Cylindrical vector beam focusing through a dielectric interface

D. P. Biss; T. G. Brown

doi:10.1364/OE.9.000490

Abstract

Cylindrical vector beams have been proposed and demonstrated for applications ranging from microscopy to high energy physics. In this paper, we analyze the three-dimensional field distributions of radial and azimuthal beams focused near a dielectric interface. We give particular attention to the classic problem of high numerical aperture focusing from an immersion lens to a glass-air interface and find that the use of radially and azimuthally polarized illumination for this type of imaging provides an impressive lateral confinement of the fields over a wide range of interface positions.

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References

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Year
Author
Publication

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253, 358–379 (1959).
[Crossref]
Hao Ling and Shung-Wu Lee, “Focusing of electromagnetic waves through a dielectric interface,” J. Opt. Soc. Am. A 1, 965–973 (1984).
[Crossref]
P. Török, P. Varga, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field. I,” J. Opt. Soc. Am. A 12, 2136–2144 (1995).
[Crossref]
S. H. Wiersma, P. Török, T. D. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. A 14, 1482–1490 (1997).
[Crossref]
Lars Egil Helseth, “Roles of polarization, phase, and amplitude in solid immersion lens systems,” Opt. Commun. 191, 161–172 (2001).
[Crossref]
T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, “Circularly symmetrical operation of a concentric-circle-grating, surface-emitting, AlGaAs/GaAs Quantum-well semiconductor-laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]
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]
D. G. Hall, “Vector-beam solutions of Maxwell’s wave equation,” Opt. Lett. 21, 9–11 (1996).
[Crossref] [PubMed]
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]
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, “Focal shift in vector beams,” Opt. Express 4, 411–419 (1999), http://epubs.osa.org/opticsexpress/tocv4n10.htm.
[Crossref] [PubMed]
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]
S. C. Tidwell, D. H. Ford, and W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2234–2239 (1990).
[Crossref] [PubMed]
K. S. Youngworth and T. G. Brown, “Inhomogeneous polarization in scanning optical microscopy,” Proc. SPIE3919 (2000).
[Crossref]
M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21, 1948–1949 (1996).
[Crossref] [PubMed]
R. Yamaguchi, T. Nose, and S. Sato, “Liquid-crystal polarizers with axially symmetric properties,” Jpn. J. Appl. Phys. 28, 1730–1731 (1989).
[Crossref]
E. G. Churin, J. Hossfeld, and T. Tschudi, “Polarization configurations with singular point formed by computer generated holograms,” Opt. Commun. 99, 13–17 (1993).
[Crossref]
K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Exp. 7, 77–87 (2000).
[Crossref]
S. Quabis, R. Dorn, M. Eberler, O. G. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]
B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485, (2000).
[Crossref] [PubMed]
L. Novotny, M.R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254, (2001).
[Crossref] [PubMed]
J. Enderlein, “Theoretical study of detection of a dipole emitter through an objective with high numerical aperture,” Opt. Lett. 25, 634–636 (2000).
[Crossref]
T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103, 6839–6850 (1999)
[Crossref]

2001 (2)

Lars Egil Helseth, “Roles of polarization, phase, and amplitude in solid immersion lens systems,” Opt. Commun. 191, 161–172 (2001).
[Crossref]

L. Novotny, M.R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254, (2001).
[Crossref] [PubMed]

2000 (4)

J. Enderlein, “Theoretical study of detection of a dipole emitter through an objective with high numerical aperture,” Opt. Lett. 25, 634–636 (2000).
[Crossref]

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

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

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485, (2000).
[Crossref] [PubMed]

1999 (3)

P. L. Greene and D. G. Hall, “Focal shift in vector beams,” Opt. Express 4, 411–419 (1999), http://epubs.osa.org/opticsexpress/tocv4n10.htm.
[Crossref] [PubMed]

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]

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103, 6839–6850 (1999)
[Crossref]

1993 (1)

E. G. Churin, J. Hossfeld, and T. Tschudi, “Polarization configurations with singular point formed by computer generated holograms,” Opt. Commun. 99, 13–17 (1993).
[Crossref]

1992 (1)

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

1990 (1)

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 symmetric properties,” Jpn. J. Appl. Phys. 28, 1730–1731 (1989).
[Crossref]

1984 (1)

Hao Ling and Shung-Wu Lee, “Focusing of electromagnetic waves through a dielectric interface,” J. Opt. Soc. Am. A 1, 965–973 (1984).
[Crossref]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253, 358–379 (1959).
[Crossref]

Anderson, E. H.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, “Circularly symmetrical 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. 86, 5251–5254, (2001).
[Crossref] [PubMed]

Booker, G. R.

