Abstract

We propose and experimentally demonstrate the generation of hybridly polarized beams by transmitting radially polarized light through a wave plate. We show that such beams span a closed circle on the surface of the Poincaré sphere whose center coincides with the center of the sphere. In addition we numerically investigate the field and energy density distribution across the focal plane of a high NA lens illuminated by such a hybrid beam. The results show an interesting polarization distribution with 3D orientation and space variant ellipticity. This kind of polarization distributions may be used for a variety of applications, e.g. particle orientation analysis, microscopy and in atomic systems.

© 2010 OSA

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References

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    [CrossRef]
  2. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
    [CrossRef] [PubMed]
  3. Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002).
    [PubMed]
  4. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
    [CrossRef] [PubMed]
  5. G. M. Lerman and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express 16(7), 4567–4581 (2008).
    [CrossRef] [PubMed]
  6. E. Descrovi, L. Vaccaro, L. Aeschimann, W. Nakagawa, U. Staufer, and H.-P. Herzig, “Optical properties of microfabricated fully-metal-coated near-field probes in collection mode,” J. Opt. Soc. Am. A 22(7), 1432–1441 (2005).
    [CrossRef]
  7. V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D Appl. Phys. 32(13), 1455–1461 (1999).
    [CrossRef]
  8. W. S. Mohammed, A. Mehta, M. Pitchumani, and E. G. Johnson, “Selective Excitation of the TE01 Mode in Hollow-Glass Waveguide Using a Subwavelength Grating,” IEEE Photon. Technol. Lett. 17(7), 1441–1443 (2005).
    [CrossRef]
  9. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
    [CrossRef]
  10. M. Born, and E. Wolf, Principles of Optics: Electromagnetic theory of propagation, interference and diffraction, 7th ed. (Cambridge University Press, 1999) pp. 24–38.
  11. X. L. Wang, Y. Li, J. Chen, C. S. Guo, J. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18(10), 10786–10795 (2010).
    [CrossRef] [PubMed]
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  13. G. Milione, H. I. Sztul, and R. R. Alfano, “Propagation of a hybrid vector polarization beam in a uniaxial crystal,” Proc. SPIE 7613, 76130I (2010).
    [CrossRef]
  14. Y. Tokizane, K. Oka, and R. Morita, “Supercontinuum optical vortex pulse generation without spatial or topological-charge dispersion,” Opt. Express 17(17), 14517–14525 (2009).
    [CrossRef] [PubMed]
  15. A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18(10), 10777–10785 (2010).
    [CrossRef] [PubMed]
  16. 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(24), 3549–3551 (2007).
    [CrossRef] [PubMed]
  17. G. Machavariani, Y. Lumer, I. Moshe, A. Meir, S. Jackel, and N. Davidson, “Birefringence-induced bifocusing for selection of radially or azimuthally polarized laser modes,” Appl. Opt. 46(16), 3304–3310 (2007).
    [CrossRef] [PubMed]
  18. M. A. Ahmed, A. Voss, M. M. Vogel, and T. Graf, “Multilayer polarizing grating mirror used for the generation of radial polarization in Yb:YAG thin-disk lasers,” Opt. Lett. 32(22), 3272–3274 (2007).
    [CrossRef] [PubMed]
  19. A. K. Spilman and T. G. Brown, “Stress birefringent, space-variant wave plates for vortex illumination,” Appl. Opt. 46(1), 61–66 (2007).
    [CrossRef]
  20. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27(5), 285–287 (2002).
    [CrossRef]
  21. T. Grosjean, D. Courjon, and M. Spajer, “An all-fiber device for generating radially and other polarized light beams,” Opt. Commun. 203(1-2), 1–5 (2002).
    [CrossRef]
  22. G. M. Lerman and U. Levy, “Generation of a radially polarized light beam using space-variant subwavelength gratings at 1064 nm,” Opt. Lett. 33(23), 2782–2784 (2008).
    [CrossRef] [PubMed]
  23. M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21(23), 1948–1950 (1996).
    [CrossRef] [PubMed]
  24. Y. Kozawa and S. Sato, “Focusing property of a double-ring-shaped radially polarized beam,” Opt. Lett. 31(6), 820–822 (2006).
    [CrossRef] [PubMed]
  25. B. Hao and J. Leger, “Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam,” Opt. Express 15(6), 3550–3556 (2007).
    [CrossRef] [PubMed]
  26. N. Davidson and N. Bokor, “High-numerical-aperture focusing of radially polarized doughnut beams with a parabolic mirror and a flat diffractive lens,” Opt. Lett. 29(12), 1318–1320 (2004).
    [CrossRef] [PubMed]
  27. E. Y. S. Yew and C. J. R. Sheppard, “Tight focusing of radially polarized Gaussian and Bessel-Gauss beams,” Opt. Lett. 32(23), 3417–3419 (2007).
    [CrossRef] [PubMed]
  28. D. Biss and T. Brown, “Cylindrical vector beam focusing through a dielectric interface,” Opt. Express 9(10), 490–497 (2001).
    [CrossRef] [PubMed]
  29. Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24(6), 1793–1798 (2007).
    [CrossRef]
  30. W. B. Chen and Q. W. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265(2), 411–417 (2006).
    [CrossRef]
  31. X. L. Wang, J. Ding, J. Q. Qin, J. Chen, Y. X. Fan, and H. T. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun. 282(17), 3421–3425 (2009).
    [CrossRef]
  32. W. B. Chen and Q. W. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
    [CrossRef]
  33. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1274), 358–379 (1959).
    [CrossRef]
  34. G. M. Lerman and U. Levy, “Tight focusing of space variant vector optical fields with no cylindrical symmetry of polarization,” Opt. Lett. 32, 2194–2196 (2007).
    [CrossRef] [PubMed]
  35. M. R. Beversluis, L. Novotny, and S. J. Stranick, “Programmable vector point-spread function engineering,” Opt. Express 14(7), 2650–2656 (2006).
    [CrossRef] [PubMed]
  36. F. K. Fatemi, and G. Beadie, “Imaging Atomic States Using Radially-Polarized Light,” in Frontiers in Optics (FiO)/Laser Science (LS) (Optical Society of America, Washington, DC, 2010), paper FWP6.

