Abstract

Linearly polarized vectorial vortices are analyzed according to their Pancharatnam phase and experimentally demonstrated using a geometric phase element consisting of space-variant subwavelength gratings. It is shown that in the absence of a Pancharatnam phase, stable vectorial vortices that have no angular momentum arise. In contrast, if a Pancharatnam phase is present the vectorial vortices have orbital angular momentum and collapse upon propagation.

© 2006 Optical Society of America

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  5. J. V. Hajnal, "Singularities in the transverse fields of electromagnetic waves," Proc. R. Soc. Lond. A 414, 433-446 and 447-468 (1987).
  6. I. Freund, "Polarization singularity indices in Gaussian laser beams," Opt. Commun. 201, 251-270 (2002).
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  7. M. R. Dennis, "Polarization singularities in paraxial vector fields: morphology and statistics," Opt. Commun. 213, 201-221 (2002).
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  8. P. Pääkkönen, J. Tervo, P. Vahimaa, J. Turunen, and F. Gori, "General vectorial decomposition of electromagnetic fields with application to propagation-invariant and rotating fields," Opt. Express 10, 949-959 (2002).
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  12. 12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
    [CrossRef]
  13. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
    [CrossRef]
  14. M. Stalder and M. Schadt, "Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters," Opt. Lett. 21, 1948-1950 (1996).
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  16. K. C. ToussaintJr., S. Park, J. E. Jureller, and N. F. Scherer, "Generation of optical vector beams with a diffractive optical element interferometer," Opt. Lett. 30, 2846-2848 (2005).
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  18. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, "Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings," Opt. Lett. 27, 1141-1143 (2002).
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    [CrossRef]
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  25. A. Niv, G. Biener, V. Kleiner, and E. Hasman, "Spiral phase elements obtained by use of discrete space-variant subwavelength gratings," Opt. Commun. 251, 306-314 (2005).
    [CrossRef]
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2005 (4)

D. Mawet, P. Riaud, O. Absil, and J. Surdej, "Annular groove phase mask coronagraph," Astro. Phys. 633, 1191-1200 (2005).

A. Niv, G. Biener, V. Kleiner, and E. Hasman, "Spiral phase elements obtained by use of discrete space-variant subwavelength gratings," Opt. Commun. 251, 306-314 (2005).
[CrossRef]

K. C. ToussaintJr., S. Park, J. E. Jureller, and N. F. Scherer, "Generation of optical vector beams with a diffractive optical element interferometer," Opt. Lett. 30, 2846-2848 (2005).
[CrossRef]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, "Rotating vectorial vortices produced by space-variant subwavelength gratings," Opt. Lett. 30, 2933-2935, (2005).
[CrossRef]

2004 (1)

2003 (1)

2002 (6)

Q. Zhan and J. R. Leger, "Interferometric measurement of the geometric phase in space-variant polarization manipulations," Opt. Commun. 213, 241-245 (2002).
[CrossRef]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, "Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings," Opt. Lett. 27, 1141-1143 (2002).

P. Pääkkönen, J. Tervo, P. Vahimaa, J. Turunen, and F. Gori, "General vectorial decomposition of electromagnetic fields with application to propagation-invariant and rotating fields," Opt. Express 10, 949-959 (2002).

D. Palacios, D. Rozas, and G. A. SwartzlanderJr., "Observed scattering into a dark optical vortex core," Phys. Rev. Lett. 88, 103902 1-4 (2002).
[CrossRef]

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

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

2000 (2)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

1999 (1)

12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
[CrossRef]

12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
[CrossRef]

1996 (1)

1992 (1)

27. P. K. Aravind, "A simple proof of Pancharatnam's theorem," Opt. Commun. 94, 191-196 (1992);C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998).
[CrossRef]

27. P. K. Aravind, "A simple proof of Pancharatnam's theorem," Opt. Commun. 94, 191-196 (1992);C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998).
[CrossRef]

1990 (1)

1987 (1)

J. V. Hajnal, "Singularities in the transverse fields of electromagnetic waves," Proc. R. Soc. Lond. A 414, 433-446 and 447-468 (1987).

1983 (3)

R. C. Enger and S.K. Case, "Optical elements with ultrahigh spatial-frequency surface corrugations," Appl. Opt. 223220-3228 (1983).

J.F. Nye, "Polarization effect in the diffraction of electromagnetic waves: the role of disclinations," Proc. R. Soc. Lond. A 387, 105-132 (1983).

J. F. Nye, "Lines of circular polarization in electromagnetic wave fields," Proc. R. Soc. London Ser. A 389, 279-290 (1983).

Absil, O.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, "Annular groove phase mask coronagraph," Astro. Phys. 633, 1191-1200 (2005).

Aravind, P. K.

27. P. K. Aravind, "A simple proof of Pancharatnam's theorem," Opt. Commun. 94, 191-196 (1992);C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998).
[CrossRef]

Biener, G.

Blit, S.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Bomzon, Z.

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, "Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings," Opt. Lett. 27, 1141-1143 (2002).

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Brosseau, C.

27. P. K. Aravind, "A simple proof of Pancharatnam's theorem," Opt. Commun. 94, 191-196 (1992);C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998).
[CrossRef]

Case, S.K.

Cescato, L. H.

Cline, D.

12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
[CrossRef]

Davidson, N.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Dennis, M. R.

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

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Enger, R. C.

Fernow, R. C.

12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
[CrossRef]

Freund, I.

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

Friesem, A. A.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Gluch, E.

Gori, F.

Hajnal, J. V.

J. V. Hajnal, "Singularities in the transverse fields of electromagnetic waves," Proc. R. Soc. Lond. A 414, 433-446 and 447-468 (1987).

