Abstract

Light focusing by a thermal lens that is induced in CS2 by an axicon-system-generated tubular light beam is demonstrated. Compared with other methods for generating doughnut-shaped beams, this optical scheme has advantages in efficiency and control of the beam parameters. The feasibility of the scheme for laser focusing and guiding of atomic beams is discussed.

© 1990 Optical Society of America

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References

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  1. C. Yeh, J. E. Pearson, W. P. Brown, Appl. Opt. 15, 2913 (1975).
    [Crossref]
  2. L. A. Newman, D. C. Smith, Appl. Phys. Lett. 38, 590 (1981).
    [Crossref]
  3. J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. P. Pearson, Phys. Rev. Lett. 41, 1361 (1978); Opt. Lett. 5, 111 (1980); D. P. Pearson, R. R. Freeman, J. E. Bjorkholm, A. Ashkin, Appl. Phys. Lett. 36, 99 (1980).
    [Crossref]
  4. V. I. Balykin, V. S. Letokhov, Opt. Commun. 64, 151 (1987).
    [Crossref]
  5. G. A. Askaryan, V. B. Studenov, JETP Lett. 10, 71 (1969); G. A. Askaryan, I. L. Chistyi, Sov. Phys. JETP 31, 76 (1970); G. A. Askaryan, V. G. Mikhalevich, V. B. Studenov, G. T. Shipulo, Sov. Phys. JETP 32, 1036 (1971).
  6. Note that the Laguerre–Gaussian TEM01mode has a nodal line across the beam. The circularly symmetric doughnut mode is, for most practical lasers, a combination of TEM01and TEM10Hermitian–Gaussian modes of slightly different frequencies [A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 689]. The resulting rotating pattern gives a time-averaged power that is symmetric about the axis. Thus, for short, guided laser pulses the trapping waveguide is not circularly symmetric: It has nodal lines that permit the light to escape.
  7. M. Rioux, R. Tremblay, P. A. Belanger, Appl. Opt. 17, 1532 (1978).
    [Crossref] [PubMed]
  8. I. Golub, Y. Beaudoin, S. L. Chin, J. Opt. Soc. Am. B 5, 2490 (1988); Opt. Lett. 13, 488 (1988); I. Golub, “On the contribution of different nonlinear mechanisms in measurements of n2of CS2at 10 μ m,” Appl. Opt. (to be published).
    [Crossref]
  9. R. G. Caro, M. C. Gower, IEEE J. Quantum Electron. QE-18, 1376 (1982).
    [Crossref]
  10. K.-H. Hellwege, ed., Landolt–BörnsteinZahlenwerte und Functionen (Springer-Verlag, Berlin, 1962), Vol. 218; R. C. Weast, M. J. Ashe, eds., CRC Handbook of Chemistry (CRC, Boca Raton, Fla., 1986).
  11. S. A. Akhmanov, R. V. Khokhlov, A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds., (North-Holland, Amsterdam, 1972), p. 1173.
  12. G. Abbate, U. Bernini, P. Maddalena, S. De Nicola, P. Mormile, G. Pierattini, Opt. Commun. 70, 502 (1989).
    [Crossref]
  13. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 416.
  14. L. W. Casperson, N. R. Kincheloe, O. M. Stafsudd, Opt. Commun. 21, 1 (1977); L. W. Casperson, Opt. Quantum Electron. 8, 537 (1976); Opt. Quantum Electron. 9, 499 (1977).
    [Crossref]

1989 (1)

G. Abbate, U. Bernini, P. Maddalena, S. De Nicola, P. Mormile, G. Pierattini, Opt. Commun. 70, 502 (1989).
[Crossref]

1988 (1)

1987 (1)

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

1982 (1)

R. G. Caro, M. C. Gower, IEEE J. Quantum Electron. QE-18, 1376 (1982).
[Crossref]

1981 (1)

L. A. Newman, D. C. Smith, Appl. Phys. Lett. 38, 590 (1981).
[Crossref]

1978 (2)

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. P. Pearson, Phys. Rev. Lett. 41, 1361 (1978); Opt. Lett. 5, 111 (1980); D. P. Pearson, R. R. Freeman, J. E. Bjorkholm, A. Ashkin, Appl. Phys. Lett. 36, 99 (1980).
[Crossref]

M. Rioux, R. Tremblay, P. A. Belanger, Appl. Opt. 17, 1532 (1978).
[Crossref] [PubMed]

1977 (1)

L. W. Casperson, N. R. Kincheloe, O. M. Stafsudd, Opt. Commun. 21, 1 (1977); L. W. Casperson, Opt. Quantum Electron. 8, 537 (1976); Opt. Quantum Electron. 9, 499 (1977).
[Crossref]

1975 (1)

1969 (1)

G. A. Askaryan, V. B. Studenov, JETP Lett. 10, 71 (1969); G. A. Askaryan, I. L. Chistyi, Sov. Phys. JETP 31, 76 (1970); G. A. Askaryan, V. G. Mikhalevich, V. B. Studenov, G. T. Shipulo, Sov. Phys. JETP 32, 1036 (1971).

