Abstract

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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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]

2014

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]

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]

2013

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]

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]

V. Kumar and N. K. Viswanathan, “Topological structures in the Poynting vector field: an experimental realization,” Opt. Lett. 38, 3886–3889 (2013).
[CrossRef]

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).

V. Kumar and N. K. Viswanathan, “Polarization singularities and fiber modal decomposition,” Proc. SPIE 8637, 86371A (2013).
[CrossRef]

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]

V. Kumar and N. K. Viswanathan, “The Pancharatnam–Berry phase in polarization singular beams,” J. Opt. 15, 044026 (2013).
[CrossRef]

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]

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]

X. Shi and Y. Ma, “Topological structure dynamics revealing collective evolution in active nematics,” Nat. Commun. 4, 3013 (2013).

N. Nagaosa and Y. Tokura, “Topological properties and dynamics of magnetic skyrmions,” Nat. Nanotechnol. 8, 899–911 (2013).
[CrossRef]

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]

2012

2011

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]

2010

I. Freund, “Optical Möbius strips in three dimensional ellipse fields: II. Lines of linear polarization,” Opt. Commun. 283, 16–28 (2010).
[CrossRef]

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]

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18, 10777–10785 (2010).
[CrossRef]

2009

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
[CrossRef]

V. Vitelli, B. Jain, and R. D. Kamien, “Topological defects in gravitational lensing shear fields,” J. Cosmol. Astropart. Phys. 2009, 034 (2009).
[CrossRef]

A. V. Novitsky and L. M. Barkovsky, “Poynting singularities in optical dynamic systems,” Phys. Rev. A 79, 033821 (2009).
[CrossRef]

2008

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]

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]

V. Vasil’ev and M. Soskin, “Topological and morphological transformations of developing singular paraxial vector light fields,” Opt. Commun. 281, 5527–5540 (2008).
[CrossRef]

M. R. Dennis, “Polarization singularity anisotropy: determining monstardom,” Opt. Lett. 33, 2572–2574 (2008).
[CrossRef]

2007

R. Zambrini and S. M. Barnett, “Angular momentum of multimode and polarization patterns,” Opt. Express 15, 15214–15227 (2007).
[CrossRef]

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]

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]

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).

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]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

2006

2005

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]

2004

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]

2003

2002

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]

I. Freund, “Polarization singularity indices in Gaussian laser beams,” Opt. Commun. 201, 251–270 (2002).
[CrossRef]

I. Freund, M. S. Soskin, and A. I. Mokhun, “Elliptic critical points in paraxial optical fields,” Opt. Commun. 208, 223–253 (2002).
[CrossRef]

M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002).
[CrossRef]

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]

2001

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]

M. V. Berry, “Geometry of phase and polarization singularities illustrated by edge diffraction and the tides,” Proc. SPIE 4403, 1–12 (2001).
[CrossRef]

I. Freund, “Polarization flowers,” Opt. Commun. 199, 47–63 (2001).
[CrossRef]

I. Freund, “Poincaré vortices,” Opt. Lett. 26, 1996–1998 (2001).
[CrossRef]

1987

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]

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]

1977

M. V. Berry and J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
[CrossRef]

1974

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
[CrossRef]

Ade, P. A. R.

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]

Aird, A.

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]

Alfano, R. R.

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]

Alonso, M. A.

Angelsky, O. V.

Arkhelyuk, A.

Austermann, J. E.

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]

Barkovsky, L. M.

A. V. Novitsky and L. M. Barkovsky, “Poynting singularities in optical dynamic systems,” Phys. Rev. A 79, 033821 (2009).
[CrossRef]

Barnett, S. M.

Beall, J. A.

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]

Beckley, A. M.

Bekshaev, A. Y.

Bender, A. N.

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]

Benson, B. A.

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]

Bernet, S.

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]

Berry, M. V.

M. V. Berry, “Geometry of phase and polarization singularities illustrated by edge diffraction and the tides,” Proc. SPIE 4403, 1–12 (2001).
[CrossRef]

M. V. Berry and J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
[CrossRef]

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
[CrossRef]

Bleem, L. E.

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]

Bock, J. J.

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]

Brady, P. C.

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]

Brown, T. G.

Cardano, F.

Carlstrom, J. E.

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]

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]

Chang, C. L.

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]

Chenault, D. B.

Chiang, H. C.

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]

Chikkatur, A. P.

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]

Cho, H.-M.

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]

Conley, A.

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]

Crawford, T. M.

