Abstract

A new mathematical model called hollow elliptical Gaussian beam (HEGB) is proposed to describe a dark-hollow laser beam with noncircular symmetry in terms of a tensor method. The HEGB can be expressed as a superposition of a series of elliptical Hermite–Gaussian modes. By using the generalized diffraction integral formulas for light passing through paraxial optical systems, analytical propagation formulas for HEGBs passing through paraxial aligned and misaligned optical systems are obtained through vector integration. As examples of applications, evolution properties of the intensity distribution of HEGBs in free-space propagation were studied. Propagation properties of HEGBs through a misaligned thin lens were also studied. The HEGB provides a convenient way to describe elliptical dark-hollow laser beams and can be used conveniently to study the motion of atoms in a dark-hollow laser beam.

© 2004 Optical Society of America

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2003

2002

Y. Cai, Q. Lin, “The elliptical Hermite–Gaussian beam and its propagation through paraxial systems,” Opt. Commun. 207, 139–147 (2002).
[CrossRef]

K. Zhu, H. Tang, X. Sun, X. Wang, T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002).
[CrossRef]

K. Zhu, H. Tang, X. Wang, T. Liu, “Flattened light beams with an axial shadow generated through superposing cosh-Gaussian beams,” Optik 113, 222–226 (2002).
[CrossRef]

J. Yin, W. Gao, H. Wang, Q. Long, Y. Wang, “Generations of dark hollow beams and their applications in laser cooling of atoms and all-optical-type Bose–Einstein condensation,” Chin. Phys. 11, 1157–1169 (2002).
[CrossRef]

2001

2000

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

1999

X. Y. Xu, V. G. Minogin, K. Lee, Y. Z. Wang, W. Jhe, “Guiding cold atoms in a hollow laser beam,” Phys. Rev. A 60, 4796–4804 (1999).
[CrossRef]

1998

O. Morsch, D. R. Meacher, “Proposal for an optical funnel trap,” Opt. Commun. 148, 49–53 (1998).
[CrossRef]

J. Yin, Y. Zhu, W. Jhe, Y. Wang, “Atom guiding and cooling in a dark hollow laser beam,” Phys. Rev. A 58, 509–513 (1998).
[CrossRef]

J. Yin, Y. Zhu, W. Wang, Y. Wang, W. Jhe, “Optical potential for atom guidance in a dark hollow laser beam,” J. Opt. Soc. Am. B 15, 25–33 (1998).
[CrossRef]

S. Kuppens, M. Rauner, M. Schiffer, K. Sengstock, W. Ertmer, “Polarization-gradient cooling in a strong doughnut-mode dipole potential,” Phys. Rev. A 58, 3068–3079 (1998).
[CrossRef]

1997

H. Ito, K. Sakaki, W. Jhe, M. Ohtsu, “Evanescent-light induced atom-guidance using a hollow optical fiber with light coupled sideways,” Opt. Commun. 141, 43–47 (1997).
[CrossRef]

M. J. Renn, A. Z. Zozulya, E. A. Donley, E. A. Cornell, D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3697 (1997).
[CrossRef]

H. Ito, K. Sakaki, M. Ohtsu, W. Jhe, “Evanescent-light guiding of atoms through hollow optical fiber for optically controlled atomic deposition,” Appl. Phys. Lett. 70, 2496–2498 (1997).
[CrossRef]

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]

Yu. B. Ovchinnikov, I. Manek, R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[CrossRef]

J. Yin, H. Noh, K. Lee, K. Kim, Y. Wang, W. Jhe, “Generation of a dark hollow beam by a small hollow fiber,” Opt. Commun. 138, 287–292 (1997).
[CrossRef]

1996

M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, D. Z. Anderson, “Evanescent-wave guiding of atoms in hollow optical fibers,” Phys. Rev. A 53, R648–R651 (1996).
[CrossRef] [PubMed]

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. I. Lee, W. Jhe, “Laser spectroscopy of atoms guiding by evanescent waves in micro-sized hollow optical fibers,” Phys. Rev. Lett. 76, 4500–4503 (1996).
[CrossRef] [PubMed]

C. Paterson, R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[CrossRef]

V. Tikhonenko, N. N. Akhmediev, “Excitation of vortex solitons in a Gaussian beam configuration,” Opt. Commun. 126, 108–112 (1996).
[CrossRef]

