Abstract

We present developments using photo-aligned liquid crystal polymers for creating vortex retarders, halfwave retarders with a continuously variable fast axis. Polarization properties of components designed to create different polarization vortex modes are presented. We assess the viability of these components using the theoretical and experimental point spread functions and optical transfer functions in Mueller matrix format, point spread matrix (PSM) and optical transfer matrix (OTM). The measured PSM and OTM of these components in an optical system is very close to the theoretically predicted values thus showing that these components should provide excellent performance in applications utilizing polarized optical vortices. The impact of aberrations and of vortex retarder misalignment on the PSM and OTM are presented.

©2008 Optical Society of America

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  1. S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
    [Crossref]
  2. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical vector beams,” Opt. Express 7, 77–87 (2000).
    [Crossref] [PubMed]
  3. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 85, 5251–5253 (2001).
    [Crossref]
  4. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for radially polarized light beam,” Phys. Rev. Lett. 91, 23 (2003).
    [Crossref]
  5. Totzeck, et al., “Polarizer device for generating a defined spatial distribution of polarization states,” US 2006/0028706, Feb. 9, 2006.
  6. A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam-Berry phase optical elements,” Opt Lett 29, 238 (2004).
    [Crossref] [PubMed]
  7. V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature419, 145 (2002).
    [Crossref] [PubMed]
  8. M. Born and E. Wolf, Principles of Optics: Electromagnetic theory of propagation, interference and diffraction of light, (Cambridge University Press, seventh ed., 1999).
    [PubMed]
  9. Y. Mushiake, K. Matzumurra, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60, 1107–1109 (1972).
    [Crossref]
  10. T. Erdogan, K. G. Sullivan, and D. G. Hall, “Enhancement and inhibition of radiation in cylindrically symmetric, periodic structures,” J. Opt. Soc. Am. B 10, 391–398 (1993).
    [Crossref]
  11. T. Erdogan, O. King, W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, AlGaAs/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
    [Crossref]
  12. S. C. Tidwell, D. H. Ford, and W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2234–2239 (1990).
    [Crossref] [PubMed]
  13. 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. Phy Lett. 77, 21 (2000)
    [Crossref]
  14. R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28, 1730 (1989).
    [Crossref]
  15. A. K. Spilman and T. G. Brown, “Stress birefringent, space-variant wave plates for vortex illumination,” Appl. Opt. 46, 61–66 (2007).
    [Crossref]
  16. G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Efficient extracavity generation of radially and azimuthally polarized beams,” Opt. Lett. 32, 11 (2007).
    [Crossref]
  17. M. Stalder and M. Schadt, “Linear polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt Lett. 21, 23 (1996).
    [Crossref]
  18. S. C. McEldowney, D. M. Shemo, R. A. Chipman, and P. K. Smith, “Creating vortex retarders using photoaligned liquid crystal polymers,” Opt. Lett. 33, 134–136 (2008).
    [Crossref] [PubMed]
  19. M. Schadt, H. Seiberle, A. Schuster, and S. M. Kelly “Photo-induced alignment and patterning of hybrid liquid crystalline polymer films on single substrates,” Jpn. J. Appl. Phys. 34, L764–L767 (1995).
    [Crossref]
  20. D. G. Hall, “Vector-beam solutions of Maxwell’s wave equation,” Opt. Lett. 21, 9–11 (1996).
    [Crossref] [PubMed]
  21. R. H. Jordan and D. G. Hall, “Free-space azimuthal paraxial wave equation: The azimuthal Bessel-Gauss beam solution,” Opt. Lett. 19, 427–429 (1994).
    [Crossref] [PubMed]
  22. P. L. Greene and D. G. Hall, “Diffraction characteristics of the azimuthal Bessel-Gauss beam,” J. Opt. Soc.Am. A 13, 962–966 (1996).
    [Crossref]
  23. P. L. Greene and D. G. Hall, “Properties and diffraction of vector Bessel-Gauss beams,” J. Opt. Soc. Am. A 15, 3020–3027 (1998).
    [Crossref]
  24. C. J. R. Sheppard and S. Saghafi, “Transverse-electric and transverse-magnetic beam modes beyond the paraxial approximation,” Opt. Lett. 24, 1543–1545 (1999).
    [Crossref]
  25. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical vector beams,” Opt. Express. 7, 77–87, (2000).
    [Crossref] [PubMed]
  26. S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
    [Crossref]
  27. J. P. McGuire, Jr. and R. A. Chipman, “Diffraction image formation in optical systems with polarization aberrations I: Formulation and example,” J. Opt. Soc. Am A. 7, 9, 1614–1626 (1990).
    [Crossref]
  28. Information on Axometrics polarimeter from http://www.axometrics.com/
  29. J. L. Pezzanitti and R. A. Chipman, “Mueller matrix imaging polarimeter,” Opt. Eng. 34, 6 (1995).
    [Crossref]

