Abstract

We analyze the optical potential for atom guidance in a dark hollow laser beam and compare it with that generated by the evanescent wave in a micrometer-sized hollow optical fiber. We calculate dependence of the optical potential on various parameters: radial position r, laser–atom detuning Δ, beam power P0, and propagation distance Z. We experimentally generated a dark hollow laser beam from a hollow optical fiber with a 7-μm hole diameter and obtained a coupling efficiency of 50% for the LP01 mode. Our study shows that a dark hollow laser beam can produce an optical potential deep enough to guide cold atoms from a magneto-optical trap.

© 1998 Optical Society of America

Full Article  |  PDF Article

Errata

Jianping Yin, Yifu Zhu, Wenbao Wang, Yuzhu Wang, and Wonho Jhe, "Optical potential for atom guidance in a dark hollow laser beam: errata," J. Opt. Soc. Am. B 15, 1816-1816 (1998)
https://www.osapublishing.org/josab/abstract.cfm?uri=josab-15-6-1816

References

  • View by:
  • |
  • |
  • |

  1. X. Wang and M. G. Littman, Opt. Lett. 18, 767 (1993).
    [CrossRef] [PubMed]
  2. C. Paterson and R. Smith, Opt. Commun. 124, 121 (1996).
    [CrossRef]
  3. H. S. Lee, B. W. Atewart, K. Choi, and H. Fenichel, Phys. Rev. A 49, 4922 (1994).
    [CrossRef] [PubMed]
  4. V. Tikhonenko and N. N. Akhmediev, Opt. Commun. 126, 108 (1996).
    [CrossRef]
  5. A. V. Mamaev, M. Saffman, and A. A. Zozulya, Phys. Rev. Lett. 77, 4544 (1996).
    [CrossRef] [PubMed]
  6. M. A. Ol’Shanii, Yu. B. Ovchinnikov, and V. S. Letokhov, Opt. Commun. 98, 77 (1993).
    [CrossRef]
  7. M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 75, 3252 (1995).
    [CrossRef]
  8. S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, Phys. Rev. A 50, 2680 (1994).
    [CrossRef] [PubMed]
  9. H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, Opt. Commun. 115, 57 (1995).
    [CrossRef]
  10. M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, and Z. Anderson, Phys. Rev. A 53, R648 (1996).
    [CrossRef]
  11. H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. Lee, and W. Jhe, Phys. Rev. Lett. 76, 4500 (1996).
    [CrossRef] [PubMed]
  12. D. J. Harris and C. M. Savage, Phys. Rev. A 51, 3967 (1995).
    [CrossRef] [PubMed]
  13. J. J. Hope and C. M. Savage, Phys. Rev. A 53, 3449 (1996).
    [CrossRef] [PubMed]
  14. V. I. Balykin, D. V. Laryushin, M. V. Subbotin, and V. S. Letokhov, JETP Lett. 63, 802 (1996).
    [CrossRef]
  15. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).
  16. C. I. Sukenik, M. G. Boshier, D. Cho, V. Sandoghdar, and E. A. Hinds, Phys. Rev. Lett. 70, 560 (1993).
    [CrossRef] [PubMed]
  17. H. Ito, K. Sakaki, M. Ohtsu, and W. Jhe, “Measurement of cavity QED energy shifts on atom guidance using evanescent light,” Phys. Rev. A (to be published).
  18. V. I. Balykin and V. S. Letokhov, Opt. Commun. 64, 151 (1987).
    [CrossRef]
  19. G. M. Gallatin and P. L. Gould, J. Opt. Soc. Am. B 8, 502 (1991).
    [CrossRef]
  20. K. I. Lee, J. A. Kim, H. R. Noh, and W. Jhe, Opt. Lett. 21, 1177 (1996).
    [CrossRef] [PubMed]
  21. J. A. Kim, K. I. Lee, H. R. Noh, and W. Jhe, Opt. Lett. 22, 117 (1997).
    [CrossRef] [PubMed]
  22. Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 77, 3331 (1996).
    [CrossRef] [PubMed]
  23. J. Yin, H. Noh, K. Lee, J. Kim, W. Jhe, and Y. Wang, “Laser guiding of atoms in a dark hollow beam,” presented at the Quantum Electronics and Laser Science Conference of the Optical Society of America, Baltimore, Maryland, May 18–23, 1997, paper QWD14.
  24. J. Yin, Y. Wang, and W. Jhe, “Dark hollow laser beams and dark-beam atom optics: generation of dark hollow beams and its applications in atom optics,” presented at the 13th International Conference on Laser Spectroscopy, Hongzhou, China, June 2–7, 1997.

