Abstract

We explore the behavior of a class of fully correlated optical beams that span the entire surface of the Poincar´e sphere. The beams can be constructed from a coaxial superposition of a fundamental Gaussian mode and a spiral-phase Laguerre-Gauss mode having orthogonal polarizations. When the orthogonal polarizations are right and left circular, the coverage extends from one pole of the sphere to the other in such a way that concentric circles on the beam map onto parallels on the Poincar´e sphere and radial lines map onto meridians. If the beam waist parameters match, the map is stereographic and the beam propagation corresponds to a rigid rotation about the pole. We present an experimental example of how a symmetrically stressed window can produce these beams and show that the predicted rotation indeed occurs when moving through the beams’ focus.

© 2010 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. S. Youngworth, and T. G. Brown, “Focusing of high numerical aperture cylindrical vector beams,” Opt. Express 7, 77–87 (2000), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-7-2-77.
    [CrossRef]
  2. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=aop-1-1-1 and references therein.
  3. D. P. Biss, and T. G. Brown, “Cylindrical vector beam focusing through a dielectric surface,” Opt. Express 9, 490–497 (2001), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-9-10-490.
    [CrossRef]
  4. D. G. Hall, “Vector-beam solutions of Maxwell’s wave equation,” Opt. Lett. 21, 9–11 (1996), http://www.opticsinfobase.org/abstract.cfm?URI=ol-21-1-9.
    [CrossRef]
  5. R. H. Jordan, and D. G. Hall, “Free-space azimuthal paraxial wave equation: the azimuthal Bessel-Gauss beam solution,” Opt. Lett. 19, 427 (1994), http://www.opticsinfobase.org/abstract.cfm?URI=ol-19-7-427.
    [CrossRef]
  6. P. L. Greene, and D. G. Hall, “Focal shift in vector beams,” Opt. Express 4, 411–419 (1999), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-4-10-411.
    [CrossRef]
  7. C. J. R. Sheppard, and P. Török, “Electromagnetic field in the focal region of an electric dipole wave,” Optik (Stuttg.) 104, 175–177 (1997).
  8. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing Light to a Tighter Spot,” Opt. Commun. 179, 1 (2000).
    [CrossRef]
  9. R. Dorn, S. Quabis, and G. Leuchs, “Sharper Focus for a Radially Polarized Light Beam,” Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef]
  10. C. J. R. Sheppard, and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43, 4322–4327 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=ao-43-22-4322.
    [CrossRef]
  11. R. Borghi, M. Santarsiero, and M. A. Alonso, “Highly focused spirally polarized beams,” J. Opt. Soc. Am. A 22, 1420–1431 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=josaa-22-7-1420.
    [CrossRef]
  12. G. Lerman, and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express 16, 4567–4581 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-7-4567.
    [CrossRef]
  13. Q. Zhan, “Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam,” Opt. Lett. 31, 1726–1728 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-11-1726.
    [CrossRef]
  14. W. Chen, and Q. Zhan, “Numerical study of an apertureless near field scanning optical microscope probe under radial polarization illumination,” Opt. Express 15, 4106–4111 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-7-4106.
    [CrossRef]
  15. K. J. Moh, X.-C. Yuan, J. Bu, S. W. Zhu, and Z. Bruce, “Gao, “Radial polarization induced surface plasmon virtual probe for two-photon fluorescence microscopy,” Opt. Lett. 34, 971–973 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-7-971.
    [CrossRef]
  16. N. Hayazawa, “Focused Excitation of Surface Plasmon Polaritons Based on Gap-Mode in Tip-Enhanced Spectroscopy,” Jpn. J. Appl. Phys. 46, 7995 (2007).
    [CrossRef]
  17. K. Venkatakrishnan, and B. Tan, “Interconnect microvia drilling with a radially polarized laser beam,” J. Micromech. Microeng. 16, 2603 (2006).
    [CrossRef]
  18. N. Moore, and M. A. Alonso, “Closed-form formula for Mie scattering of nonparaxial analogues of Gaussian beams,” Opt. Express 16, 5926–5933 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-8-5926.
    [CrossRef]
  19. A. K. Spilman, and T. G. Brown, “Stress birefringent, space-variant wave plates for vortex illumination,” Appl. Opt. 26, 61–66 (2007), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-46-1-61.
    [CrossRef]
  20. A. K. Spilman, and T. G. Brown, “Stress-induced Focal Splitting,” Opt. Express 15, 8411–8421 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-13-8411.
    [CrossRef]
  21. A. K. Spilman, A. M. Beckley, and T. G. Brown, “Focal splitting and optical vortex structure induced by stress birefringence,” Proc. SPIE 6667, 666701 (2007).
  22. N. Moore, and M. A. Alonso, “Closed-form bases for the description of monochromatic, strongly focused, electromagnetic fields,” J. Opt. Soc. Am. A 29, 2211–2218 (2009), http://www.opticsinfobase.org/abstract.cfm?uri=josaa-26-7-1754.
    [CrossRef]
  23. E. G. Sauter, “Gaussian beams and the Poincare sphere,” Microw. Opt. Technol. Lett. 4, 485–486 (1991) .
    [CrossRef]