P. Török, P. Varga, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field. I,” J. Opt. Soc. Am. A 12, 2136–2144 (1995).
[Crossref]

Brown, T. G.

L. Novotny, M.R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254, (2001).
[Crossref] [PubMed]

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

K. S. Youngworth and T. G. Brown, “Inhomogeneous polarization in scanning optical microscopy,” Proc. SPIE3919 (2000).
[Crossref]

Chemla, D. S.

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103, 6839–6850 (1999)
[Crossref]

Churin, E. G.

E. G. Churin, J. Hossfeld, and T. Tschudi, “Polarization configurations with singular point formed by computer generated holograms,” Opt. Commun. 99, 13–17 (1993).
[Crossref]

Dorn, R.

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

Egil Helseth, Lars

Lars Egil Helseth, “Roles of polarization, phase, and amplitude in solid immersion lens systems,” Opt. Commun. 191, 161–172 (2001).
[Crossref]

Enderlein, J.

J. Enderlein, “Theoretical study of detection of a dipole emitter through an objective with high numerical aperture,” Opt. Lett. 25, 634–636 (2000).
[Crossref]

Erdogan, T.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, “Circularly symmetrical 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.

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

Glöckl, O. G.

S. Quabis, R. Dorn, M. Eberler, O. G. Glöckl, 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, “Focal shift in vector beams,” Opt. Express 4, 411–419 (1999), http://epubs.osa.org/opticsexpress/tocv4n10.htm.
[Crossref] [PubMed]

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]

Ha, T.

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103, 6839–6850 (1999)
[Crossref]

Hall, D. G.

P. L. Greene and D. G. Hall, “Focal shift in vector beams,” Opt. Express 4, 411–419 (1999), http://epubs.osa.org/opticsexpress/tocv4n10.htm.
[Crossref] [PubMed]

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]

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

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]

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

Hecht, B.

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485, (2000).
[Crossref] [PubMed]

Hossfeld, J.

E. G. Churin, J. Hossfeld, and T. Tschudi, “Polarization configurations with singular point formed by computer generated holograms,” Opt. Commun. 99, 13–17 (1993).
[Crossref]

Jordan, R. H.

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]

Kimura, W. D.

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

King, O.

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

Laurence, T. A.

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103, 6839–6850 (1999)
[Crossref]

Lee, Shung-Wu

Hao Ling and Shung-Wu Lee, “Focusing of electromagnetic waves through a dielectric interface,” J. Opt. Soc. Am. A 1, 965–973 (1984).
[Crossref]

Leuchs, G.

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

Ling, Hao

Hao Ling and Shung-Wu Lee, “Focusing of electromagnetic waves through a dielectric interface,” J. Opt. Soc. Am. A 1, 965–973 (1984).
[Crossref]

Nose, T.

R. Yamaguchi, T. Nose, and S. Sato, “Liquid-crystal polarizers with axially symmetric properties,” Jpn. J. Appl. Phys. 28, 1730–1731 (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. 86, 5251–5254, (2001).
[Crossref] [PubMed]

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485, (2000).
[Crossref] [PubMed]

Quabis, S.

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

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253, 358–379 (1959).
[Crossref]

Rooks, M. J.

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

Saghafi, S.

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]

Sato, S.

R. Yamaguchi, T. Nose, and S. Sato, “Liquid-crystal polarizers with axially symmetric properties,” Jpn. J. Appl. Phys. 28, 1730–1731 (1989).
[Crossref]

Schadt, M.

M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21, 1948–1949 (1996).
[Crossref] [PubMed]

Sheppard, C. J. R.

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]

Sick, B.

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485, (2000).
[Crossref] [PubMed]

Stalder, M.

M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21, 1948–1949 (1996).
[Crossref] [PubMed]

Tidwell, S. C.

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

Török, P.

S. H. Wiersma, P. Török, T. D. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. A 14, 1482–1490 (1997).
[Crossref]

P. Török, P. Varga, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field. I,” J. Opt. Soc. Am. A 12, 2136–2144 (1995).
[Crossref]

Tschudi, T.