1997 (1)

1996 (9)

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 77, 3331 (1996).
[CrossRef] [PubMed]

C. Paterson and R. Smith, Opt. Commun. 124, 121 (1996).
[CrossRef]

V. Tikhonenko and N. N. Akhmediev, Opt. Commun. 126, 108 (1996).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Phys. Rev. Lett. 77, 4544 (1996).
[CrossRef] [PubMed]

J. J. Hope and C. M. Savage, Phys. Rev. A 53, 3449 (1996).
[CrossRef] [PubMed]

V. I. Balykin, D. V. Laryushin, M. V. Subbotin, and V. S. Letokhov, JETP Lett. 63, 802 (1996).
[CrossRef]

M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, and Z. Anderson, Phys. Rev. A 53, R648 (1996).
[CrossRef]

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. Lee, and W. Jhe, Phys. Rev. Lett. 76, 4500 (1996).
[CrossRef] [PubMed]

K. I. Lee, J. A. Kim, H. R. Noh, and W. Jhe, Opt. Lett. 21, 1177 (1996).
[CrossRef] [PubMed]

1995 (3)

D. J. Harris and C. M. Savage, Phys. Rev. A 51, 3967 (1995).
[CrossRef] [PubMed]

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 75, 3252 (1995).
[CrossRef]

H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, Opt. Commun. 115, 57 (1995).
[CrossRef]

1994 (2)

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, Phys. Rev. A 50, 2680 (1994).
[CrossRef] [PubMed]

H. S. Lee, B. W. Atewart, K. Choi, and H. Fenichel, Phys. Rev. A 49, 4922 (1994).
[CrossRef] [PubMed]

1993 (3)

M. A. Ol’Shanii, Yu. B. Ovchinnikov, and V. S. Letokhov, Opt. Commun. 98, 77 (1993).
[CrossRef]

X. Wang and M. G. Littman, Opt. Lett. 18, 767 (1993).
[CrossRef] [PubMed]

C. I. Sukenik, M. G. Boshier, D. Cho, V. Sandoghdar, and E. A. Hinds, Phys. Rev. Lett. 70, 560 (1993).
[CrossRef] [PubMed]

1991 (1)

1987 (1)

V. I. Balykin and V. S. Letokhov, Opt. Commun. 64, 151 (1987).
[CrossRef]

Akhmediev, N. N.

V. Tikhonenko and N. N. Akhmediev, Opt. Commun. 126, 108 (1996).
[CrossRef]

Anderson, D. Z.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 75, 3252 (1995).
[CrossRef]

Anderson, M. H.

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 77, 3331 (1996).
[CrossRef] [PubMed]

Anderson, Z.

M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, and Z. Anderson, Phys. Rev. A 53, R648 (1996).
[CrossRef]

Atewart, B. W.

H. S. Lee, B. W. Atewart, K. Choi, and H. Fenichel, Phys. Rev. A 49, 4922 (1994).
[CrossRef] [PubMed]

Balykin, V. I.

V. I. Balykin, D. V. Laryushin, M. V. Subbotin, and V. S. Letokhov, JETP Lett. 63, 802 (1996).
[CrossRef]

V. I. Balykin and V. S. Letokhov, Opt. Commun. 64, 151 (1987).
[CrossRef]

Boshier, M. G.

C. I. Sukenik, M. G. Boshier, D. Cho, V. Sandoghdar, and E. A. Hinds, Phys. Rev. Lett. 70, 560 (1993).
[CrossRef] [PubMed]

Cho, D.

C. I. Sukenik, M. G. Boshier, D. Cho, V. Sandoghdar, and E. A. Hinds, Phys. Rev. Lett. 70, 560 (1993).
[CrossRef] [PubMed]

Choi, K.

H. S. Lee, B. W. Atewart, K. Choi, and H. Fenichel, Phys. Rev. A 49, 4922 (1994).
[CrossRef] [PubMed]

Cornell, E. A.

M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, and Z. Anderson, Phys. Rev. A 53, R648 (1996).
[CrossRef]

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 77, 3331 (1996).
[CrossRef] [PubMed]

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 75, 3252 (1995).
[CrossRef]

Corwin, K. L.

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 77, 3331 (1996).
[CrossRef] [PubMed]

Donley, E. A.

