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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 31, Iss. 6 — Jun. 1, 2014
  • pp: A40–A45

Topological structures in vector-vortex beam fields

Vijay Kumar and Nirmal K. Viswanathan  »View Author Affiliations

JOSA B, Vol. 31, Issue 6, pp. A40-A45 (2014)

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Optical singularities of index Iu=±1/2 associated with lemon, monstar, and star topological structures in π-symmetric fields and singularities of index Ic=±1 associated with radial, circulation (elliptic), spiral, node, and saddle structures in 2π-symmetric vector fields are studied in detail here. The topological structures in the polarization ellipse orientation field, the Stokes field, and the Poynting vector field are derived from the same vector-vortex beam fields, and their interdependencies are explored using a designed experimental setup. We find that the inherently stable topological approach is much more informative for a deeper understanding of complex vector-vortex beam fields.

© 2014 Optical Society of America

OCIS Codes
(260.3160) Physical optics : Interference
(260.5430) Physical optics : Polarization
(260.6042) Physical optics : Singular optics

Original Manuscript: January 29, 2014
Revised Manuscript: April 10, 2014
Manuscript Accepted: April 10, 2014
Published: May 6, 2014

Vijay Kumar and Nirmal K. Viswanathan, "Topological structures in vector-vortex beam fields," J. Opt. Soc. Am. B 31, A40-A45 (2014)

