Argand-plane vorticity singularities in complex scalar optical fields: An experimental study using optical speckle," Opt. Express 22, 6495-6510 (2014)

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  1. M. Born, E. Wolf, Principles of Optics, 7 (Cambridge University, 1999). [CrossRef]
  2. J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52, 116–130 (1962). [CrossRef] [PubMed]
  3. K. S. Morgan, K. K. W. Siu, D. M. Paganin, “The projection approximation and edge contrast for x-ray propagation-based phase contrast imaging of a cylindrical edge,” Opt. Express 18, 9865–9878 (2010). [CrossRef] [PubMed]
  4. F. Rothschild, M. J. Kitchen, H. M. L. Faulkner, D. M. Paganin, “Duality between phase vortices and Argand-plane caustics,” Opt. Commun. 285, 4141–4151 (2012). [CrossRef]
  5. K. O’Holleran, M. R. Dennis, F. Flossman, M. J. Padgett, “Fractality of light’s darkness,” Phys. Rev. Lett. 100, 053902 (2008). [CrossRef]
  6. K. O’Holleran, F. Flossman, M. R. Dennis, M. J. Padgett, “Methodology for imaging the 3D structure of singularities in scalar and vector optical fields,” J. Opt. A Pure Appl. Opt. 11, 094020 (2009). [CrossRef]
  7. M. V. Berry, “Optical currents,” J. Opt. A Pure Appl. Opt. 11, 094001 (2009). [CrossRef]
  8. H. S. Green, E. Wolf, “A scalar representation of electromagnetic fields,” Proc. Phys. Soc. A 66, 1129–1137 (1953). [CrossRef]
  9. I. Kolar, J. Slovak, P. W. Michor, Natural Operations in Differential Geometry (Springer, 1993). [CrossRef]
  10. M. V. Berry, M. R. Dennis, “Topological events on wave dislocation lines: Birth and death of loops, and reconnection,” J. Phys. A Math. Theor. 40, 65–74 (2007). [CrossRef]
  11. M. R. Dennis, K. O’Holleran, M. J. Padgett, “Singular optics: Optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009). [CrossRef]
  12. H. F. Schouten, G. Gbur, T. D. Visser, E. Wolf, “Phase singularities of the coherence function in Young’s interference pattern,” Opt. Lett. 28, 968–970 (2003). [CrossRef] [PubMed]
  13. J. F. Nye, Natural Focusing and Fine Structure of Light (Institute of Physics, 1999).
  14. H. Schreiber, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992).
  15. L. J. Allen, H. M. L. Faulkner, M. P. Oxley, D. M. Paganin, “Phase retrieval and aberration correction in the presence of vortices in high-resolution transmission electron microscopy,” Ultramicroscopy 88, 85–97 (2001). [CrossRef] [PubMed]
  16. L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, D. M. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001). [CrossRef]
  17. M. J. Kitchen, D. M. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung issue,” Phys. Med. Biol. 49, 4335–4348 (2004). [CrossRef] [PubMed]
  18. E. A. L. Henn, J. A. Seman, E. R. F. Ramos, M. Caracanhas, P. Castilho, E. P. Olimpio, G. Roati, D. V. Magalhaes, K. M. F. Magalhaes, V. S. Bagnato, “Observation of vortex formation in an oscillation trapped Bose–Einstein condensate,” Phys. Rev. A 79, 043618 (2009). [CrossRef]
  19. M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose–Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999). [CrossRef]
  20. C. Raman, J. R. Abo-Shaeer, J. M. Vogels, K. Xu, W. Ketterle, “Vortex nucleation in a stirred Bose–Einstein condensate,” Phys. Rev. Lett. 87, 210402 (2001). [CrossRef]
  21. I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1999). [CrossRef]
  22. G. Gbur, T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222, 117–125 (2003). [CrossRef]
  23. M. L. Marasinghe, D. M. Paganin, 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]
  24. P. Liu, H. Yang, J. Rong, G. Wang, Y. Yan, “Coherence vortex evolution of partially coherent vortex beams in the focal region,” Opt. Laser Technol. 42, 99–104 (2010). [CrossRef]
  25. W. Wang, M. Takeda, “Coherence current, coherence vortex and the conservation law of coherence,” Phys. Rev. Lett. 69, 223904 (2006). [CrossRef]

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