1995

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253–3256 (1995).
[CrossRef] [PubMed]

1994

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

W. Jhe, M. Ohtsu, H. Hori, S. R. Friberg, “Atomic waveguide using evanescent waves near optical fibers,” Jpn. J. Appl. Phys. 33, L1680–L1682 (1994).
[CrossRef]

F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
[CrossRef]

1993

1991

J. Alda, S. Wang, E. Bernabeu, “Analytical expression for the complex radius of curvature tensor Q for generalized Gaussian beams,” Opt. Commun. 80, 350–352 (1991).
[CrossRef]

R. M. Herman, T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. A 8, 932–942 (1991).
[CrossRef]

1987

V. I. Balykin, V. S. Letokhov, “The possibility of deep laser focusing of an atomic beam into the AA-region,” Opt. Commun. 64, 151–156 (1987).
[CrossRef]

Akhmediev, N. N.

V. Tikhonenko, N. N. Akhmediev, “Excitation of vortex solitons in a Gaussian beam configuration,” Opt. Commun. 126, 108–112 (1996).
[CrossRef]

Alda, J.

J. Alda, S. Wang, E. Bernabeu, “Analytical expression for the complex radius of curvature tensor Q for generalized Gaussian beams,” Opt. Commun. 80, 350–352 (1991).
[CrossRef]

Anderson, D. Z.

M. J. Renn, A. Z. Zozulya, E. A. Donley, E. A. Cornell, D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3697 (1997).
[CrossRef]

M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, D. Z. Anderson, “Evanescent-wave guiding of atoms in hollow optical fibers,” Phys. Rev. A 53, R648–R651 (1996).
[CrossRef] [PubMed]

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253–3256 (1995).
[CrossRef] [PubMed]

Arlt, J.

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

Balykin, V. I.

V. I. Balykin, V. S. Letokhov, “The possibility of deep laser focusing of an atomic beam into the AA-region,” Opt. Commun. 64, 151–156 (1987).
[CrossRef]

Bernabeu, E.

J. Alda, S. Wang, E. Bernabeu, “Analytical expression for the complex radius of curvature tensor Q for generalized Gaussian beams,” Opt. Commun. 80, 350–352 (1991).
[CrossRef]

Cai, Y.

Y. Cai, X. Lu, Q. Lin, “Hollow Gaussian beam and its propagation,” Opt. Lett. 28, 1084–1086 (2003).
[CrossRef] [PubMed]

Y. Cai, Q. Lin, “The elliptical Hermite–Gaussian beam and its propagation through paraxial systems,” Opt. Commun. 207, 139–147 (2002).
[CrossRef]

Cornell, E. A.

M. J. Renn, A. Z. Zozulya, E. A. Donley, E. A. Cornell, D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3697 (1997).
[CrossRef]

M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, D. Z. Anderson, “Evanescent-wave guiding of atoms in hollow optical fibers,” Phys. Rev. A 53, R648–R651 (1996).
[CrossRef] [PubMed]

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253–3256 (1995).
[CrossRef] [PubMed]

Dholakia, K.

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

Donley, E. A.

M. J. Renn, A. Z. Zozulya, E. A. Donley, E. A. Cornell, D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3697 (1997).
[CrossRef]

M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, D. Z. Anderson, “Evanescent-wave guiding of atoms in hollow optical fibers,” Phys. Rev. A 53, R648–R651 (1996).
[CrossRef] [PubMed]

Ertmer, W.

S. Kuppens, M. Rauner, M. Schiffer, K. Sengstock, W. Ertmer, “Polarization-gradient cooling in a strong doughnut-mode dipole potential,” Phys. Rev. A 58, 3068–3079 (1998).
[CrossRef]

Friberg, S. R.

W. Jhe, M. Ohtsu, H. Hori, S. R. Friberg, “Atomic waveguide using evanescent waves near optical fibers,” Jpn. J. Appl. Phys. 33, L1680–L1682 (1994).
[CrossRef]

Gao, W.

J. Yin, W. Gao, H. Wang, Q. Long, Y. Wang, “Generations of dark hollow beams and their applications in laser cooling of atoms and all-optical-type Bose–Einstein condensation,” Chin. Phys. 11, 1157–1169 (2002).
[CrossRef]

Gori, F.

F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
[CrossRef]

Grimm, R.

Yu. B. Ovchinnikov, I. Manek, R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[CrossRef]

Herman, R. M.