2010 (4)

G. Milione, H. I. Sztul, and R. R. Alfano, “Propagation of a hybrid vector polarization beam in a uniaxial crystal,” Proc. SPIE 7613, 76130I (2010).
[CrossRef]

W. B. Chen and Q. W. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[CrossRef]

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18(10), 10777–10785 (2010).
[CrossRef] [PubMed]

X. L. Wang, Y. Li, J. Chen, C. S. Guo, J. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18(10), 10786–10795 (2010).
[CrossRef] [PubMed]

2009 (3)

2008 (2)

2007 (8)

A. K. Spilman and T. G. Brown, “Stress birefringent, space-variant wave plates for vortex illumination,” Appl. Opt. 46(1), 61–66 (2007).
[CrossRef]

B. Hao and J. Leger, “Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam,” Opt. Express 15(6), 3550–3556 (2007).
[CrossRef] [PubMed]

Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24(6), 1793–1798 (2007).
[CrossRef]

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, S. Jackel, and N. Davidson, “Birefringence-induced bifocusing for selection of radially or azimuthally polarized laser modes,” Appl. Opt. 46(16), 3304–3310 (2007).
[CrossRef] [PubMed]

G. M. Lerman and U. Levy, “Tight focusing of space variant vector optical fields with no cylindrical symmetry of polarization,” Opt. Lett. 32, 2194–2196 (2007).
[CrossRef] [PubMed]

M. A. Ahmed, A. Voss, M. M. Vogel, and T. Graf, “Multilayer polarizing grating mirror used for the generation of radial polarization in Yb:YAG thin-disk lasers,” Opt. Lett. 32(22), 3272–3274 (2007).
[CrossRef] [PubMed]

E. Y. S. Yew and C. J. R. Sheppard, “Tight focusing of radially polarized Gaussian and Bessel-Gauss beams,” Opt. Lett. 32(23), 3417–3419 (2007).
[CrossRef] [PubMed]

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(24), 3549–3551 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (2)

W. S. Mohammed, A. Mehta, M. Pitchumani, and E. G. Johnson, “Selective Excitation of the TE01 Mode in Hollow-Glass Waveguide Using a Subwavelength Grating,” IEEE Photon. Technol. Lett. 17(7), 1441–1443 (2005).
[CrossRef]

E. Descrovi, L. Vaccaro, L. Aeschimann, W. Nakagawa, U. Staufer, and H.-P. Herzig, “Optical properties of microfabricated fully-metal-coated near-field probes in collection mode,” J. Opt. Soc. Am. A 22(7), 1432–1441 (2005).
[CrossRef]

2004 (1)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

2002 (3)

2001 (1)

2000 (2)

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

1999 (1)

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D Appl. Phys. 32(13), 1455–1461 (1999).
[CrossRef]

1996 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1274), 358–379 (1959).
[CrossRef]

Aeschimann, L.