E. G. Churin, J. Hossfeld, and T. Tschudi, “Polarization configurations with singular point formed by computer generated holograms,” Opt. Commun. 99, 13–17 (1993).
[Crossref]

Varga, P.

S. H. Wiersma, P. Török, T. D. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. A 14, 1482–1490 (1997).
[Crossref]

P. Török, P. Varga, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field. I,” J. Opt. Soc. Am. A 12, 2136–2144 (1995).
[Crossref]

Visser, T. D.

S. H. Wiersma, P. Török, T. D. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. A 14, 1482–1490 (1997).
[Crossref]

Weiss, S.

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103, 6839–6850 (1999)
[Crossref]

Wicks, G. W.

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

Wiersma, S. H.

S. H. Wiersma, P. Török, T. D. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. A 14, 1482–1490 (1997).
[Crossref]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253, 358–379 (1959).
[Crossref]

Yamaguchi, R.

R. Yamaguchi, T. Nose, and S. Sato, “Liquid-crystal polarizers with axially symmetric properties,” Jpn. J. Appl. Phys. 28, 1730–1731 (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. 86, 5251–5254, (2001).
[Crossref] [PubMed]

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

K. S. Youngworth and T. G. Brown, “Inhomogeneous polarization in scanning optical microscopy,” Proc. SPIE3919 (2000).
[Crossref]

Appl. Opt. (1)

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

Appl. Phys. Lett. (1)

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, “Circularly symmetrical 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 (5)

Hao Ling and Shung-Wu Lee, “Focusing of electromagnetic waves through a dielectric interface,” J. Opt. Soc. Am. A 1, 965–973 (1984).
[Crossref]

P. Török, P. Varga, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field. I,” J. Opt. Soc. Am. A 12, 2136–2144 (1995).
[Crossref]

S. H. Wiersma, P. Török, T. D. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. A 14, 1482–1490 (1997).
[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]

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]

J. Phys. Chem. B (1)

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103, 6839–6850 (1999)
[Crossref]

Jpn. J. Appl. Phys. (1)

R. Yamaguchi, T. Nose, and S. Sato, “Liquid-crystal polarizers with axially symmetric properties,” Jpn. J. Appl. Phys. 28, 1730–1731 (1989).
[Crossref]

Opt. Commun. (3)

E. G. Churin, J. Hossfeld, and T. Tschudi, “Polarization configurations with singular point formed by computer generated holograms,” Opt. Commun. 99, 13–17 (1993).
[Crossref]

Lars Egil Helseth, “Roles of polarization, phase, and amplitude in solid immersion lens systems,” Opt. Commun. 191, 161–172 (2001).
[Crossref]

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

Opt. Exp. (1)

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

Opt. Express (1)

P. L. Greene and D. G. Hall, “Focal shift in vector beams,” Opt. Express 4, 411–419 (1999), http://epubs.osa.org/opticsexpress/tocv4n10.htm.
[Crossref] [PubMed]

Opt. Lett. (5)

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]

M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21, 1948–1949 (1996).
[Crossref] [PubMed]

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]

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

J. Enderlein, “Theoretical study of detection of a dipole emitter through an objective with high numerical aperture,” Opt. Lett. 25, 634–636 (2000).
[Crossref]

Phys. Rev. Lett. (2)

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485, (2000).
[Crossref] [PubMed]

L. Novotny, M.R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254, (2001).
[Crossref] [PubMed]

Proc. Roy. Soc. A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253, 358–379 (1959).
[Crossref]

Other (1)

K. S. Youngworth and T. G. Brown, “Inhomogeneous polarization in scanning optical microscopy,” Proc. SPIE3919 (2000).
[Crossref]

Supplementary Material (2)

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Fig. 1. Aplanatic lens focusing onto an interface

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Fig. 2. a. Focusing of radial component with incident medium (left side) n=1.518 and exiting medium (right side) n=1. The NA for the system is 1.4. The white line represents the interface of the system. The color scale is a log base 10 scale in arbitrary units. Axes are in units of wavelength. The picture on the left is the radial component. The picture on the right is the longitudinal component.

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Fig. 2. b. Focusing of radial component with incident medium (left side) n=1 and exiting medium (right side) n=3.55. The NA for the system is .85. The white line represents the interface of the system. The color scale is a log base 10 scale in arbitrary units. Axes are in the units of wavelength. The picture on the left is the radial component. The picture on the right is the longitudinal component.