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]

Hori, H.

W. Jhe, M. Ohtsu, H. Hori, S. R. Friberg, “Atomic waveguide using evanescent waves near optical fibers,” Jpn. J. Appl. Phys. 33, L1680–L1682 (1994).
[CrossRef]

Ito, H.

H. Ito, K. Sakaki, M. Ohtsu, W. Jhe, “Evanescent-light guiding of atoms through hollow optical fiber for optically controlled atomic deposition,” Appl. Phys. Lett. 70, 2496–2498 (1997).
[CrossRef]

H. Ito, K. Sakaki, W. Jhe, M. Ohtsu, “Evanescent-light induced atom-guidance using a hollow optical fiber with light coupled sideways,” Opt. Commun. 141, 43–47 (1997).
[CrossRef]

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. I. Lee, W. Jhe, “Laser spectroscopy of atoms guiding by evanescent waves in micro-sized hollow optical fibers,” Phys. Rev. Lett. 76, 4500–4503 (1996).
[CrossRef] [PubMed]

Jhe, W.

X. Y. Xu, V. G. Minogin, K. Lee, Y. Z. Wang, W. Jhe, “Guiding cold atoms in a hollow laser beam,” Phys. Rev. A 60, 4796–4804 (1999).
[CrossRef]

J. Yin, Y. Zhu, W. Wang, Y. Wang, W. Jhe, “Optical potential for atom guidance in a dark hollow laser beam,” J. Opt. Soc. Am. B 15, 25–33 (1998).
[CrossRef]

J. Yin, Y. Zhu, W. Jhe, Y. Wang, “Atom guiding and cooling in a dark hollow laser beam,” Phys. Rev. A 58, 509–513 (1998).
[CrossRef]

H. Ito, K. Sakaki, W. Jhe, M. Ohtsu, “Evanescent-light induced atom-guidance using a hollow optical fiber with light coupled sideways,” Opt. Commun. 141, 43–47 (1997).
[CrossRef]

J. Yin, H. Noh, K. Lee, K. Kim, Y. Wang, W. Jhe, “Generation of a dark hollow beam by a small hollow fiber,” Opt. Commun. 138, 287–292 (1997).
[CrossRef]

H. Ito, K. Sakaki, M. Ohtsu, W. Jhe, “Evanescent-light guiding of atoms through hollow optical fiber for optically controlled atomic deposition,” Appl. Phys. Lett. 70, 2496–2498 (1997).
[CrossRef]

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. I. Lee, W. Jhe, “Laser spectroscopy of atoms guiding by evanescent waves in micro-sized hollow optical fibers,” Phys. Rev. Lett. 76, 4500–4503 (1996).
[CrossRef] [PubMed]

W. Jhe, M. Ohtsu, H. Hori, S. R. Friberg, “Atomic waveguide using evanescent waves near optical fibers,” Jpn. J. Appl. Phys. 33, L1680–L1682 (1994).
[CrossRef]

Kim, K.

J. Yin, H. Noh, K. Lee, K. Kim, Y. Wang, W. Jhe, “Generation of a dark hollow beam by a small hollow fiber,” Opt. Commun. 138, 287–292 (1997).
[CrossRef]

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]

Kuppens, S.

S. Kuppens, M. Rauner, M. Schiffer, K. Sengstock, W. Ertmer, “Polarization-gradient cooling in a strong doughnut-mode dipole potential,” Phys. Rev. A 58, 3068–3079 (1998).
[CrossRef]

Lee, K.

X. Y. Xu, V. G. Minogin, K. Lee, Y. Z. Wang, W. Jhe, “Guiding cold atoms in a hollow laser beam,” Phys. Rev. A 60, 4796–4804 (1999).
[CrossRef]

J. Yin, H. Noh, K. Lee, K. Kim, Y. Wang, W. Jhe, “Generation of a dark hollow beam by a small hollow fiber,” Opt. Commun. 138, 287–292 (1997).
[CrossRef]

Lee, K. I.

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. I. Lee, W. Jhe, “Laser spectroscopy of atoms guiding by evanescent waves in micro-sized hollow optical fibers,” Phys. Rev. Lett. 76, 4500–4503 (1996).
[CrossRef] [PubMed]

Letokhov, V. S.

V. I. Balykin, V. S. Letokhov, “The possibility of deep laser focusing of an atomic beam into the AA-region,” Opt. Commun. 64, 151–156 (1987).
[CrossRef]

Lin, Q.