Ahmed, M. A.

Alfano, R. R.

G. Milione, H. I. Sztul, and R. R. Alfano, “Propagation of a hybrid vector polarization beam in a uniaxial crystal,” Proc. SPIE 7613, 76130I (2010).
[CrossRef]

Alonso, M. A.

Beckley, A. M.

Beversluis, M. R.

Biener, G.

Biss, D.

Bokor, N.

Bomzon, Z.

Brown, T.

Brown, T. G.

Chen, J.

X. L. Wang, Y. Li, J. Chen, C. S. Guo, J. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18(10), 10786–10795 (2010).
[CrossRef] [PubMed]

X. L. Wang, J. Ding, J. Q. Qin, J. Chen, Y. X. Fan, and H. T. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun. 282(17), 3421–3425 (2009).
[CrossRef]

Chen, W. B.

W. B. Chen and Q. W. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[CrossRef]

W. B. Chen and Q. W. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265(2), 411–417 (2006).
[CrossRef]

Courjon, D.

T. Grosjean, D. Courjon, and M. Spajer, “An all-fiber device for generating radially and other polarized light beams,” Opt. Commun. 203(1-2), 1–5 (2002).
[CrossRef]

Davidson, N.

Descrovi, E.

Ding, J.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 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(1-6), 1–7 (2000).
[CrossRef]

Fan, Y. X.

X. L. Wang, J. Ding, J. Q. Qin, J. Chen, Y. X. Fan, and H. T. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun. 282(17), 3421–3425 (2009).
[CrossRef]

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

Graf, T.

Grosjean, T.

T. Grosjean, D. Courjon, and M. Spajer, “An all-fiber device for generating radially and other polarized light beams,” Opt. Commun. 203(1-2), 1–5 (2002).
[CrossRef]

Guo, C. S.

Hao, B.

Hasman, E.

Herzig, H.-P.

Jackel, S.

Johnson, E. G.

W. S. Mohammed, A. Mehta, M. Pitchumani, and E. G. Johnson, “Selective Excitation of the TE01 Mode in Hollow-Glass Waveguide Using a Subwavelength Grating,” IEEE Photon. Technol. Lett. 17(7), 1441–1443 (2005).
[CrossRef]

Kleiner, V.

Kozawa, Y.

Leger, J.

Leger, J. R.

Lerman, G. M.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

Levy, U.

Li, Y.

Lumer, Y.

Machavariani, G.

Mehta, A.

W. S. Mohammed, A. Mehta, M. Pitchumani, and E. G. Johnson, “Selective Excitation of the TE01 Mode in Hollow-Glass Waveguide Using a Subwavelength Grating,” IEEE Photon. Technol. Lett. 17(7), 1441–1443 (2005).
[CrossRef]

Meir, A.

Milione, G.

G. Milione, H. I. Sztul, and R. R. Alfano, “Propagation of a hybrid vector polarization beam in a uniaxial crystal,” Proc. SPIE 7613, 76130I (2010).
[CrossRef]

Mohammed, W. S.

W. S. Mohammed, A. Mehta, M. Pitchumani, and E. G. Johnson, “Selective Excitation of the TE01 Mode in Hollow-Glass Waveguide Using a Subwavelength Grating,” IEEE Photon. Technol. Lett. 17(7), 1441–1443 (2005).
[CrossRef]

Morita, R.

Moshe, I.

Nakagawa, W.

Nesterov, A. V.

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D Appl. Phys. 32(13), 1455–1461 (1999).
[CrossRef]

Ni, W. J.

Niziev, V. G.

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D Appl. Phys. 32(13), 1455–1461 (1999).
[CrossRef]

Novotny, L.

Oka, K.

Pitchumani, M.