Abbate, G.

G. Abbate, U. Bernini, P. Maddalena, S. De Nicola, P. Mormile, G. Pierattini, Opt. Commun. 70, 502 (1989).
[Crossref]

Akhmanov, S. A.

S. A. Akhmanov, R. V. Khokhlov, A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds., (North-Holland, Amsterdam, 1972), p. 1173.

Ashkin, A.

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. P. Pearson, Phys. Rev. Lett. 41, 1361 (1978); Opt. Lett. 5, 111 (1980); D. P. Pearson, R. R. Freeman, J. E. Bjorkholm, A. Ashkin, Appl. Phys. Lett. 36, 99 (1980).
[Crossref]

Askaryan, G. A.

G. A. Askaryan, V. B. Studenov, JETP Lett. 10, 71 (1969); G. A. Askaryan, I. L. Chistyi, Sov. Phys. JETP 31, 76 (1970); G. A. Askaryan, V. G. Mikhalevich, V. B. Studenov, G. T. Shipulo, Sov. Phys. JETP 32, 1036 (1971).

Balykin, V. I.

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

Beaudoin, Y.

Belanger, P. A.

Bernini, U.

G. Abbate, U. Bernini, P. Maddalena, S. De Nicola, P. Mormile, G. Pierattini, Opt. Commun. 70, 502 (1989).
[Crossref]

Bjorkholm, J. E.

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. P. Pearson, Phys. Rev. Lett. 41, 1361 (1978); Opt. Lett. 5, 111 (1980); D. P. Pearson, R. R. Freeman, J. E. Bjorkholm, A. Ashkin, Appl. Phys. Lett. 36, 99 (1980).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 416.

Brown, W. P.

Caro, R. G.

R. G. Caro, M. C. Gower, IEEE J. Quantum Electron. QE-18, 1376 (1982).
[Crossref]

Casperson, L. W.

L. W. Casperson, N. R. Kincheloe, O. M. Stafsudd, Opt. Commun. 21, 1 (1977); L. W. Casperson, Opt. Quantum Electron. 8, 537 (1976); Opt. Quantum Electron. 9, 499 (1977).
[Crossref]

Chin, S. L.

De Nicola, S.

G. Abbate, U. Bernini, P. Maddalena, S. De Nicola, P. Mormile, G. Pierattini, Opt. Commun. 70, 502 (1989).
[Crossref]

Freeman, R. R.

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. P. Pearson, Phys. Rev. Lett. 41, 1361 (1978); Opt. Lett. 5, 111 (1980); D. P. Pearson, R. R. Freeman, J. E. Bjorkholm, A. Ashkin, Appl. Phys. Lett. 36, 99 (1980).
[Crossref]

Golub, I.

Gower, M. C.

R. G. Caro, M. C. Gower, IEEE J. Quantum Electron. QE-18, 1376 (1982).
[Crossref]

Khokhlov, R. V.

S. A. Akhmanov, R. V. Khokhlov, A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds., (North-Holland, Amsterdam, 1972), p. 1173.

Kincheloe, N. R.

L. W. Casperson, N. R. Kincheloe, O. M. Stafsudd, Opt. Commun. 21, 1 (1977); L. W. Casperson, Opt. Quantum Electron. 8, 537 (1976); Opt. Quantum Electron. 9, 499 (1977).
[Crossref]

Landolt–Börnstein,

K.-H. Hellwege, ed., Landolt–BörnsteinZahlenwerte und Functionen (Springer-Verlag, Berlin, 1962), Vol. 218; R. C. Weast, M. J. Ashe, eds., CRC Handbook of Chemistry (CRC, Boca Raton, Fla., 1986).

Letokhov, V. S.

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

Maddalena, P.

G. Abbate, U. Bernini, P. Maddalena, S. De Nicola, P. Mormile, G. Pierattini, Opt. Commun. 70, 502 (1989).
[Crossref]

Mormile, P.

G. Abbate, U. Bernini, P. Maddalena, S. De Nicola, P. Mormile, G. Pierattini, Opt. Commun. 70, 502 (1989).
[Crossref]

Newman, L. A.

L. A. Newman, D. C. Smith, Appl. Phys. Lett. 38, 590 (1981).
[Crossref]

Pearson, D. P.

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. P. Pearson, Phys. Rev. Lett. 41, 1361 (1978); Opt. Lett. 5, 111 (1980); D. P. Pearson, R. R. Freeman, J. E. Bjorkholm, A. Ashkin, Appl. Phys. Lett. 36, 99 (1980).
[Crossref]

Pearson, J. E.

Pierattini, G.

G. Abbate, U. Bernini, P. Maddalena, S. De Nicola, P. Mormile, G. Pierattini, Opt. Commun. 70, 502 (1989).
[Crossref]

Rioux, M.