2008 (1)

2007 (2)

2004 (1)

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam-Berry phase optical elements,” Opt Lett 29, 238 (2004).
[Crossref] [PubMed]

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for radially polarized light beam,” Phys. Rev. Lett. 91, 23 (2003).
[Crossref]

2001 (1)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 85, 5251–5253 (2001).
[Crossref]

2000 (5)

S. Quabis, R. Dorn, M. Eberler, O. Glockl, 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. Phy Lett. 77, 21 (2000)
[Crossref]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical vector beams,” Opt. Express. 7, 77–87, (2000).
[Crossref] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical vector beams,” Opt. Express 7, 77–87 (2000).
[Crossref] [PubMed]

1999 (1)

1998 (1)

1996 (3)

D. G. Hall, “Vector-beam solutions of Maxwell’s wave equation,” Opt. Lett. 21, 9–11 (1996).
[Crossref] [PubMed]

M. Stalder and M. Schadt, “Linear polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt Lett. 21, 23 (1996).
[Crossref]

P. L. Greene and D. G. Hall, “Diffraction characteristics of the azimuthal Bessel-Gauss beam,” J. Opt. Soc.Am. A 13, 962–966 (1996).
[Crossref]

1995 (2)

J. L. Pezzanitti and R. A. Chipman, “Mueller matrix imaging polarimeter,” Opt. Eng. 34, 6 (1995).
[Crossref]

M. Schadt, H. Seiberle, A. Schuster, and S. M. Kelly “Photo-induced alignment and patterning of hybrid liquid crystalline polymer films on single substrates,” Jpn. J. Appl. Phys. 34, L764–L767 (1995).
[Crossref]

1994 (1)

1993 (1)

1992 (1)

T. Erdogan, O. King, W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, AlGaAs/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]

1990 (2)

J. P. McGuire, Jr. and R. A. Chipman, “Diffraction image formation in optical systems with polarization aberrations I: Formulation and example,” J. Opt. Soc. Am A. 7, 9, 1614–1626 (1990).
[Crossref]

S. C. Tidwell, D. H. Ford, and W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2234–2239 (1990).
[Crossref] [PubMed]

1989 (1)

R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28, 1730 (1989).
[Crossref]

1972 (1)

Y. Mushiake, K. Matzumurra, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60, 1107–1109 (1972).
[Crossref]

Anderson, E. H.

T. Erdogan, O. King, W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, AlGaAs/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 85, 5251–5253 (2001).
[Crossref]

Biener, G.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam-Berry phase optical elements,” Opt Lett 29, 238 (2004).
[Crossref] [PubMed]

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. Phy Lett. 77, 21 (2000)
[Crossref]

Bomzon, Z.

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. Phy Lett. 77, 21 (2000)
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic theory of propagation, interference and diffraction of light, (Cambridge University Press, seventh ed., 1999).
[PubMed]

Brown, T. G.

A. K. Spilman and T. G. Brown, “Stress birefringent, space-variant wave plates for vortex illumination,” Appl. Opt. 46, 61–66 (2007).
[Crossref]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 85, 5251–5253 (2001).
[Crossref]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical vector beams,” Opt. Express. 7, 77–87, (2000).
[Crossref] [PubMed]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical vector beams,” Opt. Express 7, 77–87 (2000).
[Crossref] [PubMed]

Chipman, R. A.