W. S. Mohammed, A. Mehta, M. Pitchumani, and E. G. Johnson, “Selective Excitation of the TE01 Mode in Hollow-Glass Waveguide Using a Subwavelength Grating,” IEEE Photon. Technol. Lett. 17(7), 1441–1443 (2005).
[CrossRef]

Qin, J. Q.

X. L. Wang, J. Ding, J. Q. Qin, J. Chen, Y. X. Fan, and H. T. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun. 282(17), 3421–3425 (2009).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 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. R. Soc. Lond. A 253(1274), 358–379 (1959).
[CrossRef]

Sato, S.

Schadt, M.

Sheppard, C. J. R.

Spajer, M.

T. Grosjean, D. Courjon, and M. Spajer, “An all-fiber device for generating radially and other polarized light beams,” Opt. Commun. 203(1-2), 1–5 (2002).
[CrossRef]

Spilman, A. K.

Stalder, M.

Staufer, U.

Stranick, S. J.

Sztul, H. I.

G. Milione, H. I. Sztul, and R. R. Alfano, “Propagation of a hybrid vector polarization beam in a uniaxial crystal,” Proc. SPIE 7613, 76130I (2010).
[CrossRef]

Tokizane, Y.

Vaccaro, L.

Vogel, M. M.

Voss, A.

Wang, H. T.

Wang, X. L.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1274), 358–379 (1959).
[CrossRef]

Yew, E. Y. S.

Youngworth, K. S.

Zhan, Q.

Zhan, Q. W.

W. B. Chen and Q. W. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[CrossRef]

W. B. Chen and Q. W. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265(2), 411–417 (2006).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (2)

IEEE Photon. Technol. Lett. (1)

W. S. Mohammed, A. Mehta, M. Pitchumani, and E. G. Johnson, “Selective Excitation of the TE01 Mode in Hollow-Glass Waveguide Using a Subwavelength Grating,” IEEE Photon. Technol. Lett. 17(7), 1441–1443 (2005).
[CrossRef]

J. Opt. (1)

W. B. Chen and Q. W. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Phys. D Appl. Phys. (1)

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D Appl. Phys. 32(13), 1455–1461 (1999).
[CrossRef]

Opt. Commun. (4)

T. Grosjean, D. Courjon, and M. Spajer, “An all-fiber device for generating radially and other polarized light beams,” Opt. Commun. 203(1-2), 1–5 (2002).
[CrossRef]

W. B. Chen and Q. W. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265(2), 411–417 (2006).
[CrossRef]

X. L. Wang, J. Ding, J. Q. Qin, J. Chen, Y. X. Fan, and H. T. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun. 282(17), 3421–3425 (2009).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

Opt. Express (9)

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
[CrossRef] [PubMed]

D. Biss and T. Brown, “Cylindrical vector beam focusing through a dielectric interface,” Opt. Express 9(10), 490–497 (2001).
[CrossRef] [PubMed]

Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002).
[PubMed]

M. R. Beversluis, L. Novotny, and S. J. Stranick, “Programmable vector point-spread function engineering,” Opt. Express 14(7), 2650–2656 (2006).
[CrossRef] [PubMed]

G. M. Lerman and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express 16(7), 4567–4581 (2008).
[CrossRef] [PubMed]

Y. Tokizane, K. Oka, and R. Morita, “Supercontinuum optical vortex pulse generation without spatial or topological-charge dispersion,” Opt. Express 17(17), 14517–14525 (2009).
[CrossRef] [PubMed]

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18(10), 10777–10785 (2010).
[CrossRef] [PubMed]

X. L. Wang, Y. Li, J. Chen, C. S. Guo, J. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18(10), 10786–10795 (2010).
[CrossRef] [PubMed]

B. Hao and J. Leger, “Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam,” Opt. Express 15(6), 3550–3556 (2007).
[CrossRef] [PubMed]

Opt. Lett. (9)

Y. Kozawa and S. Sato, “Focusing property of a double-ring-shaped radially polarized beam,” Opt. Lett. 31(6), 820–822 (2006).
[CrossRef] [PubMed]

G. M. Lerman and U. Levy, “Tight focusing of space variant vector optical fields with no cylindrical symmetry of polarization,” Opt. Lett. 32, 2194–2196 (2007).
[CrossRef] [PubMed]