2009 (2)

2008 (2)

2007 (5)

W. Chen, and Q. Zhan, “Numerical study of an apertureless near field scanning optical microscope probe under radial polarization illumination,” Opt. Express 15, 4106–4111 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-7-4106.
[CrossRef]

A. K. Spilman, and T. G. Brown, “Stress-induced Focal Splitting,” Opt. Express 15, 8411–8421 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-13-8411.
[CrossRef]

A. K. Spilman, and T. G. Brown, “Stress birefringent, space-variant wave plates for vortex illumination,” Appl. Opt. 26, 61–66 (2007), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-46-1-61.
[CrossRef]

A. K. Spilman, A. M. Beckley, and T. G. Brown, “Focal splitting and optical vortex structure induced by stress birefringence,” Proc. SPIE 6667, 666701 (2007).

N. Hayazawa, “Focused Excitation of Surface Plasmon Polaritons Based on Gap-Mode in Tip-Enhanced Spectroscopy,” Jpn. J. Appl. Phys. 46, 7995 (2007).
[CrossRef]

2006 (2)

2005 (1)

2004 (1)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper Focus for a Radially Polarized Light Beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

2001 (1)

2000 (2)

1999 (1)

1997 (1)

C. J. R. Sheppard, and P. Török, “Electromagnetic field in the focal region of an electric dipole wave,” Optik (Stuttg.) 104, 175–177 (1997).

1996 (1)

1994 (1)

1991 (1)

E. G. Sauter, “Gaussian beams and the Poincare sphere,” Microw. Opt. Technol. Lett. 4, 485–486 (1991) .
[CrossRef]

Alonso, M. A.

Beckley, A. M.

A. K. Spilman, A. M. Beckley, and T. G. Brown, “Focal splitting and optical vortex structure induced by stress birefringence,” Proc. SPIE 6667, 666701 (2007).

Biss, D. P.

Borghi, R.

Brown, T. G.

Bruce, Z.

Bu, J.

Chen, W.

Choudhury, A.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper Focus for a Radially Polarized Light Beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing Light to a Tighter Spot,” Opt. Commun. 179, 1 (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 (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 (2000).
[CrossRef]

Greene, P. L.

Hall, D. G.

Hayazawa, N.

N. Hayazawa, “Focused Excitation of Surface Plasmon Polaritons Based on Gap-Mode in Tip-Enhanced Spectroscopy,” Jpn. J. Appl. Phys. 46, 7995 (2007).
[CrossRef]

Jordan, R. H.

Lerman, G.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper Focus for a Radially Polarized Light Beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing Light to a Tighter Spot,” Opt. Commun. 179, 1 (2000).
[CrossRef]

Levy, U.

Moh, K. J.

Moore, N.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper Focus for a Radially Polarized Light Beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing Light to a Tighter Spot,” Opt. Commun. 179, 1 (2000).
[CrossRef]

Santarsiero, M.

Sauter, E. G.

