Abstract

We report the formation of optically tunable, smooth hollow beams by reflection of a TEM00 Gaussian beam off a metal thin film. Hollow (doughnutlike) beams (HBs) with controllable profiles are created by a phase distortion at the surface. Two regimes of operation are observed: Below a certain power threshold, the HB formation is reversible and optically tunable on a time scale of milliseconds; above that threshold, alterations on the film surface make the effect permanent. Optical control of the HB shape is demonstrated by tuning the power of a second beam. High stability in the radial intensity profile and the possibility of adjusting the spatial distribution and aspect ratios make this technique promising for applications such as atom trapping and manipulation of Bose–Einstein condensates.

© 2006 Optical Society of America

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  1. T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
    [CrossRef]
  2. J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45, 1231-1237 (1998).
    [CrossRef]
  3. S. M. Iftiquar, "A tunable doughnut laser beam for cold-atom experiments," J. Opt. 5, 40-43 (2003).
    [CrossRef]
  4. E. Engel, N. Huse, T. A. Klar, and S. W. Hell, "Creating lambda/3 focal holes with a Mach-Zehnder interferometer," Appl. Phys. B 77, 11-17 (2003).
    [CrossRef]
  5. J. Courtial and M. J. Padgett, "Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes," Opt. Commun. 159, 13-18 (1999).
    [CrossRef]
  6. Y. Qian, Y. Zhang, R. Wei, and Y.-Z. Wang, "Generation of a collimated doughnut-beam for atom trapping using a single-cone axicon," Chin. Phys. Lett. 21, 1041-1043 (2004).
    [CrossRef]
  7. X. Wang and M. G. Littman, "Laser cavity for generation of variable-radius rings of light," Opt. Lett. 18, 767-770 (1993).
    [CrossRef] [PubMed]
  8. A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, "Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal," Opt. Commun. 232, 77-82 (2004).
    [CrossRef]
  9. S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, "Coherent atomic waveguides from hollow optical fibers: quantized atomic motion," Phys. Rev. A 50, 2680-2690 (1994).
    [CrossRef] [PubMed]
  10. S. Doiron and A. Haché, "Time evolution of reflective thermal lenses and measurement of thermal diffusivity in bulk solids," Appl. Opt. 43, 4250-4253 (2004).
    [CrossRef] [PubMed]
  11. C. Hu, E. T. Ogawa, and P. S. Ho, "Thermal diffusivity measurement of polymeric thin films using the photothermal displacement technique. II On-wafer measurement," J. Appl. Phys. 86, 6028-6038 (1999).
    [CrossRef]
  12. M. Born and E. Wolf, Principles of Optics (Pergamon, 1970).
  13. M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, "Photothermal displacement spectroscopy: an optical probe for solids and surfaces," Appl. Phys. A 32, 141-154 (1983).
    [CrossRef]
  14. L. Deng, K. He, T. Zhou, and C. Li, "Formation and evolution of the far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media," J. Opt. 7, 409-415 (2005).
    [CrossRef]
  15. D. V. Petrov, A. S. L. Gomes, and C. B. De Araujo, "Reflection Z-scan technique for measurements of optical properties of solids," Appl. Phys. Lett. 65, 1067-1069 (1994).
    [CrossRef]
  16. S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, "Creation of Laguerre-Gaussian laser modes using diffractive optics," Phys. Rev. A 66, 043801 (2002).
    [CrossRef]
  17. M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, "High-order Laguerre-Gaussian laser modes for studies of cold atoms," Opt. Commun. 156, 300-306 (1998).
    [CrossRef]

2005 (1)

L. Deng, K. He, T. Zhou, and C. Li, "Formation and evolution of the far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media," J. Opt. 7, 409-415 (2005).
[CrossRef]

2004 (4)

Y. Qian, Y. Zhang, R. Wei, and Y.-Z. Wang, "Generation of a collimated doughnut-beam for atom trapping using a single-cone axicon," Chin. Phys. Lett. 21, 1041-1043 (2004).
[CrossRef]

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
[CrossRef]

A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, "Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal," Opt. Commun. 232, 77-82 (2004).
[CrossRef]

S. Doiron and A. Haché, "Time evolution of reflective thermal lenses and measurement of thermal diffusivity in bulk solids," Appl. Opt. 43, 4250-4253 (2004).
[CrossRef] [PubMed]

2003 (2)

S. M. Iftiquar, "A tunable doughnut laser beam for cold-atom experiments," J. Opt. 5, 40-43 (2003).
[CrossRef]

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, "Creating lambda/3 focal holes with a Mach-Zehnder interferometer," Appl. Phys. B 77, 11-17 (2003).
[CrossRef]

2002 (1)