S. C. McEldowney, D. M. Shemo, R. A. Chipman, and P. K. Smith, “Creating vortex retarders using photoaligned liquid crystal polymers,” Opt. Lett. 33, 134–136 (2008).
[Crossref] [PubMed]

J. L. Pezzanitti and R. A. Chipman, “Mueller matrix imaging polarimeter,” Opt. Eng. 34, 6 (1995).
[Crossref]

J. P. McGuire, Jr. and R. A. Chipman, “Diffraction image formation in optical systems with polarization aberrations I: Formulation and example,” J. Opt. Soc. Am A. 7, 9, 1614–1626 (1990).
[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. Phy Lett. 77, 21 (2000)
[Crossref]

Dholakia, K.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature419, 145 (2002).
[Crossref] [PubMed]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for radially polarized light beam,” Phys. Rev. Lett. 91, 23 (2003).
[Crossref]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, 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. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Erdogan, T.

T. Erdogan, K. G. Sullivan, and D. G. Hall, “Enhancement and inhibition of radiation in cylindrically symmetric, periodic structures,” J. Opt. Soc. Am. B 10, 391–398 (1993).
[Crossref]

T. Erdogan, O. King, W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, AlGaAs/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]

Ford, D. H.

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. Phy Lett. 77, 21 (2000)
[Crossref]

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature419, 145 (2002).
[Crossref] [PubMed]

Glockl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Greene, P. L.

P. L. Greene and D. G. Hall, “Properties and diffraction of vector Bessel-Gauss beams,” J. Opt. Soc. Am. A 15, 3020–3027 (1998).
[Crossref]

P. L. Greene and D. G. Hall, “Diffraction characteristics of the azimuthal Bessel-Gauss beam,” J. Opt. Soc.Am. A 13, 962–966 (1996).
[Crossref]

Hall, D. G.

Hasman, E.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam-Berry phase optical elements,” Opt Lett 29, 238 (2004).
[Crossref] [PubMed]

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. Phy Lett. 77, 21 (2000)
[Crossref]

Jackel, S.

Jordan, R. H.

Kelly, S. M.

M. Schadt, H. Seiberle, A. Schuster, and S. M. Kelly “Photo-induced alignment and patterning of hybrid liquid crystalline polymer films on single substrates,” Jpn. J. Appl. Phys. 34, L764–L767 (1995).
[Crossref]

Kimura, W. D.

King, O.

T. Erdogan, O. King, W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, AlGaAs/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]

Kleiner, V.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam-Berry phase optical elements,” Opt Lett 29, 238 (2004).
[Crossref] [PubMed]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for radially polarized light beam,” Phys. Rev. Lett. 91, 23 (2003).
[Crossref]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Lumer, Y.

Machavariani, G.

Matzumurra, K.

Y. Mushiake, K. Matzumurra, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60, 1107–1109 (1972).
[Crossref]

McEldowney, S. C.

McGloin, D.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature419, 145 (2002).
[Crossref] [PubMed]

McGuire, Jr., J. P.

J. P. McGuire, Jr. and R. A. Chipman, “Diffraction image formation in optical systems with polarization aberrations I: Formulation and example,” J. Opt. Soc. Am A. 7, 9, 1614–1626 (1990).
[Crossref]

Meir, A.

Melville, H.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature419, 145 (2002).
[Crossref] [PubMed]

Moshe, I.

Mushiake, Y.

Y. Mushiake, K. Matzumurra, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60, 1107–1109 (1972).
[Crossref]

Nakajima, N.

Y. Mushiake, K. Matzumurra, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60, 1107–1109 (1972).
[Crossref]

Niv, A.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam-Berry phase optical elements,” Opt Lett 29, 238 (2004).
[Crossref] [PubMed]

Nose, T.

R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28, 1730 (1989).
[Crossref]

Novotny, L.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 85, 5251–5253 (2001).
[Crossref]

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. Phy Lett. 77, 21 (2000)
[Crossref]

Pezzanitti, J. L.