Siegman, A.

Note that the Laguerre–Gaussian TEM01mode has a nodal line across the beam. The circularly symmetric doughnut mode is, for most practical lasers, a combination of TEM01and TEM10Hermitian–Gaussian modes of slightly different frequencies [A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 689]. The resulting rotating pattern gives a time-averaged power that is symmetric about the axis. Thus, for short, guided laser pulses the trapping waveguide is not circularly symmetric: It has nodal lines that permit the light to escape.

Smith, D. C.

L. A. Newman, D. C. Smith, Appl. Phys. Lett. 38, 590 (1981).
[Crossref]

Stafsudd, O. M.

L. W. Casperson, N. R. Kincheloe, O. M. Stafsudd, Opt. Commun. 21, 1 (1977); L. W. Casperson, Opt. Quantum Electron. 8, 537 (1976); Opt. Quantum Electron. 9, 499 (1977).
[Crossref]

Studenov, V. B.

G. A. Askaryan, V. B. Studenov, JETP Lett. 10, 71 (1969); G. A. Askaryan, I. L. Chistyi, Sov. Phys. JETP 31, 76 (1970); G. A. Askaryan, V. G. Mikhalevich, V. B. Studenov, G. T. Shipulo, Sov. Phys. JETP 32, 1036 (1971).

Sukhorukov, A. P.

S. A. Akhmanov, R. V. Khokhlov, A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds., (North-Holland, Amsterdam, 1972), p. 1173.

Tremblay, R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 416.

Yeh, C.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

L. A. Newman, D. C. Smith, Appl. Phys. Lett. 38, 590 (1981).
[Crossref]

IEEE J. Quantum Electron. (1)

R. G. Caro, M. C. Gower, IEEE J. Quantum Electron. QE-18, 1376 (1982).
[Crossref]

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

JETP Lett. (1)

G. A. Askaryan, V. B. Studenov, JETP Lett. 10, 71 (1969); G. A. Askaryan, I. L. Chistyi, Sov. Phys. JETP 31, 76 (1970); G. A. Askaryan, V. G. Mikhalevich, V. B. Studenov, G. T. Shipulo, Sov. Phys. JETP 32, 1036 (1971).

Opt. Commun. (3)

G. Abbate, U. Bernini, P. Maddalena, S. De Nicola, P. Mormile, G. Pierattini, Opt. Commun. 70, 502 (1989).
[Crossref]

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

L. W. Casperson, N. R. Kincheloe, O. M. Stafsudd, Opt. Commun. 21, 1 (1977); L. W. Casperson, Opt. Quantum Electron. 8, 537 (1976); Opt. Quantum Electron. 9, 499 (1977).
[Crossref]

Phys. Rev. Lett. (1)

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. P. Pearson, Phys. Rev. Lett. 41, 1361 (1978); Opt. Lett. 5, 111 (1980); D. P. Pearson, R. R. Freeman, J. E. Bjorkholm, A. Ashkin, Appl. Phys. Lett. 36, 99 (1980).
[Crossref]

Other (4)

Note that the Laguerre–Gaussian TEM01mode has a nodal line across the beam. The circularly symmetric doughnut mode is, for most practical lasers, a combination of TEM01and TEM10Hermitian–Gaussian modes of slightly different frequencies [A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 689]. The resulting rotating pattern gives a time-averaged power that is symmetric about the axis. Thus, for short, guided laser pulses the trapping waveguide is not circularly symmetric: It has nodal lines that permit the light to escape.

K.-H. Hellwege, ed., Landolt–BörnsteinZahlenwerte und Functionen (Springer-Verlag, Berlin, 1962), Vol. 218; R. C. Weast, M. J. Ashe, eds., CRC Handbook of Chemistry (CRC, Boca Raton, Fla., 1986).

S. A. Akhmanov, R. V. Khokhlov, A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds., (North-Holland, Amsterdam, 1972), p. 1173.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 416.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. See text for definitions of labels.

Fig. 2
Fig. 2

a, Focusing by a tubular beam: relative change in the diameter of the probe laser beam as a function of CO2 laser power for two different doughnut modes that correspond to axicon separations of ×, L = 3 cm; □, L = 6 cm. b, Defocusing by a Gaussian laser beam: relative change in the diameter of the probe laser beam as a function of CO2 laser power.

Fig. 3
Fig. 3

Arrangement for focusing and confinement of an atomic beam incident from the left-hand side by a counterpropagating axicon-pair-generated tubular laser beam.

Equations (3)

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Δ n th = d n / d T × Δ T = d n / d T × Φ α t I / ρ C p ,
f = ω 2 / Δ n l ,
Δ n th = ( d n / d T ) Δ T = ( d n / d T ) P / 4 π κ l ( 1 e α l ) ln ( 2 γ a 2 / ω 2 ) ,

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