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]

Crites, A.

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]

Cummings, M. E.

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]

Dashti, M.

de Haan, T.

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]

de Lisio, C.

Denisenko, V.

Denisenko, V. G.

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]

Dennis, M. R.

M. R. Dennis, “Polarization singularity anisotropy: determining monstardom,” Opt. Lett. 33, 2572–2574 (2008).
[CrossRef]

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]

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]

M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002).
[CrossRef]

Ding, J.

Dobbs, M. A.

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]

Egorov, R. I.

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]

Everett, W.

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]

Flossmann, F.

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]

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]

Fraser, M.

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]

Freund, I.

I. Freund, “Ordinary polarization singularities in three-dimensional optical fields,” Opt. Lett. 37, 2223–2225 (2012).
[CrossRef]

I. Freund, “Optical Möbius strips in three dimensional ellipse fields: II. Lines of linear polarization,” Opt. Commun. 283, 16–28 (2010).
[CrossRef]

M. S. Soskin, V. Denisenko, and I. Freund, “Optical polarization singularities and elliptic stationary points,” Opt. Lett. 28, 1475–1477 (2003).
[CrossRef]

I. Freund, “Polarization singularity indices in Gaussian laser beams,” Opt. Commun. 201, 251–270 (2002).
[CrossRef]

I. Freund, M. S. Soskin, and A. I. Mokhun, “Elliptic critical points in paraxial optical fields,” Opt. Commun. 208, 223–253 (2002).
[CrossRef]

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]

I. Freund, “Polarization flowers,” Opt. Commun. 199, 47–63 (2001).
[CrossRef]

I. Freund, “Poincaré vortices,” Opt. Lett. 26, 1996–1998 (2001).
[CrossRef]

Fürhapter, S.

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]

Gaensslen, R. E.

H. C. Lee and R. E. Gaensslen, Advances in Fingerprint Technology (CRC Press, 2001).

Gallicchio, J.

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]

Galushko, Y.

Galvez, E. J.

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]

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).

Gao, J.

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]

Geng, J.

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]

George, E. M.

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]

Goldstein, D. L.

Görlitz, A.

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]

Guo, C.-S.

Gupta, S.

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]

Gustavson, T. L.

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]

Hajnal, J. V.

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]

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]

Halverson, N. W.

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]

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]

Han, Y.-J.

Hannay, J. H.

M. V. Berry and J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
[CrossRef]

Hanson, D.

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]

Hanson, S. G.

Harrington, N.

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]

Henning, J. W.

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]

Hilton, G. C.

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]

Hirst, L. S.

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]

Holder, G. P.

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]

Holzapfel, W. L.

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]

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]

Hoover, S.

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]

Hrubes, J. D.

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]

Huang, N.

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]

Hubmayr, J.

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]

Inouye, S.

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]

Irwin, K. D.

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]

Isaeva, V. V.

V. V. Isaeva, N. V. Kasyanov, and E. V. Presnov, “Topological singularities and symmetry breaking in development,” Biosystems 109, 280–298 (2012).
[CrossRef]

Jain, B.

V. Vitelli, B. Jain, and R. D. Kamien, “Topological defects in gravitational lensing shear fields,” J. Cosmol. Astropart. Phys. 2009, 034 (2009).
[CrossRef]

Jesacher, A.

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]

Kamien, R. D.

V. Vitelli, B. Jain, and R. D. Kamien, “Topological defects in gravitational lensing shear fields,” J. Cosmol. Astropart. Phys. 2009, 034 (2009).
[CrossRef]

Karimi, E.

Kasyanov, N. V.

V. V. Isaeva, N. V. Kasyanov, and E. V. Presnov, “Topological singularities and symmetry breaking in development,” Biosystems 109, 280–298 (2012).
[CrossRef]

Keen, S.

Keisler, R.

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]

Ketterle, W.

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]

Kharitonovtta, Y.

Khrobatin, R.

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).

Knox, L.

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]

Kovac, J. M.

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]

Kumar, V.

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]

V. Kumar and N. K. Viswanathan, “The Pancharatnam–Berry phase in polarization singular beams,” J. Opt. 15, 044026 (2013).
[CrossRef]

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]

V. Kumar and N. K. Viswanathan, “Topological structures in the Poynting vector field: an experimental realization,” Opt. Lett. 38, 3886–3889 (2013).
[CrossRef]

V. Kumar and N. K. Viswanathan, “Polarization singularities and fiber modal decomposition,” Proc. SPIE 8637, 86371A (2013).
[CrossRef]

Leach, J.