J. L. Pezzanitti and R. A. Chipman, “Mueller matrix imaging polarimeter,” Opt. Eng. 34, 6 (1995).
[Crossref]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for radially polarized light beam,” Phys. Rev. Lett. 91, 23 (2003).
[Crossref]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Rooks, M. J.

T. Erdogan, O. King, W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, AlGaAs/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]

Saghafi, S.

Sato, S.

R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28, 1730 (1989).
[Crossref]

Schadt, M.

M. Stalder and M. Schadt, “Linear polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt Lett. 21, 23 (1996).
[Crossref]

M. Schadt, H. Seiberle, A. Schuster, and S. M. Kelly “Photo-induced alignment and patterning of hybrid liquid crystalline polymer films on single substrates,” Jpn. J. Appl. Phys. 34, L764–L767 (1995).
[Crossref]

Schuster, A.

M. Schadt, H. Seiberle, A. Schuster, and S. M. Kelly “Photo-induced alignment and patterning of hybrid liquid crystalline polymer films on single substrates,” Jpn. J. Appl. Phys. 34, L764–L767 (1995).
[Crossref]

Seiberle, H.

M. Schadt, H. Seiberle, A. Schuster, and S. M. Kelly “Photo-induced alignment and patterning of hybrid liquid crystalline polymer films on single substrates,” Jpn. J. Appl. Phys. 34, L764–L767 (1995).
[Crossref]

Shemo, D. M.

Sheppard, C. J. R.

Sibbett, W.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature419, 145 (2002).
[Crossref] [PubMed]

Smith, P. K.

Spilman, A. K.

Stalder, M.

M. Stalder and M. Schadt, “Linear polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt Lett. 21, 23 (1996).
[Crossref]

Sullivan, K. G.

Tidwell, S. C.

Totzeck,

Totzeck, et al., “Polarizer device for generating a defined spatial distribution of polarization states,” US 2006/0028706, Feb. 9, 2006.

Wicks, W.

T. Erdogan, O. King, W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, AlGaAs/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic theory of propagation, interference and diffraction of light, (Cambridge University Press, seventh ed., 1999).
[PubMed]

Yamaguchi, R.

R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28, 1730 (1989).
[Crossref]

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 85, 5251–5253 (2001).
[Crossref]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical vector beams,” Opt. Express. 7, 77–87, (2000).
[Crossref] [PubMed]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical vector beams,” Opt. Express 7, 77–87 (2000).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phy 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. Phy Lett. 77, 21 (2000)
[Crossref]

Appl. Phys. Lett. (1)

T. Erdogan, O. King, W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, AlGaAs/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]

J. Opt. Soc. Am A. (1)

J. P. McGuire, Jr. and R. A. Chipman, “Diffraction image formation in optical systems with polarization aberrations I: Formulation and example,” J. Opt. Soc. Am A. 7, 9, 1614–1626 (1990).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Opt. Soc.Am. A (1)

P. L. Greene and D. G. Hall, “Diffraction characteristics of the azimuthal Bessel-Gauss beam,” J. Opt. Soc.Am. A 13, 962–966 (1996).
[Crossref]

Jpn. J. Appl. Phys. (2)

M. Schadt, H. Seiberle, A. Schuster, and S. M. Kelly “Photo-induced alignment and patterning of hybrid liquid crystalline polymer films on single substrates,” Jpn. J. Appl. Phys. 34, L764–L767 (1995).
[Crossref]

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[Crossref]

Opt Lett (1)

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam-Berry phase optical elements,” Opt Lett 29, 238 (2004).
[Crossref] [PubMed]

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[Crossref]

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[Crossref]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

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[Crossref]

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[Crossref] [PubMed]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref] [PubMed]

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[PubMed]

Information on Axometrics polarimeter from http://www.axometrics.com/

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Figures (17)

Fig. 1.
Fig. 1. m=3: (a) linear retardance map (in nm) (b) fast axis orientation map, (c) transmission between crossed polarizers.