M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, and Z. Anderson, Phys. Rev. A 53, R648 (1996).
[CrossRef]

Fenichel, H.

H. S. Lee, B. W. Atewart, K. Choi, and H. Fenichel, Phys. Rev. A 49, 4922 (1994).
[CrossRef] [PubMed]

Gallatin, G. M.

Gould, P. L.

Harris, D. J.

D. J. Harris and C. M. Savage, Phys. Rev. A 51, 3967 (1995).
[CrossRef] [PubMed]

Hinds, E. A.

C. I. Sukenik, M. G. Boshier, D. Cho, V. Sandoghdar, and E. A. Hinds, Phys. Rev. Lett. 70, 560 (1993).
[CrossRef] [PubMed]

Hope, J. J.

J. J. Hope and C. M. Savage, Phys. Rev. A 53, 3449 (1996).
[CrossRef] [PubMed]

Ito, H.

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. Lee, and W. Jhe, Phys. Rev. Lett. 76, 4500 (1996).
[CrossRef] [PubMed]

H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, Opt. Commun. 115, 57 (1995).
[CrossRef]

Jhe, W.

J. A. Kim, K. I. Lee, H. R. Noh, and W. Jhe, Opt. Lett. 22, 117 (1997).
[CrossRef] [PubMed]

K. I. Lee, J. A. Kim, H. R. Noh, and W. Jhe, Opt. Lett. 21, 1177 (1996).
[CrossRef] [PubMed]

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. Lee, and W. Jhe, Phys. Rev. Lett. 76, 4500 (1996).
[CrossRef] [PubMed]

H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, Opt. Commun. 115, 57 (1995).
[CrossRef]

Kim, J. A.

Laryushin, D. V.

V. I. Balykin, D. V. Laryushin, M. V. Subbotin, and V. S. Letokhov, JETP Lett. 63, 802 (1996).
[CrossRef]

Lee, H. S.

H. S. Lee, B. W. Atewart, K. Choi, and H. Fenichel, Phys. Rev. A 49, 4922 (1994).
[CrossRef] [PubMed]

Lee, K.

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. Lee, and W. Jhe, Phys. Rev. Lett. 76, 4500 (1996).
[CrossRef] [PubMed]

Lee, K. I.

Letokhov, V. S.

V. I. Balykin, D. V. Laryushin, M. V. Subbotin, and V. S. Letokhov, JETP Lett. 63, 802 (1996).
[CrossRef]

M. A. Ol’Shanii, Yu. B. Ovchinnikov, and V. S. Letokhov, Opt. Commun. 98, 77 (1993).
[CrossRef]

V. I. Balykin and V. S. Letokhov, Opt. Commun. 64, 151 (1987).
[CrossRef]

Littman, M. G.

Lu, Z. T.

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 77, 3331 (1996).
[CrossRef] [PubMed]

Mamaev, A. V.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Phys. Rev. Lett. 77, 4544 (1996).
[CrossRef] [PubMed]

Marksteiner, S.

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, Phys. Rev. A 50, 2680 (1994).
[CrossRef] [PubMed]

Montgomery, D.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 75, 3252 (1995).
[CrossRef]

Nakata, T.

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. Lee, and W. Jhe, Phys. Rev. Lett. 76, 4500 (1996).
[CrossRef] [PubMed]

H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, Opt. Commun. 115, 57 (1995).
[CrossRef]

Noh, H. R.

Ohtsu, M.

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. Lee, and W. Jhe, Phys. Rev. Lett. 76, 4500 (1996).
[CrossRef] [PubMed]

H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, Opt. Commun. 115, 57 (1995).
[CrossRef]

Ol’Shanii, M. A.

M. A. Ol’Shanii, Yu. B. Ovchinnikov, and V. S. Letokhov, Opt. Commun. 98, 77 (1993).
[CrossRef]

Ovchinnikov, Yu. B.

M. A. Ol’Shanii, Yu. B. Ovchinnikov, and V. S. Letokhov, Opt. Commun. 98, 77 (1993).
[CrossRef]

Paterson, C.

C. Paterson and R. Smith, Opt. Commun. 124, 121 (1996).
[CrossRef]

Renn, M. J.

M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, and Z. Anderson, Phys. Rev. A 53, R648 (1996).
[CrossRef]

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 77, 3331 (1996).
[CrossRef] [PubMed]

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 75, 3252 (1995).
[CrossRef]

Rolston, S. L.