Leanhardt, A. E.

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]

Lee, A. T.

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]

Lee, H. C.

H. C. Lee and R. E. Gaensslen, Advances in Fingerprint Technology (CRC Press, 2001).

Leitch, E.

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]

Leitch, E. M.

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]

Li, D.

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]

Liang, C.

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]

Love, G. D.

Luong-Van, D.

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]

Ma, Y.

X. Shi and Y. Ma, “Topological structure dynamics revealing collective evolution in active nematics,” Nat. Commun. 4, 3013 (2013).

Maginnis, T.

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]

Maier, M.

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]

Maksimyak, A. P.

Maksimyak, P. P.

Marrucci, L.

Marsden, G.

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]

Maurer, C.

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]

McCullough, K. R.

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).

McMahon, J. J.

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]

Mehl, J.

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]

Meyer, S. S.

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]

Milione, G.

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]

Mocanu, L.

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]

Mokhun, A.

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).

Mokhun, A. I.

I. Freund, M. S. Soskin, and A. I. Mokhun, “Elliptic critical points in paraxial optical fields,” Opt. Commun. 208, 223–253 (2002).
[CrossRef]

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]

Mokhun, I.

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]

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).

Mokhun, I. I.

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

Montroy, T. E.

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]

Nagali, E.

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]

Nagaosa, N.

N. Nagaosa and Y. Tokura, “Topological properties and dynamics of magnetic skyrmions,” Nat. Nanotechnol. 8, 899–911 (2013).
[CrossRef]

Natoli, T.

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]

Ni, W.-J.

Nibarger, J. P.

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]

Nolan, D. A.

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]

Novitsky, A. V.

A. V. Novitsky and L. M. Barkovsky, “Poynting singularities in optical dynamic systems,” Phys. Rev. A 79, 033821 (2009).
[CrossRef]

Novosad, V.

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]

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
[CrossRef]

J. F. Nye, Natural Focusing and Fine Structure of Light (Institute of Physics, 1999).

O’Holleran, K.

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]

Ossowski, A.

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]

Padgett, M. J.

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]

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]

Padin, S.

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]

Philip, G. M.

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]

Presnov, E. V.

V. V. Isaeva, N. V. Kasyanov, and E. V. Presnov, “Topological singularities and symmetry breaking in development,” Biosystems 109, 280–298 (2012).
[CrossRef]

Pritchard, D. E.

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]

Pryke, C.

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]

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]

Rasouli, S.

Reichardt, C. L.

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]

Ritsch-Marte, M.

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]

Rojec, B. L.

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]

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).

Rong, Z.-Y.

Rosenband, T.

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]

Ruhl, J. E.

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]

Saliwanchik, B. R.

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]

Sansoni, L.

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]

Santamato, E.

Saunter, C.

Sayre, J. T.

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]

Schaffer, K. K.

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]

Schulz, B.

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]

Schwarz, U. T.

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]

Sciarrino, F.

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]

Selinger, J. V.

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]

Selinger, R. L. B.

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]

Shaw, J. A.

Shi, X.

X. Shi and Y. Ma, “Topological structure dynamics revealing collective evolution in active nematics,” Nat. Commun. 4, 3013 (2013).

Slussarenko, S.

Smecher, G.

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]

Soskin, M.

V. Vasil’ev and M. Soskin, “Topological and morphological transformations of developing singular paraxial vector light fields,” Opt. Commun. 281, 5527–5540 (2008).
[CrossRef]

Soskin, M. S.

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]

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]

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]

M. S. Soskin, V. Denisenko, and I. Freund, “Optical polarization singularities and elliptic stationary points,” Opt. Lett. 28, 1475–1477 (2003).
[CrossRef]

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]

I. Freund, M. S. Soskin, and A. I. Mokhun, “Elliptic critical points in paraxial optical fields,” Opt. Commun. 208, 223–253 (2002).
[CrossRef]

Stark, A. A.

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]

Story, K. T.

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]

Sztul, H. I.

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]

Tabor, M.

M. Tabor, Chaos and Integrability in Nonlinear Dynamics: An Introduction (Wiley, 1989).

Tokura, Y.

N. Nagaosa and Y. Tokura, “Topological properties and dynamics of magnetic skyrmions,” Nat. Nanotechnol. 8, 899–911 (2013).
[CrossRef]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

J. P. Torres and L. Torner, Twisted Photons (Wiley-VCH, 2011).

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

J. P. Torres and L. Torner, Twisted Photons (Wiley-VCH, 2011).

Toussaint, K. C.