M. A. Ahmed, A. Voss, M. M. Vogel, and T. Graf, “Multilayer polarizing grating mirror used for the generation of radial polarization in Yb:YAG thin-disk lasers,” Opt. Lett. 32(22), 3272–3274 (2007).
[CrossRef] [PubMed]

E. Y. S. Yew and C. J. R. Sheppard, “Tight focusing of radially polarized Gaussian and Bessel-Gauss beams,” Opt. Lett. 32(23), 3417–3419 (2007).
[CrossRef] [PubMed]

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(24), 3549–3551 (2007).
[CrossRef] [PubMed]

G. M. Lerman and U. Levy, “Generation of a radially polarized light beam using space-variant subwavelength gratings at 1064 nm,” Opt. Lett. 33(23), 2782–2784 (2008).
[CrossRef] [PubMed]

N. Davidson and N. Bokor, “High-numerical-aperture focusing of radially polarized doughnut beams with a parabolic mirror and a flat diffractive lens,” Opt. Lett. 29(12), 1318–1320 (2004).
[CrossRef] [PubMed]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27(5), 285–287 (2002).
[CrossRef]

M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21(23), 1948–1950 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

Proc. R. Soc. Lond. A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1274), 358–379 (1959).
[CrossRef]

Proc. SPIE (1)

G. Milione, H. I. Sztul, and R. R. Alfano, “Propagation of a hybrid vector polarization beam in a uniaxial crystal,” Proc. SPIE 7613, 76130I (2010).
[CrossRef]

Other (3)

F. K. Fatemi, and G. Beadie, “Imaging Atomic States Using Radially-Polarized Light,” in Frontiers in Optics (FiO)/Laser Science (LS) (Optical Society of America, Washington, DC, 2010), paper FWP6.

M. Born, and E. Wolf, Principles of Optics: Electromagnetic theory of propagation, interference and diffraction, 7th ed. (Cambridge University Press, 1999) pp. 24–38.

G. Milione, and R. R. Alfano, Cylindrical vector beam transformations and hybrid vector beams” in Frontiers in Optics (FiO)/Laser Science (LS) (Optical Society of America, Washington, DC, 2010), paper FWC4.

Supplementary Material (1)

» Media 1: MOV (897 KB)     

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Figures (4)

Fig. 1
Fig. 1

(a) Standard Poincaré sphere representation of a polarization state. The radially polarized field spans the equator of the sphere (b) polarization distribution obtained by transmitting a radially polarized light through a QWP oriented at 45 degrees with respect to the x axis. Blue – right handed polarization, red– left handed polarization, green – linear polarization. (c) HBs projections on the Poincaré sphere, where each circle corresponds to a different orientation of the QWP used to generate these beams. (d) HBs projections on the Poincaré sphere, where each circle corresponds to a different phase retardation of the wave plate used to generate these beams.

Fig. 2
Fig. 2

(a) and (b) schematics of polarization distributions that would be obtained by a radially polarized field transmitted through a QWP oriented at 45 and 0 degrees, respectively. (c) and (d) pictures of the experimentally generated fields of (a) and (b) respectively, being transmitted through an analyzer. The arrows show the orientation of the analyzer.

Fig. 3
Fig. 3

(a) Energy density components and the total energy density at the focal plane of a NA = 0.94 lens illuminated by the HB of Fig. 2(a). (b) The polarization ellipses at the focal plane having a 3D orientation distribution (Media 1). The colors are related to the total energy density at the focus. (c) Cross sections through the center of (b). (d) and (e) polarization projections on the x-y and the x-z planes, respectively.

Fig. 4
Fig. 4

(a) Calculated energy density in the x-z plane. (b) The cross section of the energy density along the dashed line in (a). (c) Consecutive polarization projections on the x-z plane demonstrating the evolution of the polarization distribution as the beam propagates through the focal plane. All calculations were performed for a NA = 0.94 lens.

Equations (3)

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E = T w p V r
E = ( cos ( θ ) cos ( Γ 2 ) i sin ( Γ 2 ) cos ( 2 ψ θ ) sin ( θ ) cos ( Γ 2 ) i sin ( Γ 2 ) sin ( 2 ψ θ ) )
I = cos 2 ( Γ 2 ) cos 2 ( ϕ θ ) + sin 2 ( Γ 2 ) cos 2 ( ϕ 2 ψ + θ )

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