E. G. Sauter, “Gaussian beams and the Poincare sphere,” Microw. Opt. Technol. Lett. 4, 485–486 (1991) .
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard, and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43, 4322–4327 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=ao-43-22-4322.
[CrossRef]

C. J. R. Sheppard, and P. Török, “Electromagnetic field in the focal region of an electric dipole wave,” Optik (Stuttg.) 104, 175–177 (1997).

Spilman, A. K.

A. K. Spilman, and T. G. Brown, “Stress-induced Focal Splitting,” Opt. Express 15, 8411–8421 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-13-8411.
[CrossRef]

A. K. Spilman, and T. G. Brown, “Stress birefringent, space-variant wave plates for vortex illumination,” Appl. Opt. 26, 61–66 (2007), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-46-1-61.
[CrossRef]

A. K. Spilman, A. M. Beckley, and T. G. Brown, “Focal splitting and optical vortex structure induced by stress birefringence,” Proc. SPIE 6667, 666701 (2007).

Tan, B.

K. Venkatakrishnan, and B. Tan, “Interconnect microvia drilling with a radially polarized laser beam,” J. Micromech. Microeng. 16, 2603 (2006).
[CrossRef]

Török, P.

C. J. R. Sheppard, and P. Török, “Electromagnetic field in the focal region of an electric dipole wave,” Optik (Stuttg.) 104, 175–177 (1997).

Venkatakrishnan, K.

K. Venkatakrishnan, and B. Tan, “Interconnect microvia drilling with a radially polarized laser beam,” J. Micromech. Microeng. 16, 2603 (2006).
[CrossRef]

Youngworth, K. S.

Yuan, X.-C.

Zhan, Q.

Zhu, S. W.

Appl. Opt. (2)

J. Micromech. Microeng. (1)

K. Venkatakrishnan, and B. Tan, “Interconnect microvia drilling with a radially polarized laser beam,” J. Micromech. Microeng. 16, 2603 (2006).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

N. Hayazawa, “Focused Excitation of Surface Plasmon Polaritons Based on Gap-Mode in Tip-Enhanced Spectroscopy,” Jpn. J. Appl. Phys. 46, 7995 (2007).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

E. G. Sauter, “Gaussian beams and the Poincare sphere,” Microw. Opt. Technol. Lett. 4, 485–486 (1991) .
[CrossRef]

Opt. Commun. (1)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing Light to a Tighter Spot,” Opt. Commun. 179, 1 (2000).
[CrossRef]

Opt. Express (7)

P. L. Greene, and D. G. Hall, “Focal shift in vector beams,” Opt. Express 4, 411–419 (1999), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-4-10-411.
[CrossRef]

K. S. Youngworth, and T. G. Brown, “Focusing of high numerical aperture cylindrical vector beams,” Opt. Express 7, 77–87 (2000), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-7-2-77.
[CrossRef]

D. P. Biss, and T. G. Brown, “Cylindrical vector beam focusing through a dielectric surface,” Opt. Express 9, 490–497 (2001), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-9-10-490.
[CrossRef]

G. Lerman, and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express 16, 4567–4581 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-7-4567.
[CrossRef]

N. Moore, and M. A. Alonso, “Closed-form formula for Mie scattering of nonparaxial analogues of Gaussian beams,” Opt. Express 16, 5926–5933 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-8-5926.
[CrossRef]

W. Chen, and Q. Zhan, “Numerical study of an apertureless near field scanning optical microscope probe under radial polarization illumination,” Opt. Express 15, 4106–4111 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-7-4106.
[CrossRef]

A. K. Spilman, and T. G. Brown, “Stress-induced Focal Splitting,” Opt. Express 15, 8411–8421 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-13-8411.
[CrossRef]

Opt. Lett. (4)

Optik (Stuttg.) (1)

C. J. R. Sheppard, and P. Török, “Electromagnetic field in the focal region of an electric dipole wave,” Optik (Stuttg.) 104, 175–177 (1997).

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper Focus for a Radially Polarized Light Beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Proc. SPIE (1)

A. K. Spilman, A. M. Beckley, and T. G. Brown, “Focal splitting and optical vortex structure induced by stress birefringence,” Proc. SPIE 6667, 666701 (2007).

Other (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=aop-1-1-1 and references therein.

Supplementary Material (1)

» Media 1: MOV (1586 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics