Abstract

We present a theoretical and experimental investigation of an interferometric technique for converting a linearly polarized Gaussian beam into a radially polarized doughnut beam. The experimental setup accomplishes the coherent summation of two orthogonally polarized TEM01 and TEM10 beams that are obtained from the transformation of a TEM00 beam by use of a simple binary diffractive optical element. We have shown that the degree of radial polarization is maximum at a given distance from the interferometer output port that depends on the diameter of the incident beam at the interferometer input port.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
    [CrossRef]
  2. B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
    [CrossRef]
  3. D. P. Biss, T. G. Brown, “Cylindrical vector beam focusing through a dielectric interface,” Opt. Express 9, 490–497 (2001).
    [CrossRef] [PubMed]
  4. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, G. Leuchs, “The focus of light-theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109–113 (2001).
    [CrossRef]
  5. Q. Zhan, J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10, 324–331 (2002).
    [CrossRef] [PubMed]
  6. V. G. Niziev, A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 1455–1461 (1999).
    [CrossRef]
  7. A. V. Nesterov, V. G. Niziev, “Laser beams with axially symmetric polarization,” J. Phys. D 33, 1817–1822 (2000).
    [CrossRef]
  8. B. Sick, B. Hecht, L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485 (2000).
    [CrossRef] [PubMed]
  9. L. Novotny, M. R. Beversluis, K. S. Youngworth, T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
    [CrossRef] [PubMed]
  10. J. Azoulay, A. Débarre, R. Jaffiol, P. Tchénio, “Original tools for single-molecule spectroscopy,” Single Mol. 2, 241–249 (2001).
    [CrossRef]
  11. F. Treussart, R. Alléaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
    [CrossRef] [PubMed]
  12. C. Varin, M. Piché, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74, S83–S88 (2002).
    [CrossRef]
  13. T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
    [CrossRef]
  14. K. T. Gahagan, G. A. Swartzlander, “Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap,” J. Opt. Soc. Am. B 16533–537 (1999).
    [CrossRef]
  15. K. S. Youngworth, T. G. Brown, “Inhomogeneous polarization in scanning optical microscopy,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing VII, J. Conchello, C. J. Cogswell, A. G. Tescher, and T. Wilson, eds., Proc. SPIE3919, 75–85 (2000).
  16. S. C. Tidwell, D. H. Ford, W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2234–2239 (1990).
    [CrossRef] [PubMed]
  17. M. Stalder, M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21, 1948–1950 (1996).
    [CrossRef] [PubMed]
  18. Z. Bomzon, V. Kleiner, E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal strip grating,” Appl. Phys. Lett. 79, 1587–1589 (2001).
    [CrossRef]
  19. R. Oron, S. Blit, N. Davidson, A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
    [CrossRef]
  20. D. J. Armstrong, M. C. Philips, A. V. Smith, “Generation of radially polarized beams with an image-rotating resonator,” Appl. Opt. 42, 3550–3554 (2003).
    [CrossRef] [PubMed]
  21. H. Kogelnik, T. Li, “Laser beams and resonator,” Appl. Opt. 5, 1550–1567 (1966).
    [CrossRef] [PubMed]
  22. R. Bourouis, K. Aït-Ameur, H. Ladjouze, “Optimization of the Gaussian beam flattening using a phase-plate,” J. Mod. Opt. 44, 1417–1427 (1997).
    [CrossRef]
  23. K. Aït-Ameur, F. Sanchez, M. Brunel, “High transverse mode discrimination in apertured resonators using diffractive binary optics,” Opt. Commun. 184, 73–78 (2000).
    [CrossRef]
  24. K. Aït-Ameur, “Effects of a phase aperture on the fundamental mode of a hard-apertured cavity,” J. Mod. Opt. 49, 1157–1168 (2002).
    [CrossRef]
  25. M. Fromager, K. Aït-Ameur, “Transformation of an elliptic into a circular beam using a diffractive binary optic,” Opt. Commun. 190, 45–49 (2001).
    [CrossRef]
  26. A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).

2003 (1)

2002 (4)

K. Aït-Ameur, “Effects of a phase aperture on the fundamental mode of a hard-apertured cavity,” J. Mod. Opt. 49, 1157–1168 (2002).
[CrossRef]

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

F. Treussart, R. Alléaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

C. Varin, M. Piché, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74, S83–S88 (2002).
[CrossRef]

2001 (6)

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

J. Azoulay, A. Débarre, R. Jaffiol, P. Tchénio, “Original tools for single-molecule spectroscopy,” Single Mol. 2, 241–249 (2001).
[CrossRef]

Z. Bomzon, V. Kleiner, E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal strip grating,” Appl. Phys. Lett. 79, 1587–1589 (2001).
[CrossRef]