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  1. S. Inouye, S. Gupta, T. Rosenband, A. P. Chikkatur, A. Görlitz, T. L. Gustavson, A. E. Leanhardt, D. E. Pritchard, and W. Ketterle, “Observation of vortex phase singularities in Bose-Einstein condensates,” Phys. Rev. Lett. 87, 080402 (2001). [CrossRef]
  2. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974). [CrossRef]
  3. H. C. Lee and R. E. Gaensslen, Advances in Fingerprint Technology (CRC Press, 2001).
  4. V. V. Isaeva, N. V. Kasyanov, and E. V. Presnov, “Topological singularities and symmetry breaking in development,” Biosystems 109, 280–298 (2012). [CrossRef]
  5. L. S. Hirst, A. Ossowski, M. Fraser, J. Geng, J. V. Selinger, and R. L. B. Selinger, “Morphology transition in lipid vesicles due to in-plane order and topological defects,” Proc. Natl. Acad. Sci. USA 110, 3242–3247 (2013). [CrossRef]
  6. J. M. Kovac, E. M. Leitch, C. Pryke, J. E. Carlstrom, N. W. Halverson, and W. L. Holzapfel, “Detection of polarization in the cosmic microwave background using DASI,” Nature 420, 772–787 (2002). [CrossRef]
  7. D. Hanson, S. Hoover, A. Crites, P. A. R. Ade, A. Aird, J. E. Austermann, J. A. Beall, A. N. Bender, B. A. Benson, L. E. Bleem, J. J. Bock, J. E. Carlstrom, C. L. Chang, H. C. Chiang, H.-M. Cho, A. Conley, T. M. Crawford, T. de Haan, M. A. Dobbs, W. Everett, J. Gallicchio, J. Gao, E. M. George, N. W. Halverson, N. Harrington, J. W. Henning, G. C. Hilton, G. P. Holder, W. L. Holzapfel, J. D. Hrubes, N. Huang, J. Hubmayr, K. D. Irwin, R. Keisler, L. Knox, A. T. Lee, E. Leitch, D. Li, C. Liang, D. Luong-Van, G. Marsden, J. J. McMahon, J. Mehl, S. S. Meyer, L. Mocanu, T. E. Montroy, T. Natoli, J. P. Nibarger, V. Novosad, S. Padin, C. Pryke, C. L. Reichardt, J. E. Ruhl, B. R. Saliwanchik, J. T. Sayre, K. K. Schaffer, B. Schulz, G. Smecher, A. A. Stark, K. T. Story, C. Tucker, K. Vanderlinde, J. D. Vieira, M. P. Viero, G. Wang, V. Yefremenko, O. Zahn, and M. Zemcov, and SPTpol Collaboration, “Detection of B-mode polarization in the cosmic microwave background with data from the South Pole Telescope,” Phys. Rev. Lett. 111, 141301 (2013). [CrossRef]
  8. V. Vitelli, B. Jain, and R. D. Kamien, “Topological defects in gravitational lensing shear fields,” J. Cosmol. Astropart. Phys. 2009, 034 (2009). [CrossRef]
  9. X. Shi and Y. Ma, “Topological structure dynamics revealing collective evolution in active nematics,” Nat. Commun. 4, 3013 (2013).
  10. N. Nagaosa and Y. Tokura, “Topological properties and dynamics of magnetic skyrmions,” Nat. Nanotechnol. 8, 899–911 (2013). [CrossRef]
  11. “The power of analogies,” Nat. Photonics8, 1 (2014).
  12. M. V. Berry and J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977). [CrossRef]
  13. M. Tabor, Chaos and Integrability in Nonlinear Dynamics: An Introduction (Wiley, 1989).
  14. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006). [CrossRef]
  15. P. C. Brady, K. A. Travis, T. Maginnis, and M. E. Cummings, “Polaro–cryptic mirror of the lookdown as a biological model for open ocean camouflage,” Proc. Natl. Acad. Sci. USA 110, 9764–9769 (2013). [CrossRef]
  16. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007). [CrossRef]
  17. E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterization of single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010). [CrossRef]
  18. J. V. Hajnal, “Singularities in the transverse fields of electromagnetic waves. I. Theory,” Proc. R. Soc. London Math. Phys. Sci. 414, 433–446 (1987). [CrossRef]
  19. J. V. Hajnal, “Singularities in the transverse fields of electromagnetic waves. II. Observations on the electric field,” Proc. R. Soc. London Math. Phys. Sci. 414, 447–468 (1987). [CrossRef]
  20. J. F. Nye, Natural Focusing and Fine Structure of Light (Institute of Physics, 1999).
  21. M. V. Berry, “Geometry of phase and polarization singularities illustrated by edge diffraction and the tides,” Proc. SPIE 4403, 1–12 (2001). [CrossRef]
  22. I. Freund, “Polarization flowers,” Opt. Commun. 199, 47–63 (2001). [CrossRef]
  23. I. Freund, “Polarization singularity indices in Gaussian laser beams,” Opt. Commun. 201, 251–270 (2002). [CrossRef]
  24. I. Freund, M. S. Soskin, and A. I. Mokhun, “Elliptic critical points in paraxial optical fields,” Opt. Commun. 208, 223–253 (2002). [CrossRef]
  25. M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002). [CrossRef]
  26. M. S. Soskin, V. Denisenko, and I. Freund, “Optical polarization singularities and elliptic stationary points,” Opt. Lett. 28, 1475–1477 (2003). [CrossRef]
  27. V. G. Denisenko, R. I. Egorov, and M. S. Soskin, “Measurement of the morphological forms of polarization singularities and their statistical weights in optical vector fields,” J. Exp. Theor. Phys. Lett. 80, 17–19 (2004). [CrossRef]
  28. F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901 (2005). [CrossRef]
  29. V. I. Vasil’ev and M. S. Soskin, “Topological scenarios of the creation and annihilation of polarization singularities in nonstationary optical fields,” JETP Lett. 87, 83–86 (2008). [CrossRef]