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, "Creation of Laguerre-Gaussian laser modes using diffractive optics," Phys. Rev. A 66, 043801 (2002).
[CrossRef]

1999 (2)

J. Courtial and M. J. Padgett, "Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes," Opt. Commun. 159, 13-18 (1999).
[CrossRef]

C. Hu, E. T. Ogawa, and P. S. Ho, "Thermal diffusivity measurement of polymeric thin films using the photothermal displacement technique. II On-wafer measurement," J. Appl. Phys. 86, 6028-6038 (1999).
[CrossRef]

1998 (2)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45, 1231-1237 (1998).
[CrossRef]

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, "High-order Laguerre-Gaussian laser modes for studies of cold atoms," Opt. Commun. 156, 300-306 (1998).
[CrossRef]

1994 (2)

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, "Coherent atomic waveguides from hollow optical fibers: quantized atomic motion," Phys. Rev. A 50, 2680-2690 (1994).
[CrossRef] [PubMed]

D. V. Petrov, A. S. L. Gomes, and C. B. De Araujo, "Reflection Z-scan technique for measurements of optical properties of solids," Appl. Phys. Lett. 65, 1067-1069 (1994).
[CrossRef]

1993 (1)

1983 (1)

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, "Photothermal displacement spectroscopy: an optical probe for solids and surfaces," Appl. Phys. A 32, 141-154 (1983).
[CrossRef]

Abraham, E. R. I.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, "Creation of Laguerre-Gaussian laser modes using diffractive optics," Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Allen, L.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45, 1231-1237 (1998).
[CrossRef]

Amer, N. M.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, "Photothermal displacement spectroscopy: an optical probe for solids and surfaces," Appl. Phys. A 32, 141-154 (1983).
[CrossRef]

Arlt, J.

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, "High-order Laguerre-Gaussian laser modes for studies of cold atoms," Opt. Commun. 156, 300-306 (1998).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45, 1231-1237 (1998).
[CrossRef]

Boccara, A. C.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, "Photothermal displacement spectroscopy: an optical probe for solids and surfaces," Appl. Phys. A 32, 141-154 (1983).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1970).

Buchter, S. C.

A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, "Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal," Opt. Commun. 232, 77-82 (2004).
[CrossRef]

Clifford, M. A.

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, "High-order Laguerre-Gaussian laser modes for studies of cold atoms," Opt. Commun. 156, 300-306 (1998).
[CrossRef]

Courtial, J.

J. Courtial and M. J. Padgett, "Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes," Opt. Commun. 159, 13-18 (1999).
[CrossRef]

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, "High-order Laguerre-Gaussian laser modes for studies of cold atoms," Opt. Commun. 156, 300-306 (1998).
[CrossRef]

De Araujo, C. B.

D. V. Petrov, A. S. L. Gomes, and C. B. De Araujo, "Reflection Z-scan technique for measurements of optical properties of solids," Appl. Phys. Lett. 65, 1067-1069 (1994).
[CrossRef]

Deng, L.

L. Deng, K. He, T. Zhou, and C. Li, "Formation and evolution of the far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media," J. Opt. 7, 409-415 (2005).
[CrossRef]

Dholakia, K.

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, "High-order Laguerre-Gaussian laser modes for studies of cold atoms," Opt. Commun. 156, 300-306 (1998).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45, 1231-1237 (1998).
[CrossRef]

Doiron, S.

Engel, E.

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, "Creating lambda/3 focal holes with a Mach-Zehnder interferometer," Appl. Phys. B 77, 11-17 (2003).
[CrossRef]

Fournier, D.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, "Photothermal displacement spectroscopy: an optical probe for solids and surfaces," Appl. Phys. A 32, 141-154 (1983).
[CrossRef]

Fujii, M.

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
[CrossRef]

Gomes, A. S. L.

D. V. Petrov, A. S. L. Gomes, and C. B. De Araujo, "Reflection Z-scan technique for measurements of optical properties of solids," Appl. Phys. Lett. 65, 1067-1069 (1994).
[CrossRef]

Haché, A.

He, K.

L. Deng, K. He, T. Zhou, and C. Li, "Formation and evolution of the far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media," J. Opt. 7, 409-415 (2005).
[CrossRef]

Hell, S. W.

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, "Creating lambda/3 focal holes with a Mach-Zehnder interferometer," Appl. Phys. B 77, 11-17 (2003).
[CrossRef]

Ho, P. S.

C. Hu, E. T. Ogawa, and P. S. Ho, "Thermal diffusivity measurement of polymeric thin films using the photothermal displacement technique. II On-wafer measurement," J. Appl. Phys. 86, 6028-6038 (1999).
[CrossRef]

Hu, C.