Y. Cai, X. Lu, Q. Lin, “Hollow Gaussian beam and its propagation,” Opt. Lett. 28, 1084–1086 (2003).
[CrossRef] [PubMed]

Y. Cai, Q. Lin, “The elliptical Hermite–Gaussian beam and its propagation through paraxial systems,” Opt. Commun. 207, 139–147 (2002).
[CrossRef]

Littman, M. G.

Liu, T.

K. Zhu, H. Tang, X. Wang, T. Liu, “Flattened light beams with an axial shadow generated through superposing cosh-Gaussian beams,” Optik 113, 222–226 (2002).
[CrossRef]

K. Zhu, H. Tang, X. Sun, X. Wang, T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002).
[CrossRef]

Long, Q.

J. Yin, W. Gao, H. Wang, Q. Long, Y. Wang, “Generations of dark hollow beams and their applications in laser cooling of atoms and all-optical-type Bose–Einstein condensation,” Chin. Phys. 11, 1157–1169 (2002).
[CrossRef]

Lu, X.

Manek, I.

Yu. B. Ovchinnikov, I. Manek, R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[CrossRef]

Marksteiner, S.

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

Meacher, D. R.

O. Morsch, D. R. Meacher, “Proposal for an optical funnel trap,” Opt. Commun. 148, 49–53 (1998).
[CrossRef]

Minogin, V. G.

X. Y. Xu, V. G. Minogin, K. Lee, Y. Z. Wang, W. Jhe, “Guiding cold atoms in a hollow laser beam,” Phys. Rev. A 60, 4796–4804 (1999).
[CrossRef]

Montgomery, D.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253–3256 (1995).
[CrossRef] [PubMed]

Morsch, O.

O. Morsch, D. R. Meacher, “Proposal for an optical funnel trap,” Opt. Commun. 148, 49–53 (1998).
[CrossRef]

Nakata, T.

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. I. Lee, W. Jhe, “Laser spectroscopy of atoms guiding by evanescent waves in micro-sized hollow optical fibers,” Phys. Rev. Lett. 76, 4500–4503 (1996).
[CrossRef] [PubMed]

Noh, H.

J. Yin, H. Noh, K. Lee, K. Kim, Y. Wang, W. Jhe, “Generation of a dark hollow beam by a small hollow fiber,” Opt. Commun. 138, 287–292 (1997).
[CrossRef]

Ohtsu, M.

H. Ito, K. Sakaki, W. Jhe, M. Ohtsu, “Evanescent-light induced atom-guidance using a hollow optical fiber with light coupled sideways,” Opt. Commun. 141, 43–47 (1997).
[CrossRef]

H. Ito, K. Sakaki, M. Ohtsu, W. Jhe, “Evanescent-light guiding of atoms through hollow optical fiber for optically controlled atomic deposition,” Appl. Phys. Lett. 70, 2496–2498 (1997).
[CrossRef]

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. I. Lee, W. Jhe, “Laser spectroscopy of atoms guiding by evanescent waves in micro-sized hollow optical fibers,” Phys. Rev. Lett. 76, 4500–4503 (1996).
[CrossRef] [PubMed]

W. Jhe, M. Ohtsu, H. Hori, S. R. Friberg, “Atomic waveguide using evanescent waves near optical fibers,” Jpn. J. Appl. Phys. 33, L1680–L1682 (1994).
[CrossRef]

Ovchinnikov, Yu. B.

Yu. B. Ovchinnikov, I. Manek, R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[CrossRef]

Paterson, C.

C. Paterson, R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[CrossRef]

Rauner, M.

S. Kuppens, M. Rauner, M. Schiffer, K. Sengstock, W. Ertmer, “Polarization-gradient cooling in a strong doughnut-mode dipole potential,” Phys. Rev. A 58, 3068–3079 (1998).
[CrossRef]

Renn, M. J.

M. J. Renn, A. Z. Zozulya, E. A. Donley, E. A. Cornell, D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3697 (1997).
[CrossRef]

M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, D. Z. Anderson, “Evanescent-wave guiding of atoms in hollow optical fibers,” Phys. Rev. A 53, R648–R651 (1996).
[CrossRef] [PubMed]

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253–3256 (1995).
[CrossRef] [PubMed]

Rolston, S.