Hasman, E.

He, P.

12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
[CrossRef]

Jureller, J. E.

Kim, G. H.

12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
[CrossRef]

Kimura, W. D.

12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
[CrossRef]

Kleiner, V.

Kusche, K. P.

12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
[CrossRef]

Leger, J. R.

Q. Zhan and J. R. Leger, "Interferometric measurement of the geometric phase in space-variant polarization manipulations," Opt. Commun. 213, 241-245 (2002).
[CrossRef]

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Liu, Y.

12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
[CrossRef]

12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
[CrossRef]

Mawet, D.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, "Annular groove phase mask coronagraph," Astro. Phys. 633, 1191-1200 (2005).

Niv, A.

Nye, J. F.

J. F. Nye, "Lines of circular polarization in electromagnetic wave fields," Proc. R. Soc. London Ser. A 389, 279-290 (1983).

Nye, J.F.

J.F. Nye, "Polarization effect in the diffraction of electromagnetic waves: the role of disclinations," Proc. R. Soc. Lond. A 387, 105-132 (1983).

Oron, R.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Pääkkönen, P.

Palacios, D.

D. Palacios, D. Rozas, and G. A. SwartzlanderJr., "Observed scattering into a dark optical vortex core," Phys. Rev. Lett. 88, 103902 1-4 (2002).
[CrossRef]

Park, S.

Pogorelsky, I. V.

12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
[CrossRef]

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Riaud, P.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, "Annular groove phase mask coronagraph," Astro. Phys. 633, 1191-1200 (2005).

Romea, R. D.

12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
[CrossRef]

Rozas, D.

D. Palacios, D. Rozas, and G. A. SwartzlanderJr., "Observed scattering into a dark optical vortex core," Phys. Rev. Lett. 88, 103902 1-4 (2002).
[CrossRef]

Schadt, M.

Scherer, N. F.

Stalder, M.

Steinhauer, L. C.

12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
[CrossRef]

Streibl, N.

Surdej, J.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, "Annular groove phase mask coronagraph," Astro. Phys. 633, 1191-1200 (2005).

Swartzlander, G. A.

D. Palacios, D. Rozas, and G. A. SwartzlanderJr., "Observed scattering into a dark optical vortex core," Phys. Rev. Lett. 88, 103902 1-4 (2002).
[CrossRef]

Tervo, J.

Toussaint, K. C.

Turunen, J.

Vahimaa, P.

Wang, X.

12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
[CrossRef]

Zhan, Q.

Q. Zhan and J. R. Leger, "Interferometric measurement of the geometric phase in space-variant polarization manipulations," Opt. Commun. 213, 241-245 (2002).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Astro. Phys. (1)

D. Mawet, P. Riaud, O. Absil, and J. Surdej, "Annular groove phase mask coronagraph," Astro. Phys. 633, 1191-1200 (2005).

Nucl. Instrum. Meth. Phys Res. A (1)

12. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Meth. Phys Res. A 424, 296-303 (1999);W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, "Laser acceleration of relativistic electons using the inverse Cherenkov effect," Phys. Rev. Lett. 74, 546-549 (1995).
[CrossRef]

Opt. Commun. (6)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

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

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

Q. Zhan and J. R. Leger, "Interferometric measurement of the geometric phase in space-variant polarization manipulations," Opt. Commun. 213, 241-245 (2002).
[CrossRef]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, "Spiral phase elements obtained by use of discrete space-variant subwavelength gratings," Opt. Commun. 251, 306-314 (2005).
[CrossRef]

27. P. K. Aravind, "A simple proof of Pancharatnam's theorem," Opt. Commun. 94, 191-196 (1992);C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. Lett. (1)

D. Palacios, D. Rozas, and G. A. SwartzlanderJr., "Observed scattering into a dark optical vortex core," Phys. Rev. Lett. 88, 103902 1-4 (2002).
[CrossRef]

Proc. R. Soc. Lond. A (2)

J.F. Nye, "Polarization effect in the diffraction of electromagnetic waves: the role of disclinations," Proc. R. Soc. Lond. A 387, 105-132 (1983).

J. V. Hajnal, "Singularities in the transverse fields of electromagnetic waves," Proc. R. Soc. Lond. A 414, 433-446 and 447-468 (1987).

Proc. R. Soc. London Ser. A (1)

J. F. Nye, "Lines of circular polarization in electromagnetic wave fields," Proc. R. Soc. London Ser. A 389, 279-290 (1983).

Other (6)

M. S. Soskin, M.V. Vasnetsov, "Singular optics," in Progress in Optics, Vol.42, E. Wolf ed. (Elsevier, Netherlands, Amsterdam, 2001), pp. 219-276.

E. Collett, Polarized Light (Marcel Dekker, New York, 1993).

S. Pancharatnam, "Generalized theory of interference and its applications. Part I. Coherent pencils," Proc. Ind. Acad. Sci. A 44 (1956) 247 [reprinted in S. Pancharatnam, Collected Works (Oxford University Press, 1975)].

E. Hasman, G. Biener, A. Niv, and V. Kleiner, "Space-variant polarization manipulation," in Progress in Optics, vol.47, E. Wolf ed. (Elsevier, Netherlands, Amsterdam, 2005), pp. 215-289.

L. Allen, M.J. Padgett, and M. Babiker, in Progress in Optics, vol.39, E. Wolf ed. (Elsevier, Netherlands, Amsterdam, 1999), pp. 291-372.

M. Born and E. Wolf, Principles of Optics, seventh ed. (Cambridge University Press, Cambridge, UK, 1999), Section 15.5.2.

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