  30. F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization singularities in 2D and 3D speckle fields,” Phys. Rev. Lett. 100, 203902 (2008). [CrossRef]
  31. M. R. Dennis, “Polarization singularity anisotropy: determining monstardom,” Opt. Lett. 33, 2572–2574 (2008). [CrossRef]
  32. V. Vasil’ev and M. Soskin, “Topological and morphological transformations of developing singular paraxial vector light fields,” Opt. Commun. 281, 5527–5540 (2008). [CrossRef]
  33. A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18, 10777–10785 (2010). [CrossRef]
  34. I. Freund, “Ordinary polarization singularities in three-dimensional optical fields,” Opt. Lett. 37, 2223–2225 (2012). [CrossRef]
  35. E. J. Galvez, B. L. Rojec, and K. R. McCullough, “Imaging optical singularities: understanding the duality of C-points and optical vortices,” Proc. SPIE 8637, 863706 (2013).
  36. V. Kumar and N. K. Viswanathan, “Polarization singularities and fiber modal decomposition,” Proc. SPIE 8637, 86371A (2013). [CrossRef]
  37. V. Kumar, G. M. Philip, and N. K. Viswanathan, “Formation and morphological transformation of polarization singularities: hunting the monstar,” J. Opt. 15, 044027 (2013). [CrossRef]
  38. V. Kumar and N. K. Viswanathan, “The Pancharatnam–Berry phase in polarization singular beams,” J. Opt. 15, 044026 (2013). [CrossRef]
  39. F. Cardano, E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Generation and dynamics of optical beams with polarization singularities,” Opt. Express 21, 8815–8820 (2013). [CrossRef]
  40. C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007). [CrossRef]
  41. X.-L. Wang, J. Ding, W.-J. Ni, C.-S. Guo, and H.-T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32, 3549–3551 (2007). [CrossRef]
  42. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009). [CrossRef]
  43. G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011). [CrossRef]
  44. F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012). [CrossRef]
  45. S. Tripathi and K. C. Toussaint, “Versatile generation of optical vector fields and vector beams using a non-interferometric approach,” Opt. Express 20, 10788–10795 (2012). [CrossRef]
  46. Z.-Y. Rong, Y.-J. Han, S.-Z. Wang, and C.-S. Guo, “Generation of arbitrary vector beams with cascaded liquid crystal spatial light modulators,” Opt. Express 22, 1636–1644 (2014). [CrossRef]
  47. J. Leach, S. Keen, M. J. Padgett, C. Saunter, and G. D. Love, “Direct measurement of the skew angle of the Poynting vector in a helically phased beam,” Opt. Express 14, 11919–11924 (2006). [CrossRef]
  48. I. Mokhun, R. Khrobatin, A. Mokhun, and J. Viktorovskaya, “The behavior of the Poynting vector in the area of elementary polarization singularities,” Opt. Appl. 37, 261–277 (2007).
  49. A. Y. Bekshaev and M. S. Soskin, “Transverse energy flows in vectorial fields of paraxial beams with singularities,” Opt. Commun. 271, 332–348 (2007). [CrossRef]
  50. O. V. Angelsky, ed., Optical Correlation Techniques and Applications (SPIE, 2007).
  51. A. V. Novitsky and L. M. Barkovsky, “Poynting singularities in optical dynamic systems,” Phys. Rev. A 79, 033821 (2009). [CrossRef]
  52. I. Mokhun, A. Arkhelyuk, Y. Galushko, Y. Kharitonovtta, and J. Viktorovskaya, “Experimental analysis of the Poynting vector characteristics,” Appl. Opt. 51, C158–C162 (2012). [CrossRef]
  53. M. Yeganeh, S. Rasouli, M. Dashti, S. Slussarenko, E. Santamato, and E. Karimi, “Reconstructing the Poynting vector skew angle and wavefront of optical vortex beams via two-channel Moiré deflectometery,” Opt. Lett. 38, 887–889 (2013). [CrossRef]
  54. V. Kumar and N. K. Viswanathan, “Topological structures in the Poynting vector field: an experimental realization,” Opt. Lett. 38, 3886–3889 (2013). [CrossRef]
  55. I. Freund, “Poincaré vortices,” Opt. Lett. 26, 1996–1998 (2001). [CrossRef]
  56. I. Freund, A. I. Mokhun, M. S. Soskin, O. V. Angelsky, and I. I. Mokhun, “Stokes singularity relations,” Opt. Lett. 27, 545–547 (2002). [CrossRef]
  57. J. P. Torres and L. Torner, Twisted Photons (Wiley-VCH, 2011).
  58. R. Zambrini and S. M. Barnett, “Angular momentum of multimode and polarization patterns,” Opt. Express 15, 15214–15227 (2007). [CrossRef]
  59. E. J. Galvez, B. L. Rojec, V. Kumar, and N. K. Viswanathan, “Generation of isolated asymmetric umbilics in light’s polarization,” Phys. Rev. A 89, 031801(R) (2014). [CrossRef]
  60. I. Freund, “Optical Möbius strips in three dimensional ellipse fields: II. Lines of linear polarization,” Opt. Commun. 283, 16–28 (2010). [CrossRef]
  61. O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, S. G. Hanson, and C. Y. Zenkova, “Orbital rotation without orbital angular momentum: mechanical action of the spin part of the internal energy flow in light beams,” Opt. Express 20, 3563–3571 (2012). [CrossRef]

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