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

Ronchi, L.

S. Wang, L. Ronchi, “Principles and design of optical arrays,” in Progress in Optics, Vol. XXV, E. Wolf, ed. (Elsevier Science, Amsterdam, 1988), p. 279.

Sakaki, K.

H. Ito, K. Sakaki, M. Ohtsu, W. Jhe, “Evanescent-light guiding of atoms through hollow optical fiber for optically controlled atomic deposition,” Appl. Phys. Lett. 70, 2496–2498 (1997).
[CrossRef]

H. Ito, K. Sakaki, W. Jhe, M. Ohtsu, “Evanescent-light induced atom-guidance using a hollow optical fiber with light coupled sideways,” Opt. Commun. 141, 43–47 (1997).
[CrossRef]

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. I. Lee, W. Jhe, “Laser spectroscopy of atoms guiding by evanescent waves in micro-sized hollow optical fibers,” Phys. Rev. Lett. 76, 4500–4503 (1996).
[CrossRef] [PubMed]

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]

Savage, C. M.

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

Schiffer, M.

S. Kuppens, M. Rauner, M. Schiffer, K. Sengstock, W. Ertmer, “Polarization-gradient cooling in a strong doughnut-mode dipole potential,” Phys. Rev. A 58, 3068–3079 (1998).
[CrossRef]

Sengstock, K.

S. Kuppens, M. Rauner, M. Schiffer, K. Sengstock, W. Ertmer, “Polarization-gradient cooling in a strong doughnut-mode dipole potential,” Phys. Rev. A 58, 3068–3079 (1998).
[CrossRef]

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]

Smith, R.

C. Paterson, R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[CrossRef]

Sun, X.

K. Zhu, H. Tang, X. Sun, X. Wang, T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002).
[CrossRef]

Tang, H.

K. Zhu, H. Tang, X. Sun, X. Wang, T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002).
[CrossRef]

K. Zhu, H. Tang, X. Wang, T. Liu, “Flattened light beams with an axial shadow generated through superposing cosh-Gaussian beams,” Optik 113, 222–226 (2002).
[CrossRef]

Tikhonenko, V.

V. Tikhonenko, N. N. Akhmediev, “Excitation of vortex solitons in a Gaussian beam configuration,” Opt. Commun. 126, 108–112 (1996).
[CrossRef]

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]

Tovar, A. A.

Vdovin, O.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253–3256 (1995).
[CrossRef] [PubMed]

Wang, H.

J. Yin, W. Gao, H. Wang, Q. Long, Y. Wang, “Generations of dark hollow beams and their applications in laser cooling of atoms and all-optical-type Bose–Einstein condensation,” Chin. Phys. 11, 1157–1169 (2002).
[CrossRef]

Wang, S.

J. Alda, S. Wang, E. Bernabeu, “Analytical expression for the complex radius of curvature tensor Q for generalized Gaussian beams,” Opt. Commun. 80, 350–352 (1991).
[CrossRef]

S. Wang, L. Ronchi, “Principles and design of optical arrays,” in Progress in Optics, Vol. XXV, E. Wolf, ed. (Elsevier Science, Amsterdam, 1988), p. 279.

Wang, W.

Wang, X.

K. Zhu, H. Tang, X. Sun, X. Wang, T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002).
[CrossRef]

K. Zhu, H. Tang, X. Wang, T. Liu, “Flattened light beams with an axial shadow generated through superposing cosh-Gaussian beams,” Optik 113, 222–226 (2002).
[CrossRef]

X. Wang, M. G. Littman, “Laser cavity for generation of variable-radius rings of light,” Opt. Lett. 18, 767–770 (1993).
[CrossRef] [PubMed]

Wang, Y.

J. Yin, W. Gao, H. Wang, Q. Long, Y. Wang, “Generations of dark hollow beams and their applications in laser cooling of atoms and all-optical-type Bose–Einstein condensation,” Chin. Phys. 11, 1157–1169 (2002).
[CrossRef]

J. Yin, Y. Zhu, W. Wang, Y. Wang, W. Jhe, “Optical potential for atom guidance in a dark hollow laser beam,” J. Opt. Soc. Am. B 15, 25–33 (1998).
[CrossRef]

J. Yin, Y. Zhu, W. Jhe, Y. Wang, “Atom guiding and cooling in a dark hollow laser beam,” Phys. Rev. A 58, 509–513 (1998).
[CrossRef]

J. Yin, H. Noh, K. Lee, K. Kim, Y. Wang, W. Jhe, “Generation of a dark hollow beam by a small hollow fiber,” Opt. Commun. 138, 287–292 (1997).
[CrossRef]

Wang, Y. Z.