C. Hu, E. T. Ogawa, and P. S. Ho, "Thermal diffusivity measurement of polymeric thin films using the photothermal displacement technique. II On-wafer measurement," J. Appl. Phys. 86, 6028-6038 (1999).
[CrossRef]

Huse, N.

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, "Creating lambda/3 focal holes with a Mach-Zehnder interferometer," Appl. Phys. B 77, 11-17 (2003).
[CrossRef]

Iftiquar, S. M.

S. M. Iftiquar, "A tunable doughnut laser beam for cold-atom experiments," J. Opt. 5, 40-43 (2003).
[CrossRef]

Iketaki, Y.

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
[CrossRef]

Kaivola, M.

A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, "Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal," Opt. Commun. 232, 77-82 (2004).
[CrossRef]

Kennedy, S. A.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, "Creation of Laguerre-Gaussian laser modes using diffractive optics," Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Klar, T. A.

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, "Creating lambda/3 focal holes with a Mach-Zehnder interferometer," Appl. Phys. B 77, 11-17 (2003).
[CrossRef]

Kohn, S.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, "Photothermal displacement spectroscopy: an optical probe for solids and surfaces," Appl. Phys. A 32, 141-154 (1983).
[CrossRef]

Li, C.

L. Deng, K. He, T. Zhou, and C. Li, "Formation and evolution of the far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media," J. Opt. 7, 409-415 (2005).
[CrossRef]

Littman, M. G.

Marksteiner, S.

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, "Coherent atomic waveguides from hollow optical fibers: quantized atomic motion," Phys. Rev. A 50, 2680-2690 (1994).
[CrossRef] [PubMed]

Ogawa, E. T.

C. Hu, E. T. Ogawa, and P. S. Ho, "Thermal diffusivity measurement of polymeric thin films using the photothermal displacement technique. II On-wafer measurement," J. Appl. Phys. 86, 6028-6038 (1999).
[CrossRef]

Olmstead, M. A.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, "Photothermal displacement spectroscopy: an optical probe for solids and surfaces," Appl. Phys. A 32, 141-154 (1983).
[CrossRef]

Padgett, M. J.

J. Courtial and M. J. Padgett, "Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes," Opt. Commun. 159, 13-18 (1999).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45, 1231-1237 (1998).
[CrossRef]

Petrov, D. V.

D. V. Petrov, A. S. L. Gomes, and C. B. De Araujo, "Reflection Z-scan technique for measurements of optical properties of solids," Appl. Phys. Lett. 65, 1067-1069 (1994).
[CrossRef]

Porterfield, J. Z.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, "Creation of Laguerre-Gaussian laser modes using diffractive optics," Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Qian, Y.

Y. Qian, Y. Zhang, R. Wei, and Y.-Z. Wang, "Generation of a collimated doughnut-beam for atom trapping using a single-cone axicon," Chin. Phys. Lett. 21, 1041-1043 (2004).
[CrossRef]

Rolston, S. L.

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, "Coherent atomic waveguides from hollow optical fibers: quantized atomic motion," Phys. Rev. A 50, 2680-2690 (1994).
[CrossRef] [PubMed]

Savage, C. M.

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, "Coherent atomic waveguides from hollow optical fibers: quantized atomic motion," Phys. Rev. A 50, 2680-2690 (1994).
[CrossRef] [PubMed]

Shevchenko, A.

A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, "Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal," Opt. Commun. 232, 77-82 (2004).
[CrossRef]

Szabo, M. J.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, "Creation of Laguerre-Gaussian laser modes using diffractive optics," Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Tabiryan, N. V.

A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, "Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal," Opt. Commun. 232, 77-82 (2004).
[CrossRef]

Teslow, H.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, "Creation of Laguerre-Gaussian laser modes using diffractive optics," Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Toyama, N.

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
[CrossRef]

Wang, X.

Wang, Y.-Z.

Y. Qian, Y. Zhang, R. Wei, and Y.-Z. Wang, "Generation of a collimated doughnut-beam for atom trapping using a single-cone axicon," Chin. Phys. Lett. 21, 1041-1043 (2004).
[CrossRef]

Watanabe, T.

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
[CrossRef]

Watanabe, Y.

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
[CrossRef]

Wei, R.

Y. Qian, Y. Zhang, R. Wei, and Y.-Z. Wang, "Generation of a collimated doughnut-beam for atom trapping using a single-cone axicon," Chin. Phys. Lett. 21, 1041-1043 (2004).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1970).

Zhang, Y.

Y. Qian, Y. Zhang, R. Wei, and Y.-Z. Wang, "Generation of a collimated doughnut-beam for atom trapping using a single-cone axicon," Chin. Phys. Lett. 21, 1041-1043 (2004).
[CrossRef]

Zhou, T.