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, Phys. Rev. A 50, 2680 (1994).
[CrossRef] [PubMed]

Saffman, M.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Phys. Rev. Lett. 77, 4544 (1996).
[CrossRef] [PubMed]

Sakaki, K.

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. Lee, and W. Jhe, Phys. Rev. Lett. 76, 4500 (1996).
[CrossRef] [PubMed]

H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, Opt. Commun. 115, 57 (1995).
[CrossRef]

Sandoghdar, V.

C. I. Sukenik, M. G. Boshier, D. Cho, V. Sandoghdar, and E. A. Hinds, Phys. Rev. Lett. 70, 560 (1993).
[CrossRef] [PubMed]

Savage, C. M.

J. J. Hope and C. M. Savage, Phys. Rev. A 53, 3449 (1996).
[CrossRef] [PubMed]

D. J. Harris and C. M. Savage, Phys. Rev. A 51, 3967 (1995).
[CrossRef] [PubMed]

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, Phys. Rev. A 50, 2680 (1994).
[CrossRef] [PubMed]

Smith, R.

C. Paterson and R. Smith, Opt. Commun. 124, 121 (1996).
[CrossRef]

Subbotin, M. V.

V. I. Balykin, D. V. Laryushin, M. V. Subbotin, and V. S. Letokhov, JETP Lett. 63, 802 (1996).
[CrossRef]

Sukenik, C. I.

C. I. Sukenik, M. G. Boshier, D. Cho, V. Sandoghdar, and E. A. Hinds, Phys. Rev. Lett. 70, 560 (1993).
[CrossRef] [PubMed]

Tikhonenko, V.

V. Tikhonenko and N. N. Akhmediev, Opt. Commun. 126, 108 (1996).
[CrossRef]

Vdovin, O.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 75, 3252 (1995).
[CrossRef]

Wang, X.

Wieman, C. E.

M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, and Z. Anderson, Phys. Rev. A 53, R648 (1996).
[CrossRef]

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 77, 3331 (1996).
[CrossRef] [PubMed]

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 75, 3252 (1995).
[CrossRef]

Zoller, P.

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, Phys. Rev. A 50, 2680 (1994).
[CrossRef] [PubMed]

Zozulya, A. A.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Phys. Rev. Lett. 77, 4544 (1996).
[CrossRef] [PubMed]

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

JETP Lett. (1)

V. I. Balykin, D. V. Laryushin, M. V. Subbotin, and V. S. Letokhov, JETP Lett. 63, 802 (1996).
[CrossRef]

Opt. Commun. (5)

H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, Opt. Commun. 115, 57 (1995).
[CrossRef]

C. Paterson and R. Smith, Opt. Commun. 124, 121 (1996).
[CrossRef]

V. Tikhonenko and N. N. Akhmediev, Opt. Commun. 126, 108 (1996).
[CrossRef]

M. A. Ol’Shanii, Yu. B. Ovchinnikov, and V. S. Letokhov, Opt. Commun. 98, 77 (1993).
[CrossRef]

V. I. Balykin and V. S. Letokhov, Opt. Commun. 64, 151 (1987).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (5)

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, Phys. Rev. A 50, 2680 (1994).
[CrossRef] [PubMed]

H. S. Lee, B. W. Atewart, K. Choi, and H. Fenichel, Phys. Rev. A 49, 4922 (1994).
[CrossRef] [PubMed]

M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, and Z. Anderson, Phys. Rev. A 53, R648 (1996).
[CrossRef]

D. J. Harris and C. M. Savage, Phys. Rev. A 51, 3967 (1995).
[CrossRef] [PubMed]

J. J. Hope and C. M. Savage, Phys. Rev. A 53, 3449 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. Lee, and W. Jhe, Phys. Rev. Lett. 76, 4500 (1996).
[CrossRef] [PubMed]

C. I. Sukenik, M. G. Boshier, D. Cho, V. Sandoghdar, and E. A. Hinds, Phys. Rev. Lett. 70, 560 (1993).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Phys. Rev. Lett. 77, 4544 (1996).
[CrossRef] [PubMed]

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 75, 3252 (1995).
[CrossRef]

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 77, 3331 (1996).
[CrossRef] [PubMed]

Other (4)

J. Yin, H. Noh, K. Lee, J. Kim, W. Jhe, and Y. Wang, “Laser guiding of atoms in a dark hollow beam,” presented at the Quantum Electronics and Laser Science Conference of the Optical Society of America, Baltimore, Maryland, May 18–23, 1997, paper QWD14.