X. Y. Xu, V. G. Minogin, K. Lee, Y. Z. Wang, W. Jhe, “Guiding cold atoms in a hollow laser beam,” Phys. Rev. A 60, 4796–4804 (1999).
[CrossRef]

Wieman, C. E.

M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, D. Z. Anderson, “Evanescent-wave guiding of atoms in hollow optical fibers,” Phys. Rev. A 53, R648–R651 (1996).
[CrossRef] [PubMed]

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253–3256 (1995).
[CrossRef] [PubMed]

Wiggins, T. A.

Xu, X. Y.

X. Y. Xu, V. G. Minogin, K. Lee, Y. Z. Wang, W. Jhe, “Guiding cold atoms in a hollow laser beam,” Phys. Rev. A 60, 4796–4804 (1999).
[CrossRef]

Yin, J.

J. Yin, W. Gao, H. Wang, Q. Long, Y. Wang, “Generations of dark hollow beams and their applications in laser cooling of atoms and all-optical-type Bose–Einstein condensation,” Chin. Phys. 11, 1157–1169 (2002).
[CrossRef]

J. Yin, Y. Zhu, W. Wang, Y. Wang, W. Jhe, “Optical potential for atom guidance in a dark hollow laser beam,” J. Opt. Soc. Am. B 15, 25–33 (1998).
[CrossRef]

J. Yin, Y. Zhu, W. Jhe, Y. Wang, “Atom guiding and cooling in a dark hollow laser beam,” Phys. Rev. A 58, 509–513 (1998).
[CrossRef]

J. Yin, H. Noh, K. Lee, K. Kim, Y. Wang, W. Jhe, “Generation of a dark hollow beam by a small hollow fiber,” Opt. Commun. 138, 287–292 (1997).
[CrossRef]

Zhu, K.

K. Zhu, H. Tang, X. Wang, T. Liu, “Flattened light beams with an axial shadow generated through superposing cosh-Gaussian beams,” Optik 113, 222–226 (2002).
[CrossRef]

K. Zhu, H. Tang, X. Sun, X. Wang, T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002).
[CrossRef]

Zhu, Y.

J. Yin, Y. Zhu, W. Wang, Y. Wang, W. Jhe, “Optical potential for atom guidance in a dark hollow laser beam,” J. Opt. Soc. Am. B 15, 25–33 (1998).
[CrossRef]

J. Yin, Y. Zhu, W. Jhe, Y. Wang, “Atom guiding and cooling in a dark hollow laser beam,” Phys. Rev. A 58, 509–513 (1998).
[CrossRef]

Zoller, P.

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

Zozulya, A. Z.

M. J. Renn, A. Z. Zozulya, E. A. Donley, E. A. Cornell, D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3697 (1997).
[CrossRef]

Appl. Phys. Lett.

H. Ito, K. Sakaki, M. Ohtsu, W. Jhe, “Evanescent-light guiding of atoms through hollow optical fiber for optically controlled atomic deposition,” Appl. Phys. Lett. 70, 2496–2498 (1997).
[CrossRef]

Chin. Phys.

J. Yin, W. Gao, H. Wang, Q. Long, Y. Wang, “Generations of dark hollow beams and their applications in laser cooling of atoms and all-optical-type Bose–Einstein condensation,” Chin. Phys. 11, 1157–1169 (2002).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

W. Jhe, M. Ohtsu, H. Hori, S. R. Friberg, “Atomic waveguide using evanescent waves near optical fibers,” Jpn. J. Appl. Phys. 33, L1680–L1682 (1994).
[CrossRef]

Opt. Commun.