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

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, G. Leuchs, “The focus of light-theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109–113 (2001).
[CrossRef]

M. Fromager, K. Aït-Ameur, “Transformation of an elliptic into a circular beam using a diffractive binary optic,” Opt. Commun. 190, 45–49 (2001).
[CrossRef]

2000 (4)

K. Aït-Ameur, F. Sanchez, M. Brunel, “High transverse mode discrimination in apertured resonators using diffractive binary optics,” Opt. Commun. 184, 73–78 (2000).
[CrossRef]

A. V. Nesterov, V. G. Niziev, “Laser beams with axially symmetric polarization,” J. Phys. D 33, 1817–1822 (2000).
[CrossRef]

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

R. Oron, S. Blit, N. Davidson, A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

1999 (2)

1997 (2)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

R. Bourouis, K. Aït-Ameur, H. Ladjouze, “Optimization of the Gaussian beam flattening using a phase-plate,” J. Mod. Opt. 44, 1417–1427 (1997).
[CrossRef]

1996 (1)

1990 (1)

1966 (1)

1959 (2)

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
[CrossRef]

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

Aït-Ameur, K.

K. Aït-Ameur, “Effects of a phase aperture on the fundamental mode of a hard-apertured cavity,” J. Mod. Opt. 49, 1157–1168 (2002).
[CrossRef]

M. Fromager, K. Aït-Ameur, “Transformation of an elliptic into a circular beam using a diffractive binary optic,” Opt. Commun. 190, 45–49 (2001).
[CrossRef]

K. Aït-Ameur, F. Sanchez, M. Brunel, “High transverse mode discrimination in apertured resonators using diffractive binary optics,” Opt. Commun. 184, 73–78 (2000).
[CrossRef]

R. Bourouis, K. Aït-Ameur, H. Ladjouze, “Optimization of the Gaussian beam flattening using a phase-plate,” J. Mod. Opt. 44, 1417–1427 (1997).
[CrossRef]

Alléaume, R.

F. Treussart, R. Alléaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

Armstrong, D. J.

Azoulay, J.

J. Azoulay, A. Débarre, R. Jaffiol, P. Tchénio, “Original tools for single-molecule spectroscopy,” Single Mol. 2, 241–249 (2001).
[CrossRef]

Beversluis, M. R.

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

Biss, D. P.

Blit, S.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Bomzon, Z.

Z. Bomzon, V. Kleiner, E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal strip grating,” Appl. Phys. Lett. 79, 1587–1589 (2001).
[CrossRef]

Bourouis, R.

R. Bourouis, K. Aït-Ameur, H. Ladjouze, “Optimization of the Gaussian beam flattening using a phase-plate,” J. Mod. Opt. 44, 1417–1427 (1997).
[CrossRef]

Brown, T. G.

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

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

K. S. Youngworth, T. G. Brown, “Inhomogeneous polarization in scanning optical microscopy,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing VII, J. Conchello, C. J. Cogswell, A. G. Tescher, and T. Wilson, eds., Proc. SPIE3919, 75–85 (2000).

Brunel, M.

K. Aït-Ameur, F. Sanchez, M. Brunel, “High transverse mode discrimination in apertured resonators using diffractive binary optics,” Opt. Commun. 184, 73–78 (2000).
[CrossRef]

Courty, J. M.

F. Treussart, R. Alléaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

Davidson, N.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Débarre, A.

J. Azoulay, A. Débarre, R. Jaffiol, P. Tchénio, “Original tools for single-molecule spectroscopy,” Single Mol. 2, 241–249 (2001).
[CrossRef]

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, G. Leuchs, “The focus of light-theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109–113 (2001).
[CrossRef]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, G. Leuchs, “The focus of light-theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109–113 (2001).
[CrossRef]

Ford, D. H.

Friesem, A. A.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Fromager, M.

M. Fromager, K. Aït-Ameur, “Transformation of an elliptic into a circular beam using a diffractive binary optic,” Opt. Commun. 190, 45–49 (2001).
[CrossRef]

Gahagan, K. T.

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, G. Leuchs, “The focus of light-theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109–113 (2001).
[CrossRef]

Hasman, E.

Z. Bomzon, V. Kleiner, E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal strip grating,” Appl. Phys. Lett. 79, 1587–1589 (2001).
[CrossRef]

Hecht, B.

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

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Jaffiol, R.

J. Azoulay, A. Débarre, R. Jaffiol, P. Tchénio, “Original tools for single-molecule spectroscopy,” Single Mol. 2, 241–249 (2001).
[CrossRef]

Kimura, W. D.

Kleiner, V.

Z. Bomzon, V. Kleiner, E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal strip grating,” Appl. Phys. Lett. 79, 1587–1589 (2001).
[CrossRef]

Kogelnik, H.

