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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 2 — Jan. 21, 2008
  • pp: 695–709

Singular polarimetry: Evolution of polarization singularities in electromagnetic waves propagating in a weakly anisotropic medium

Konstantin Yu. Bliokh, Avi Niv, Vladimir Kleiner, and Erez Hasman  »View Author Affiliations

Optics Express, Vol. 16, Issue 2, pp. 695-709 (2008)

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We describe the evolution of a paraxial electromagnetic wave characterizing by a non-uniform polarization distribution with singularities and propagating in a weakly anisotropic medium. Our approach is based on the Stokes vector evolution equation applied to a non-uniform initial polarization field. In the case of a homogeneous medium, this equation is integrated analytically. This yields a 3-dimensional distribution of the polarization parameters containing singularities, i.e. C-lines of circular polarization and L-surfaces of linear polarization. The general theory is applied to specific examples of the unfolding of a vectorial vortex in birefringent and dichroic media.

© 2008 Optical Society of America

OCIS Codes
(260.1180) Physical optics : Crystal optics
(260.2130) Physical optics : Ellipsometry and polarimetry
(260.5430) Physical optics : Polarization
(260.6042) Physical optics : Singular optics

ToC Category:
Physical Optics

Original Manuscript: October 29, 2007
Revised Manuscript: December 13, 2007
Manuscript Accepted: December 15, 2007
Published: January 8, 2008

Konstantin Yu. Bliokh, Avi Niv, Vladimir Kleiner, and Erez Hasman, "Singular polarimetry: Evolution of polarization singularities in electromagnetic waves propagating in a weakly anisotropic medium," Opt. Express 16, 695-709 (2008)

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  1. M. V. Berry, "Singularities in waves and rays," in Les Houches Session XXV - Physics of Defects, R. Balian, M. Kléman, and J.-P. Poirier, eds., (North-Holland, 1981).
  2. J. F.  Nye, Natural Focusing and Fine Structure of Light: caustics and wave dislocations (IoP Publishing, 1999).
  3. M. S. Soskin and M. V. Vasnetsov, "Singular optics," Prog. Opt. 42, 219-276 (2001). [CrossRef]
  4. L. Allen, M. J. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291-372 (1999). [CrossRef]
  5. J. F. Nye, "Lines of circular polarization in electromagnetic wave fields," Proc. R. Soc. London A 389, 279-290 (1983). [CrossRef]
  6. J. F. Nye and J. V. Hajnal, "The wave structure of monochromatic electromagnetic radiation," Proc. R. Soc. London A 409, 21-36 (1987). [CrossRef]
  7. M. V. Berry and M. R. Dennis, "Polarization singularities in isotropic random vector waves," Proc. R. Soc. London A 457, 141−155 (2001). [CrossRef]
  8. I.  Freund, "Polarization singularity indices in Gaussian laser beams," Opt. Commun. 201, 251-270 (2002). [CrossRef]
  9. M. R. Dennis, "Polarization singularities in paraxial vector fields: morphology and statistics," Opt. Commun. 213, 201-221 (2002). [CrossRef]
  10. J.  Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001). [CrossRef]
  11. I.  Freund, N. Shvartsman, and V. Freilikher, "Optical dislocation networks in highly random media," Opt. Commun. 101, 247-264 (1993). [CrossRef]
  12. E.  Hasman, G.  Biener, A.  Niv, and V.  Kleiner, "Space-variant polarization manipulation," Prog. Opt. 47, 215-289 (2005). [CrossRef]
  13. A.  Niv, G.  Biener, V.  Kleiner, and E. Hasman, "Manipulation of the Pancharatnam phase in vectorial vortices," Opt. Express 14, 4208-4220 (2006). [CrossRef] [PubMed]
  14. K. Yu. Bliokh, "Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect," Phys. Rev. Lett. 97, 043901 (2006). [CrossRef] [PubMed]
  15. 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] [PubMed]
  16. F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, "Stokes parameters in the unfolding of an optical vortex through a birefringent crystal," Opt. Express 14, 11402-11411 (2006). [CrossRef] [PubMed]
  17. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).
  18. C. Brosseau, Fundamentals of Polarized Light (John Wiley and Sons, 1998).
  19. R. M. A.  Azzam, "Propagation of partially polarized light through anisotropic media with or without depolarization: a differential 4x4 matrix calculus," J. Opt. Soc. Am. 68, 1756-1767 (1978). [CrossRef]
  20. C. S.  Brown and A. E.  Bak, "Unified formalism for polarization optics with application to polarimetry on a twisted optical fiber," Opt. Eng. 34, 1625-1635 (1995). [CrossRef]
  21. C.  Brosseau, "Evolution of the Stokes parameters in optically anisotropic media," Opt. Lett. 20, 1221-1223 (1995). [CrossRef] [PubMed]
  22. H.  Kuratsuji and S.  Kakigi, "Maxwell-Schrödinger equation for polarized light and evolution of the Stokes parameters," Phys. Rev. Lett. 80, 1888-1891 (1998). [CrossRef]
  23. S. E.  Segre, "New formalism for the analysis of polarization evolution for radiation in a weakly nonuniform, fully anisotropic medium: a magnetized plasma," J. Opt. Soc. Am. A 18, 2601-2606 (2001). [CrossRef]
  24. R.  Botet, H.  Kuratsuji, and R.  Seto, "Novel aspects of evolution of the Stokes parameters for an electromagnetic wave in anisotropic media," Prog. Theor. Phys. 116, 285-294 (2006). [CrossRef]
  25. K. Y.  Bliokh, D. Y.  Frolov, and Y. A.  Kravtsov, "Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium," Phys. Rev. A 75, 053821 (2007). [CrossRef]
  26. Y. A.  Kravtsov, B.  Bieg, and K. Y.  Bliokh, "Stokes-vector evolution in a weakly anisotropic inhomogeneous medium," J. Opt. Soc. Am. A 24, 3388-3396 (2007). [CrossRef]
  27. R.  Barakat, "Bilinear constraints between elements of the 4x4 Mueller-Jones transfer matrix of polarization theory," Opt. Commun. 38, 159-161 (1981). [CrossRef]
  28. R.  Simon, "The connection between Mueller and Jones matrices of polarization optics," Opt. Commun. 42, 293-297 (1982). [CrossRef]
  29. S. R.  Cloude, "Group theory and polarization algebra," Optik 75, 26-32 (1986).
  30. T.  Opartny and J.  Perina, "Non-image-forming polarization optical devices and Lorentz transformation - an analogy," Phys. Lett. A 181, 199-202 (1993). [CrossRef]
  31. D.  Han, Y. S.  Kim, and M. E.  Noz, "Polarization optics and bilinear representation of the Lorentz group," Phys. Lett. A. 219, 26-32 (1996). [CrossRef]
  32. V. B. Berestetskii, E. M. Lifshits, and L. P. Pitaevskii, Quantum Electrodynamics (Pergamon, Oxford, 1982).
  33. C. P. Slichter, Principles of Magnetic Resonance (Springer-Verlag, New York, 1989).
  34. H.  Goldstein, C.  Poole, and J. Safko, Classical Mechanics (Addison Wesley, San Francisco, 2002).
  35. A. D.  Kiselev, "Singularities in polarization resolved angular patterns: transmittance of nematic liquid crystal cells," J. Phys.: Condens. Matter 19, 246102 (2007). [CrossRef]

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