H. Ito, K. Sakaki, W. Jhe, M. Ohtsu, “Evanescent-light induced atom-guidance using a hollow optical fiber with light coupled sideways,” Opt. Commun. 141, 43–47 (1997).
[CrossRef]

J. Yin, H. Noh, K. Lee, K. Kim, Y. Wang, W. Jhe, “Generation of a dark hollow beam by a small hollow fiber,” Opt. Commun. 138, 287–292 (1997).
[CrossRef]

O. Morsch, D. R. Meacher, “Proposal for an optical funnel trap,” Opt. Commun. 148, 49–53 (1998).
[CrossRef]

C. Paterson, R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[CrossRef]

V. Tikhonenko, N. N. Akhmediev, “Excitation of vortex solitons in a Gaussian beam configuration,” Opt. Commun. 126, 108–112 (1996).
[CrossRef]

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

V. I. Balykin, V. S. Letokhov, “The possibility of deep laser focusing of an atomic beam into the AA-region,” Opt. Commun. 64, 151–156 (1987).
[CrossRef]

K. Zhu, H. Tang, X. Sun, X. Wang, T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002).
[CrossRef]

F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
[CrossRef]

J. Alda, S. Wang, E. Bernabeu, “Analytical expression for the complex radius of curvature tensor Q for generalized Gaussian beams,” Opt. Commun. 80, 350–352 (1991).
[CrossRef]

Y. Cai, Q. Lin, “The elliptical Hermite–Gaussian beam and its propagation through paraxial systems,” Opt. Commun. 207, 139–147 (2002).
[CrossRef]

Opt. Lett.

Optik

K. Zhu, H. Tang, X. Wang, T. Liu, “Flattened light beams with an axial shadow generated through superposing cosh-Gaussian beams,” Optik 113, 222–226 (2002).
[CrossRef]

Phys. Rev. A

J. Yin, Y. Zhu, W. Jhe, Y. Wang, “Atom guiding and cooling in a dark hollow laser beam,” Phys. Rev. A 58, 509–513 (1998).
[CrossRef]

S. Kuppens, M. Rauner, M. Schiffer, K. Sengstock, W. Ertmer, “Polarization-gradient cooling in a strong doughnut-mode dipole potential,” Phys. Rev. A 58, 3068–3079 (1998).
[CrossRef]

X. Y. Xu, V. G. Minogin, K. Lee, Y. Z. Wang, W. Jhe, “Guiding cold atoms in a hollow laser beam,” Phys. Rev. A 60, 4796–4804 (1999).
[CrossRef]

M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, D. Z. Anderson, “Evanescent-wave guiding of atoms in hollow optical fibers,” Phys. Rev. A 53, R648–R651 (1996).
[CrossRef] [PubMed]

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

M. J. Renn, A. Z. Zozulya, E. A. Donley, E. A. Cornell, D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3697 (1997).
[CrossRef]

Phys. Rev. Lett.

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]

Yu. B. Ovchinnikov, I. Manek, R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[CrossRef]

H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. I. Lee, W. Jhe, “Laser spectroscopy of atoms guiding by evanescent waves in micro-sized hollow optical fibers,” Phys. Rev. Lett. 76, 4500–4503 (1996).
[CrossRef] [PubMed]

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253–3256 (1995).
[CrossRef] [PubMed]

Other

S. Wang, L. Ronchi, “Principles and design of optical arrays,” in Progress in Optics, Vol. XXV, E. Wolf, ed. (Elsevier Science, Amsterdam, 1988), p. 279.

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Figures (5)

Fig. 1
Fig. 1

3D normalized intensity distribution and corresponding contour graph of HEGB for various n values at z=0. (a) n=5, (b) n=15.

Fig. 2
Fig. 2

Misaligned optical system.

Fig. 3
Fig. 3

3D relative intensity distribution of a HEGB at different propagation distances. (a) z=0, (b) z=0.3zx, (c) z=5zx, (d) z=10zx.

Fig. 4
Fig. 4

Optical system of a misaligned lens.

Fig. 5
Fig. 5

Contour graph of a HEGB passing through a misaligned thin lens at two propagation distances. (a) z=40 mm, (b) z=60 mm.

Equations (58)