L. Deng, K. He, T. Zhou, and C. Li, "Formation and evolution of the far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media," J. Opt. 7, 409-415 (2005).
[CrossRef]

Zoller, P.

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, "Coherent atomic waveguides from hollow optical fibers: quantized atomic motion," Phys. Rev. A 50, 2680-2690 (1994).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. A (1)

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, "Photothermal displacement spectroscopy: an optical probe for solids and surfaces," Appl. Phys. A 32, 141-154 (1983).
[CrossRef]

Appl. Phys. B (1)

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, "Creating lambda/3 focal holes with a Mach-Zehnder interferometer," Appl. Phys. B 77, 11-17 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

D. V. Petrov, A. S. L. Gomes, and C. B. De Araujo, "Reflection Z-scan technique for measurements of optical properties of solids," Appl. Phys. Lett. 65, 1067-1069 (1994).
[CrossRef]

Chin. Phys. Lett. (1)

Y. Qian, Y. Zhang, R. Wei, and Y.-Z. Wang, "Generation of a collimated doughnut-beam for atom trapping using a single-cone axicon," Chin. Phys. Lett. 21, 1041-1043 (2004).
[CrossRef]

J. Appl. Phys. (1)

C. Hu, E. T. Ogawa, and P. S. Ho, "Thermal diffusivity measurement of polymeric thin films using the photothermal displacement technique. II On-wafer measurement," J. Appl. Phys. 86, 6028-6038 (1999).
[CrossRef]

J. Mod. Opt. (1)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45, 1231-1237 (1998).
[CrossRef]

J. Opt. (2)

S. M. Iftiquar, "A tunable doughnut laser beam for cold-atom experiments," J. Opt. 5, 40-43 (2003).
[CrossRef]

L. Deng, K. He, T. Zhou, and C. Li, "Formation and evolution of the far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media," J. Opt. 7, 409-415 (2005).
[CrossRef]

Opt. Commun. (3)

J. Courtial and M. J. Padgett, "Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes," Opt. Commun. 159, 13-18 (1999).
[CrossRef]

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, "High-order Laguerre-Gaussian laser modes for studies of cold atoms," Opt. Commun. 156, 300-306 (1998).
[CrossRef]

A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, "Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal," Opt. Commun. 232, 77-82 (2004).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, "Coherent atomic waveguides from hollow optical fibers: quantized atomic motion," Phys. Rev. A 50, 2680-2690 (1994).
[CrossRef] [PubMed]

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, "Creation of Laguerre-Gaussian laser modes using diffractive optics," Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Rev. Sci. Instrum. (1)

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
[CrossRef]

Other (1)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1970).

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Figures (7)

Fig. 1
Fig. 1

Calculated far-field intensity distribution for various amounts of phase distortion on the reflection plane: 1, Δ ϕ 0 = 0 ; 2, Δ ϕ 0 = π 2 ; 3, Δ ϕ 0 = π ; 4, Δ ϕ 0 = 2 π . The curvature radius R = 10 cm , the beam radius w 0 = 55 μ m .

Fig. 2
Fig. 2

Far-field intensity profiles of the reflected beam for incidence power (a) below and (b) above the reversibility threshold of Au ( 125 nm ) on glass. The reduced power curves were taken after exposure of 10 s to show reversibility.

Fig. 3
Fig. 3

Intensity profiles of the reflected probe beam at different pump beam intensities.

Fig. 4
Fig. 4

Example of a permanent HB. The image was taken at low power after the Cr film ( 125 nm ) was exposed to 2.9 kW cm 2 of intensity.

Fig. 5
Fig. 5

Time evolution of the far-field permanent HB for an incident intensity of 2.8 kW cm 2 on a 125 nm Cr film on glass.

Fig. 6
Fig. 6

Intensity profiles of reflected beams at different fluences after a fixed exposure time of 10 s on a Au film ( 125 nm ) . Data were recorded at the reduced power.

Fig. 7
Fig. 7

Exposure time required for the intensity at the center of the HB to reach zero as a function of incident intensity on a Cr film ( 125 nm ) on glass.

Equations (5)

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

I ( r ) = I 0 exp ( 2 r 2 w 2 ) ,
I ( r ) 0 J 0 ( k 0 r 1 r D ) exp [ r 2 w 2 i ϕ ( r ) ] r d r 2 ,
ϕ ( r ) = k 0 n 0 r 2 2 R + Δ ϕ ( r )
Δ ϕ ( r ) = Δ ϕ 0 exp ( 2 r 2 w b 2 ) ,
Δ ϕ 0 = k 0 H = k 0 β th E π w 2 ρ C P ,

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