Travis, K. A.

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]

Tripathi, S.

Tucker, C.

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]

Tyo, J. S.

Vanderlinde, K.

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]

Vasil’ev, V.

V. Vasil’ev and M. Soskin, “Topological and morphological transformations of developing singular paraxial vector light fields,” Opt. Commun. 281, 5527–5540 (2008).
[CrossRef]

Vasil’ev, V. I.

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]

Vieira, J. D.

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]

Viero, M. P.

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]

Viktorovskaya, J.

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]

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).

Viswanathan, N. K.

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]

V. Kumar and N. K. Viswanathan, “The Pancharatnam–Berry phase in polarization singular beams,” J. Opt. 15, 044026 (2013).
[CrossRef]

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]

V. Kumar and N. K. Viswanathan, “Polarization singularities and fiber modal decomposition,” Proc. SPIE 8637, 86371A (2013).
[CrossRef]

V. Kumar and N. K. Viswanathan, “Topological structures in the Poynting vector field: an experimental realization,” Opt. Lett. 38, 3886–3889 (2013).
[CrossRef]

Vitelli, V.

V. Vitelli, B. Jain, and R. D. Kamien, “Topological defects in gravitational lensing shear fields,” J. Cosmol. Astropart. Phys. 2009, 034 (2009).
[CrossRef]

Wang, G.

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]

Wang, H.-T.

Wang, S.-Z.

Wang, X.-L.

Yefremenko, V.

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]

Yeganeh, M.

Zahn, O.

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]

Zambrini, R.

Zemcov, M.

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]

Zenkova, C. Y.

Zhan, Q.

Adv. Opt. Photon.

Appl. Opt.

Biosystems

V. V. Isaeva, N. V. Kasyanov, and E. V. Presnov, “Topological singularities and symmetry breaking in development,” Biosystems 109, 280–298 (2012).
[CrossRef]

J. Cosmol. Astropart. Phys.

V. Vitelli, B. Jain, and R. D. Kamien, “Topological defects in gravitational lensing shear fields,” J. Cosmol. Astropart. Phys. 2009, 034 (2009).
[CrossRef]

J. Exp. Theor. Phys. Lett.

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]

J. Opt.

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]

V. Kumar and N. K. Viswanathan, “The Pancharatnam–Berry phase in polarization singular beams,” J. Opt. 15, 044026 (2013).
[CrossRef]

J. Phys. A

M. V. Berry and J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
[CrossRef]

JETP Lett.

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]

Nat. Commun.

X. Shi and Y. Ma, “Topological structure dynamics revealing collective evolution in active nematics,” Nat. Commun. 4, 3013 (2013).

Nat. Nanotechnol.

N. Nagaosa and Y. Tokura, “Topological properties and dynamics of magnetic skyrmions,” Nat. Nanotechnol. 8, 899–911 (2013).
[CrossRef]

Nat. Phys.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

Nature

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]

New J. Phys.

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]

Opt. Appl.

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).

Opt. Commun.

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]

I. Freund, “Optical Möbius strips in three dimensional ellipse fields: II. Lines of linear polarization,” Opt. Commun. 283, 16–28 (2010).
[CrossRef]

V. Vasil’ev and M. Soskin, “Topological and morphological transformations of developing singular paraxial vector light fields,” Opt. Commun. 281, 5527–5540 (2008).
[CrossRef]

I. Freund, “Polarization flowers,” Opt. Commun. 199, 47–63 (2001).
[CrossRef]

I. Freund, “Polarization singularity indices in Gaussian laser beams,” Opt. Commun. 201, 251–270 (2002).
[CrossRef]

I. Freund, M. S. Soskin, and A. I. Mokhun, “Elliptic critical points in paraxial optical fields,” Opt. Commun. 208, 223–253 (2002).
[CrossRef]

M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

A. V. Novitsky and L. M. Barkovsky, “Poynting singularities in optical dynamic systems,” Phys. Rev. A 79, 033821 (2009).
[CrossRef]

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]

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]

Phys. Rev. Lett.

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]

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]

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]

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]

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]

Proc. Natl. Acad. Sci. USA

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]

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]

Proc. R. Soc. London A

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
[CrossRef]

Proc. R. Soc. London Math. Phys. Sci.

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]

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]

Proc. SPIE

M. V. Berry, “Geometry of phase and polarization singularities illustrated by edge diffraction and the tides,” Proc. SPIE 4403, 1–12 (2001).
[CrossRef]

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).