J. Yin, Y. Wang, and W. Jhe, “Dark hollow laser beams and dark-beam atom optics: generation of dark hollow beams and its applications in atom optics,” presented at the 13th International Conference on Laser Spectroscopy, Hongzhou, China, June 2–7, 1997.

H. Ito, K. Sakaki, M. Ohtsu, and W. Jhe, “Measurement of cavity QED energy shifts on atom guidance using evanescent light,” Phys. Rev. A (to be published).

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).

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 (12)

Fig. 1
Fig. 1

Intensity distribution I(r) for the LP01 mode in a HOF versus radial distance r. The radius of the hollow region and the core are a=3.5 μm and b=7.3 μm, respectively.

Fig. 2
Fig. 2

Total potential in the hollow fiber, consisting of the repulsive optical potential and the attractive potential owing to the cavity QED effect, versus the radial distance r. The input laser power P0=100 mW.

Fig. 3
Fig. 3

Intensity distribution I(r) for the output beam in free space from the LP01 mode in the HOF versus radial distance r at z1=50 mm.

Fig. 4
Fig. 4

Schematic drawing of the experimental setup used to generate a dark hollow-divergent laser beam with the microcollimation technique for the output beam of the LP01 mode in the hollow fiber. L, HOF, OBJ, and VA stand for a lens, hollow optical fiber, objective lens, and variable aperture, respectively.

Fig. 5
Fig. 5

Measured radial intensity distribution of the DHB at (a) z=400 mm and (b) z=1000 mm. Each horizontal block represents 370 μm.

Fig. 6
Fig. 6

Square of the beam radius of the DHB, r02, versus the propagation distance z. The black squares are the experimental data, and the solid curve is the theoretical calculation.

Fig. 7
Fig. 7

Beam waist ω(Z) of a doughnut laser beam and that of the DHB from the LP01 mode versus the propagation distance Z. The parameters are ω0=81 μm, ZR=26.44 mm, and λ =0.78 μm.

Fig. 8
Fig. 8

Radial distribution of the optical potential in the DHB at z=100 mm. The laser power P0=100 mW.

Fig. 9
Fig. 9

Optical potential of the DHB versus the laser–atom detuning Δ with (a) different laser powers P0 and the propagation distance z=100 mm and (b) different propagation distance z and the laser power P0=100 mW.

Fig. 10
Fig. 10

Optical potential of the DHB versus the laser power P0 with (a) Δ=0.10 GHz and at different distances z and (b) at z =100 mm and with different detunings Δ.

Fig. 11
Fig. 11

Maximum optical potential of the DHB at the optimal detuning ΔOpt versus (a) the laser power P0 and (b) the propagation distance z.

Fig. 12
Fig. 12

Optical potential of the DHB versus the propagation distance z with (a) P0=100 mW and different detunings Δ and (b) Δ=0.10 GHz and different powers P0.

Equations (17)

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

n0<n2<n1.
Eholl(r)=AI1(vr),r<a,
Ecore(r)=BJ1(ur)+CY1(ur),arb,
Eclad(r)=DK1(wr),b<r,
UEW(r)=hΔ4π ln1+I(r)/I01+4(Δ/Γ)2,
Ucp(r)=-e π|deg|224ε0a3 0 dρ ρ2 cosh(2πρr/a)sinh(πρ)×arctanρλeg4a n12-1n12+1 ηGeo,
UTP(r)=UEW(r)+UCP(r).
E(r1, θ1, z1)=c0aAI1(vr)rJ1(2πrρ)dr+ab[BJ1(ur)+CY1(ur)]rJ1(2πrρ)dr+bDK1(wr)rJ1(2πrρ)dr,
c=2πiλz1 expiz1+r22z1+θ1-π2,ρ=r1λz1.
r0(z1)=0.02685z1.
I(r, Z)=4I0ω0ω(Z)2 2r2ω2(Z) exp-2r2ω2(Z),
ω2(Z)=ω02(1+kZ2/ZR2).
I(r0, Z)=Imax(Z)=2P0eπω2(Z).
r2=r02(Z)=ω2(Z)2=ω022 1+kZ2(πω02/λ)2.
UOP(r)=2 Δln1+I(r)/I04(Δ/Γ)2.
Δopt(Z, P0)Γ4 I(Z, P0)I0=Γ2 12eI0 P0πω2(Z)P0ω(Z).
Umax(Z, P0)Γ ln 58 I(Z, P0)I0=Γ ln 54 12eI0 P0πω2(Z)P0ω(Z).

Metrics