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Ladjouze, H.

R. Bourouis, K. Aït-Ameur, H. Ladjouze, “Optimization of the Gaussian beam flattening using a phase-plate,” J. Mod. Opt. 44, 1417–1427 (1997).
[CrossRef]

Le Floc’h, V.

F. Treussart, R. Alléaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

Leger, J. R.

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, G. Leuchs, “The focus of light-theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109–113 (2001).
[CrossRef]

Li, T.

Nesterov, A. V.

A. V. Nesterov, V. G. Niziev, “Laser beams with axially symmetric polarization,” J. Phys. D 33, 1817–1822 (2000).
[CrossRef]

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

Niziev, V. G.

A. V. Nesterov, V. G. Niziev, “Laser beams with axially symmetric polarization,” J. Phys. D 33, 1817–1822 (2000).
[CrossRef]

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

Novotny, L.

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

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

Oron, R.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Philips, M. C.

Piché, M.

C. Varin, M. Piché, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74, S83–S88 (2002).
[CrossRef]

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, G. Leuchs, “The focus of light-theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109–113 (2001).
[CrossRef]

Richards, B.

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

Roch, J.-F.

F. Treussart, R. Alléaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

Sanchez, F.

K. Aït-Ameur, F. Sanchez, M. Brunel, “High transverse mode discrimination in apertured resonators using diffractive binary optics,” Opt. Commun. 184, 73–78 (2000).
[CrossRef]

Sasada, H.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Schadt, M.

Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Sick, B.

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

Siegman, A. E.

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).

Smith, A. V.

Stalder, M.

Swartzlander, G. A.

Tchénio, P.

J. Azoulay, A. Débarre, R. Jaffiol, P. Tchénio, “Original tools for single-molecule spectroscopy,” Single Mol. 2, 241–249 (2001).
[CrossRef]

Tidwell, S. C.

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Treussart, F.

F. Treussart, R. Alléaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

Varin, C.

C. Varin, M. Piché, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74, S83–S88 (2002).
[CrossRef]

Wolf, E.

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
[CrossRef]

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

Xiao, L. T.

F. Treussart, R. Alléaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

Youngworth, K. S.

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

K. S. Youngworth, T. G. Brown, “Inhomogeneous polarization in scanning optical microscopy,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing VII, J. Conchello, C. J. Cogswell, A. G. Tescher, and T. Wilson, eds., Proc. SPIE3919, 75–85 (2000).

Zhan, Q.

Appl. Opt. (3)

Appl. Phys. B (2)

C. Varin, M. Piché, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74, S83–S88 (2002).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, G. Leuchs, “The focus of light-theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109–113 (2001).
[CrossRef]

Appl. Phys. Lett. (2)

Z. Bomzon, V. Kleiner, E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal strip grating,” Appl. Phys. Lett. 79, 1587–1589 (2001).
[CrossRef]

R. Oron, S. Blit, N. Davidson, A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

J. Mod. Opt. (2)

K. Aït-Ameur, “Effects of a phase aperture on the fundamental mode of a hard-apertured cavity,” J. Mod. Opt. 49, 1157–1168 (2002).
[CrossRef]

R. Bourouis, K. Aït-Ameur, H. Ladjouze, “Optimization of the Gaussian beam flattening using a phase-plate,” J. Mod. Opt. 44, 1417–1427 (1997).
[CrossRef]

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

J. Phys. D (2)

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

A. V. Nesterov, V. G. Niziev, “Laser beams with axially symmetric polarization,” J. Phys. D 33, 1817–1822 (2000).
[CrossRef]

Opt. Commun. (2)

K. Aït-Ameur, F. Sanchez, M. Brunel, “High transverse mode discrimination in apertured resonators using diffractive binary optics,” Opt. Commun. 184, 73–78 (2000).
[CrossRef]

M. Fromager, K. Aït-Ameur, “Transformation of an elliptic into a circular beam using a diffractive binary optic,” Opt. Commun. 190, 45–49 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. Lett. (4)

F. Treussart, R. Alléaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

B. Sick, B. Hecht, 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, T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. A (2)

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
[CrossRef]

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

Single Mol. (1)

J. Azoulay, A. Débarre, R. Jaffiol, P. Tchénio, “Original tools for single-molecule spectroscopy,” Single Mol. 2, 241–249 (2001).
[CrossRef]

Other (2)

K. S. Youngworth, T. G. Brown, “Inhomogeneous polarization in scanning optical microscopy,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing VII, J. Conchello, C. J. Cogswell, A. G. Tescher, and T. Wilson, eds., Proc. SPIE3919, 75–85 (2000).

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).

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.