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Fig. 3. a. Azimuthally polarized light focused onto an interface with NA=1.4 and entering medium n=1.518, and exiting medium n=1. The white line represents the interface of the system. The color scale is a log base 10 scale in arbitrary units. Axes are in the units of wavelengths.

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Fig. 3. b. Azimuthally polarized light focused onto an interface with NA=.85 and entering medium n=1, and exiting medium n=3.55. The white line represents the interface of the system. The color scale is a log base 10 scale in arbitrary units. Axes are in units of wavelengths.

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Fig. 4. (2.1 MB) Movie of the defocusing of a radial beam. The beam is entering through a medium of oil (n=1.518) and exiting into a medium of air (n=1). The white line represents the position of the interface. The color scale is a logarithmic base 10 scale. Axes are in units of wavelengths.[Media 2]

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Fig. 5. Full width of half maximum of the focal spot for light of linear and radial polarization (total electric field intensity) and the longitudinal component of the radially polarized beams focused through an immersion lens (NA=1.4). Blue stars correspond to the radially polarized beam (total intensity), red triangles to linearly polarized beams, and green squares represent the longitudinal component of the radial polarization. Both interface positions and the FWHM are given in wavelengths. An interface at a negative position is inside the geometrical focus.

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Equations (11)

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{\vec{E}}_{f} (θ, ϕ) = ℓ_{o} (θ) \cos^{1 ⁄ 2} θ [\begin{matrix} - \sin ϕ \\ \cos ϕ \\ 0 \end{matrix}] .

\vec{E_{f}} (ρ, z) = \int_{0}^{θ_{max}} ℓ_{o} (θ) {\vec{E_{f}^{\infty}} \cos}^{1 ⁄ 2} θ \sin θ d θ,

\vec{E_{f}} (ρ, z) = \int_{0}^{θ_{max}} ℓ_{o} (θ) \vec{E_{f}^{\infty}} \cos^{1 ⁄ 2} θ \sin θ d θ,

\vec{E_{t}} (ρ, z) = \int_{0}^{θ_{max}} ℓ_{o} (θ) \vec{E_{f}^{\infty}} \cos^{1 ⁄ 2} θ \sin θ d θ,

\vec{E_{f}^{\infty}} = e^{i k_{1} z \cos θ} [\begin{matrix} 0 \\ J_{1} (ρ k_{1} \sin θ) \\ 0 \end{matrix}],

\vec{E_{r}^{\infty}} = r^{s} e^{- i k_{1} z \cos θ} e^{i 2 k_{1} z_{0} \cos θ} [\begin{matrix} 0 \\ J_{1} (ρ k_{1} \sin θ) \\ 0 \end{matrix}],

\vec{E_{t}^{\infty}} = t^{s} e^{i k_{1} z_{0} \cos θ} e^{i k_{2} \sqrt{1 - {(\frac{k_{1}}{k_{2}} \sin θ)}^{2}} (z - z_{0})} [\begin{matrix} 0 \\ J_{1} (ρ k_{1} \sin θ) \\ 0 \end{matrix}] .

\vec{E_{f}^{\infty}} = e^{i k_{1} z \cos θ} [\begin{matrix} i \cos θ J_{1} (ρ k_{1} \sin θ) \\ 0 \\ - \sin θ J_{0} (ρ k_{1} \sin θ) \end{matrix}],

\vec{E_{r}^{\infty}} = - r^{p} e^{- i k_{1} z \cos θ} e^{i 2 k_{1} z_{o} \cos θ} [\begin{matrix} i \cos θ J_{1} (ρ k_{1} \sin θ) \\ 0 \\ \sin θ J_{0} (ρ k_{1} \sin θ) \end{matrix}],

\vec{E_{t}^{\infty}} = t^{p} e^{i k_{1} z_{0} \cos θ} e^{i k_{2} \sqrt{1 - {(\frac{k_{1}}{k_{2}} \sin θ)}^{2}} (z - z_{0})} [\begin{matrix} i \sqrt{1 - {(\frac{k_{1}}{k_{2}} \sin θ)}^{2}} J_{1} (ρ k_{1} \sin θ) \\ 0 \\ \frac{k_{1}}{k_{2}} \sin θ J_{0} (ρ k_{1} \sin θ) \end{matrix}] .

ℓ_{o} (θ) = E_{o} \exp (- β^{2} \frac{\sin^{2} θ}{\sin^{2} θ_{max}}) J_{1} (2 β \frac{\sin θ}{\sin θ_{max}}) .

Abstract

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