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Fig. 2.
Fig. 2. m=2.0: (a) linear retardance map (in nm) (b) fast axis orientation map, (c) transmission between crossed polarizers.

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Fig. 3.
Fig. 3. m=1: (a) linear retardance map (in nm) (b) fast axis orientation map, (c) transmission between crossed polarizers.

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Fig. 4.
Fig. 4. Expanded view of measured fast axis orientation showing a 6mm×6mm central region of the m=3 vortex retarder

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Fig. 5.
Fig. 5. Schematic of the PSM measurement

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Fig. 6.
Fig. 6. Comparison of the predicted PSM (left) and measured PSM (right) for the m=1 vortex retarder.

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Fig. 7.
Fig. 7. Comparison of the predicted PSM (left) and measured PSM (right) for the m=2 vortex retarder.

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Fig. 8.
Fig. 8. Comparison of the predicted PSM (left) and measured PSM (right) for the m=3 vortex retarder.

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Fig. 9.
Fig. 9. Comparison between predicted intensity PSF with (a) no analyzer, (b) horizontal linear analyzer, (c) vertical linear analyzer and measured intensity PSF with (d) no analyzer, (e) horizontal linear analyzer, (f) vertical linear analyzer.

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Fig. 10.
Fig. 10. Predicted magnitude OTM (left) and phase OTM (right)

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Fig. 11.
Fig. 11. Comparison of predicted vs. measured MTF (left) and PTF (right) for an m=1 vortex retarder for the case of horizontal polarized input and no analyzer.

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Fig. 12.
Fig. 12. Comparison of predicted vs. measured MTF (left) and PTF (right) for an m=2 vortex retarder for the case of horizontal polarized input and no analyzer.

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Fig. 13.
Fig. 13. Comparison of predicted vs. measured MTF (left) and PTF (right) for an m=3 vortex retarder for the case of horizontal polarized input and no analyzer.

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Fig. 14.
Fig. 14. PSM for m=2 vortex retarder for ideal case (left) and with 0.2 waves of coma (right).

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Fig. 15.
Fig. 15. PSM for m=2 vortex retarder for ideal case (left) and with 0.2 waves of astigmatism (right).

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Fig. 16.
Fig. 16. MTF (top) and PTF(bottom) comparison between aberration free predicted, measured, predicted with 0.1 waves of astigmatism, and predicted with 0.1 waves of coma for an m=2 vortex retarder with horizontal linear input and no analyzer.

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Fig. 17.
Fig. 17. PSM for an m=2 vortex retarder shifted from the center by 1% (left), 5% (right).

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Equations (11)

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PAM ( h , ρ , λ ) = P ( h , ρ ) exp ( j k W ( h , ρ , λ ) ) J VR ( h , ρ , λ ) ;
PAM ( m ϕ ) = ( cos ( m ϕ ) sin ( m ϕ ) sin ( m ϕ ) − cos ( m ϕ ) ) ;
U i = h * U o
h = C exp [ j k Ψ ( ξ , η ; u , v ) [ ℱ { j 11 } ℱ { j 12 } ℱ { j 21 } ℱ { j 22 } ]
C = − A 2 4 λ 2 z 1 z 2 exp [ j k ( z 1 + z 2 ) ] .
Ψ ( ξ , η ; u , v ) = ξ 2 + η 2 2 z 1 + u 2 + v 2 2 z 2
P c ( ξ 1 , η 1 ; ξ 2 , η 2 ; u , v ) = h ( ξ 1 , η 1 ; u , v ) ⊗ h * ( ξ 2 , η 2 ; u , v )
P = S · P C · S − 1
S = [ 1 0 0 1 1 0 0 − 1 0 1 1 0 0 − j − j 0 ]
H ( v u , v v ) = ℱ { P s } N .
N = 1 2 ∬ ∞ ( ∣ H 11 ( p , q ) ∣ 2 + ∣ H 21 ( p , q ) ∣ 2 + ∣ H 12 ( p , q ) ∣ 2 + ∣ H 22 ( p , q ) ∣ 2 ) dpdq

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