V. Kumar and N. K. Viswanathan, “Polarization singularities and fiber modal decomposition,” Proc. SPIE 8637, 86371A (2013).
[CrossRef]

Other

J. F. Nye, Natural Focusing and Fine Structure of Light (Institute of Physics, 1999).

M. Tabor, Chaos and Integrability in Nonlinear Dynamics: An Introduction (Wiley, 1989).

H. C. Lee and R. E. Gaensslen, Advances in Fingerprint Technology (CRC Press, 2001).

“The power of analogies,” Nat. Photonics8, 1 (2014).

J. P. Torres and L. Torner, Twisted Photons (Wiley-VCH, 2011).

O. V. Angelsky, ed., Optical Correlation Techniques and Applications (SPIE, 2007).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1.
Fig. 1.

Fundamental generic topological structures in π - and 2π-symmetric fields. (a) Lemon, (b) monstar, (c) star, (a′) spiral, (b′) node, and (c′) saddle.

Fig. 2.
Fig. 2.

Experimental setup for realizing optical topologies in vector-vortex beam fields. P, polarizer; H, half-wave plate; SPP, spiral-phase plate; BS, beam splitter; M, mirror; DP, Dove prism; PBS, polarization beam splitter; Q, quarter-wave plate; ISP, imaging Stokes polarimeter.

Fig. 3.
Fig. 3.

Simulated streamline plots of Stokes fields. (a) Ψ, (b) Φ12, (c) Φ23, and (d) Φ31 for lemon topological pattern. (a′)–(d′) are the corresponding fields for the star pattern. Background is the color-coded Ψ and Φ fields. Color bar is π/2+π/2 for half-index maps and π+π for integer-index maps.

Fig. 4.
Fig. 4.

Experimentally measured streamline plots of Stokes fields. (a) Ψ, (b) Φ12, (c) Φ23, and (d) Φ31 for lemon topological pattern. (a′)–(d′) are the corresponding fields for the star pattern.

Fig. 5.
Fig. 5.

Poynting vector densities of vector-vortex beam with lemon topological pattern. Simulation: (a) orbital, (b) spin, and (c) total. (a′)–(c′) are the corresponding experimentally measured plots.

Fig. 6.
Fig. 6.

Poynting vector densities of vector-vortex beam with star topological pattern. Simulation: (a) orbital, (b) spin, and (c) total. (a′)–(c′) are the corresponding experimentally measured plots.

Fig. 7.
Fig. 7.

Streamline plots of lemon pattern (Ψ field) for (a) φ=π/4 and (b) φ=π/2 (b). (a′) and (b′) are the corresponding streamline plots of the Φ12 field.

Fig. 8.
Fig. 8.

Streamline plots of vector-vortex beam with (a) monstar topological pattern and (b) corresponding node pattern.

Fig. 9.
Fig. 9.

(a) Half-index dipole in linear basis (e^H,e^V); (b) Φ12, (c) Φ23, and (d) Φ31 are the corresponding Stokes vortices. (a′)–(d′) are the corresponding plots in the (e^D,e^A) basis.

Fig. 10.
Fig. 10.

(a) Half-index dipole and its corresponding (b) orbital, (c) spin, and (d) total Poynting vector densities.

Fig. 11.
Fig. 11.

(a) C-line singularities, (b) corresponding Stokes field S23, and (c) spin Poynting vector density. (a′)–(c′) are the corresponding experimentally measured plots.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

S0=|a1|2+|a2|2,
S1=|a1|2|a2|2,
S2=2S01Re(Ex*Ey),
S2=2S01Im(Ex*Ey).
S12=S1+iS2,
S23=S2+iS3,
S31=S3+iS1,
Φ12=arg(S1+iS2),
Φ23=arg(S2+iS3),
Φ31=arg(S3+iS1).
Ψ=Φ122.
P⃗o=1k(Iiφi+Ijφj),
P⃗s=12k[e⃗z×S3],
P⃗o(s)=P⃗+o(s)+P⃗o(s)=P⃗xo(s)+P⃗yo(s),
P⃗=P⃗o+P⃗s.
E⃗=E1e^1+eiφE2e^2,
E1=a[x+sign(l1)iy]|l1|er22w0,
E2=b[x+sign(l2)iy]|l2|er22w0.
E⃗=[(cosβreilϕ+sinβeiγreilϕ)e^+ae^+]er22w.

Metrics