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

En(r, 0)=G0r2w02nexp-r2w02,n=0, 1, 2,,
x2n=n!2nm=0n(-1)mnmLm(2x2),n=0, 1,,
En(r, 0)=G0n!2nm=0n(-1)mnmLm2 r2w02exp-r2w02.
En(r, z)=G0n!2nm=0n(-1)mnm×(A-B/q0)m(A+B/q0)m+1 Lm2 r2w2(z)×exp-ikr22qexp(-ikz),
1q=C+D/q0A+B/q0,
w2(z)=-λπ Im(qi)=w02A2+Bλπw022,
ABCD=1z01,
En(r)=G0n!2nw0w(z)exp{-i[kz+ϕ(z)]}×expik2R(z)-1w2(z)r2×m=0n(-1)mnmLm2 r2w02exp[-2imϕ(z)].
zR=kw022,
w(z)=w0[1+(z/zR)2]1/2,R(z)=z+zR2/z,
ϕ(z)=tan-1(z/zR).
En(r, 0)=G0ik2rTQ-1rnexp-ik2rTQ-1r,
n=0, 1, 2, 3,
Q-1=q0xx-1q0xy-1q0xy-1q0yy-1,
λ=632.8nm,
Q-1=-0.002i-0.0005i-0.0005i-0.0009i mm-1,
wx0=1mm,wy0=1.5mm,
wxy0=2mm.
α=12arctan2w0xyw0x-w0y.
(rTQ-1r)n=(2n)!23nm=0n1(n-m)!(2m)! H2m(2|Q-1/2r|),
En(r, 0)=G0(2n)!23nexp-ik2rTQ-1r×m=0n1(n-m)!(2m)! H2m[|(ikQ-1)1/2r|],
n=0, 1, 2, 3 .
Ep(r, 0)=exp-ik2rTQ-1rHp(ikrTQ-1r),
p=0, 1, 2, 3,
Ep(r2, z)=[det(A+BQ1-1)]-1/2[1-2/det(B-1AQ1+I)]p/2exp-ik2r2TQ2-1r2×Hp{[1-2/det(B-1AQ1+I)]-1/2×ikr2T(A+BQ1-1)-1T(AQ1+B)-1r2},
Q2-1=(C+DQ1-1)(A+BQ1-1)-1.
En(r2, z)=G0(2n)!23n [det(A+BQ1-1)]-1/2×exp-ik2r2TQ2-1r2m=0n1(n-m)!(2m)!×[1-2/det(B-1AQ1+I)]mH2m×{[1-2/det(B-1AQ1+I)]-1/2×ikr2T(A+BQ1-1)-1T(AQ1+B)-1r2},
E2(x2, y2)=-ik2πbE1(x1, y1)×exp-ik2a [a(x12+y12)-2(x1x2+y1y2)+d(x22+y22)+ex1+fy1+gx2+hy2]dx1dy1.
e=2(αTx+βTx),
f=2(αTy+βTy),
g=2(bγT-dαT)x+2(bδT-dβT)x,
h=2(bγT-dαT)y+2(bδT-dβT)y,
αT=1-a,βT=l-b,γT=-c,
δT=±1-d,
E(r2)=-ik2π[det(B)]1/2E(r1)exp-ik2 (r1TB-1Ar1-2r1TB-1r2+r2TDB-1r2)×exp-ik2 (r1TB-1ef+r2TB-1gh)dr1,
A=a00a,B=b00b,C=c00c,
D=d00d.
(B-1A)T=B-1A,
(DB-1)T=DB-1,
C-DB-1A=-(B-1)T.
En(r, 0)=G0(2n)!23n [det(A+BQ1-1)]exp-ik2r2TQ2-1r2×exp-ik2r2TB-1T(A+BQ1-1)-1ef×exp-ik2r2TB-1ggexpik8efTB-1T(A+BQ1-1)efm=0n1(n-m)!(2m)!×[1-2/det(B-1AQ+I)]m×H2m[1-2/det(B-1AQ1+I)]-1/2×ikr2-12efT(A+BQ1-1)-1T(AQ1+B)-1r2-12ef1/2,
-exp-(x-b)22aHp(x)dx
=2πa(1-2a)p/2Hpb1-2a
A=1001,B=z00z,C=0000,
D=1001.
λ=632.8nm,wx0=1mm,
wy0=1.5mm,wxy0=2mm,n=10,
Q-1=-0.20i-0.05i-0.05i-0.09i m-1.
A=1-(z-z1)/f001-(z-z1)/f,
B=z-z1(z-z1)/f00z-z1(z-z1)/f,
C=-1/f00-1/f,
D=1-z1/f001-z1/f,
αT=z-z1f,βT=z1(z-z1)f,γT=1f,
δT=z1f,
e=2 (z-z1)xf,f=0,g=2z1Åxf,h=0.
λ=632.8nm,x=0.5mm,f=15mm,
z1=20mm,n=10,
Q-1=-0.20i-0.05i-0.05i-0.09i m-1.

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