Figures (11)

Fig. 1
Fig. 1

Intensity distributions of the coherent superposition of (a) TEM 10 , (b) TEM 01 beams that are orthogonally polarized. (c) The resulting beam is a doughnut beam radially polarized.

Fig. 2
Fig. 2

Intensity distributions of a radially polarized beam after passing a linear polarizer having its axis oriented (a) vertically, (b) at 45°, (c) horizontally.

Fig. 3
Fig. 3

Schematic of the phase step of height h etched in a thin polymer film having a refractive index n and deposited on a glass plate. This step produces a phase shift ϕ = 2 π h ( n 1 ) λ between the two parts of the laser beam illuminating the polymer edge.

Fig. 4
Fig. 4

Experimental setup to produce a radially polarized beam from the superposition of the two beams coming out of orthogonally oriented ϕ = π phase steps. This setup relies on a Mach–Zehnder interferometer. A CW doubled Nd : YVO 4 laser is first spatially filtered by passing through a pinhole and then sent to the interferometer after collimation. T, pinhole; PBS, polarizing beam splitter; PS, ϕ = π phase step; VD, variable delay made of two tilted BK7 glass plates. Note that it is important to set the two phase steps at the same distance from the interferometer output port.

Fig. 5
Fig. 5

Two-dimensional beam intensity patterns of (a) incident Gaussian beam, (b) far-field diffraction pattern of this collimated Gaussian beam diffracted by the phase step positioned on the optical axis ( Δ = 0 ) .

Fig. 6
Fig. 6

Theoretical (left side) and experimental (right side) x = 0 , cross section intensity diffraction patterns of a collimated Gaussian beam (radius W = 0.4 mm ) diffracted on a centered ( Δ = 0 ) phase step ϕ = π in (a) the near-field and (b) the far-field regions. The dotted curve is a fit by the intensity distribution I 01 = E 01 2 of a perfect TEM 01 beam.

Fig. 7
Fig. 7

Theoretical (left side) and experimental (right side) diffraction patterns of a collimated Gaussian beam (radius W = 0.4 mm ) diffracted on a phase step ϕ = π displaced from the incident beam optical axis ( Δ = 0.7 ) . Two cases are displayed, (a) near-field, (b) far-field diffraction intensity patterns.

Fig. 8
Fig. 8

Variation of the degree of radial polarization η as a function of the distance z P from the phase steps in the two cases Δ θ < 1 ° and Δ θ < 5 ° . The incident Gaussian beam radius is W = 1 mm .

Fig. 9
Fig. 9

Variation of the optimal distance z P max as a function of W 2 (squares), where W is the radius of the incident Gaussian beam. The dotted line represents a fit with use of the linear variation of the Rayleigh range z R = π W 2 ( λ M 2 ) versus W 2 , yielding M 2 = 3 .

Fig. 10
Fig. 10

Two-dimensional beam intensity pattern of the beam emerging from the Mach–Zehnder interferometer including the two phase steps in a plane located at distance z P from the output port. The incident Gaussian beam radius is W = 1 mm . Two cases are displayed: (a) corresponds to the optimum position z P max = 2 m for the best conversion of linear into radial polarization; (b) corresponds to z P = 5 m .

Fig. 11
Fig. 11

Experimental beam pattern recorded at position z P = z P max ; (a) total intensity, (b) intensity distribution after passing an analyzer oriented at 45°.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

E 10 ( x , y ) = E 0 2 x W u x exp [ ( x 2 + y 2 W 2 ) ] ,
E 01 ( x , y ) = E 0 2 y W u y exp [ ( x 2 + y 2 W 2 ) ] ,
E T ( x , y ) = E 10 + E 01 = E 0 W exp [ ( x 2 + y 2 W 2 ) ] [ x u x + y u y ] .
τ ( x , y ) = { 1 for y > y 0 exp ( i ϕ ) for y y 0 .
E in ( x , y ) = exp [ ( x 2 + y 2 W 2 ) ] .
E ( x P , y P , z P ) = i λ + + τ ( x , y ) E in ( x , y ) exp ( i k r ) r d x d y ,
r z P in the denominator ,
r z P + ( x P x ) 2 + ( y P y ) 2 2 z P in the numerator .
I ( x P , y P , z P ) = + F ( x ) d x [ + τ ( x , y ) F ( y ) d y ] 2 ,
F ( u ) = exp ( u 2 W 2 ) exp [ i k ( u P u ) 2 2 z P ] ,
1 z p 1 z p = 1 f
τ L ( x , y ) = exp [ i k ( x 2 + x 2 ) 2 f ] .
E T ( x p , y p , z p ) = E 1 ( x p , y p , z p ) + E 2 ( x p , y p , z p ) .
η = P Δ θ P T ,
z R = π W 2 λ M 2 ,

Metrics