Abstract

Using a propagation cell that discriminated against the buildup of stimulated Raman emission, we succeeded in observing self-focusing in pressurized air without interference from any competing nonlinear process. Measurements were made for air pressures between 20 and 40 atm. The data yielded a nonlinear refractive index n2. = (2.9 ± 0.3) × 10−16 esu per atmosphere of air at 300 K for a 308-nm laser beam.

© 1989 Optical Society of America

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References

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  1. Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975).
    [CrossRef]
  2. J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
    [CrossRef]
  3. S. A. Akhmanov, R. V. Khokhlov, and A. P. Sukhorukov in Laser Handbook, F. T. Arecchi and E. O. Schulz-Du Bois, eds. (North-Holland, Amsterdam, 1972), p. 1151.
  4. W. E. Martin and R. T. Winfield, Appl. Opt. 27, 567 (1988).
    [CrossRef] [PubMed]
  5. P. L. Kelley and J. P. E. Taran, Appl. Opt. 27, 4787 (1988).
    [CrossRef] [PubMed]
  6. G. L. McAllister, J. H. Marburger, and L. G. DeShazer, Phys. Rev. Lett. 21, 1648 (1968).
    [CrossRef]
  7. D. V. Vlasov, R. A. Garaev, V. V. Korobkin, and R. V. Serov, Sov. Phys. JETP 49, 1033 (1979).
  8. D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, Phys. Rev. A 39, 3003 (1989);M. A. Henesian, D. M. Pennington, C. D. Swift, and R. W. Hellwarth, 1986 Laser Program Annual Rep. UCRL-50021-86 (Lawrence Livermore National Laboratory, Livermore, Calif., 1987), pp. 4–71.
    [CrossRef] [PubMed]
  9. V. S. Averbakh, A. I. Makarov, and V. I. Talanov, Sov. J. Quantum Electron. 8, 472 (1978).
    [CrossRef]
  10. E. E. Hagenlocker, R. W. Minck, and W. G. Rado, Phys. Rev. 154, 226 (1967).
    [CrossRef]
  11. M. G. Littman, Appl. Opt. 23, 4465 (1984).
    [CrossRef] [PubMed]
  12. P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
    [CrossRef]
  13. V. K. Saulyev, Integration of Equations of Parabolic Type by the Method of Nets (Macmillan, New York, 1964).
  14. E. L. Dawes, Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1969).
  15. R. W. Hellwarth, A. Owyoung, and N. George, Phys. Rev. A 4, 2342 (1971).
    [CrossRef]
  16. A. Owyoung, Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1972).
  17. N. Bloembergen and P. Lallemand, Phys. Rev. Lett. 16, 81 (1966).
    [CrossRef]
  18. G. C. Herring, M. J. Dyer, and W. K. Bischel, Opt. Lett. 11, 348 (1986).
    [CrossRef] [PubMed]
  19. C. M. Penney, R. L. St. Peters, and M. Lapp, J. Opt. Soc. Am. 64, 712 (1974).
    [CrossRef]
  20. V. Mizrahi and D. P. Shelton, Phys. Rev. Lett. 55, 696 (1985).
    [CrossRef] [PubMed]
  21. P. Sitz and R. Yaris, J.Chem. Phys. 49, 3546 (1968).
    [CrossRef]

1989 (1)

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, Phys. Rev. A 39, 3003 (1989);M. A. Henesian, D. M. Pennington, C. D. Swift, and R. W. Hellwarth, 1986 Laser Program Annual Rep. UCRL-50021-86 (Lawrence Livermore National Laboratory, Livermore, Calif., 1987), pp. 4–71.
[CrossRef] [PubMed]

1988 (2)

1986 (1)

1985 (1)

V. Mizrahi and D. P. Shelton, Phys. Rev. Lett. 55, 696 (1985).
[CrossRef] [PubMed]

1984 (1)

1979 (1)

D. V. Vlasov, R. A. Garaev, V. V. Korobkin, and R. V. Serov, Sov. Phys. JETP 49, 1033 (1979).

1978 (1)

V. S. Averbakh, A. I. Makarov, and V. I. Talanov, Sov. J. Quantum Electron. 8, 472 (1978).
[CrossRef]

1975 (2)

Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975).
[CrossRef]

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

1974 (1)

1971 (1)

R. W. Hellwarth, A. Owyoung, and N. George, Phys. Rev. A 4, 2342 (1971).
[CrossRef]

1968 (2)

P. Sitz and R. Yaris, J.Chem. Phys. 49, 3546 (1968).
[CrossRef]

G. L. McAllister, J. H. Marburger, and L. G. DeShazer, Phys. Rev. Lett. 21, 1648 (1968).
[CrossRef]

1967 (1)

E. E. Hagenlocker, R. W. Minck, and W. G. Rado, Phys. Rev. 154, 226 (1967).
[CrossRef]

1966 (1)

N. Bloembergen and P. Lallemand, Phys. Rev. Lett. 16, 81 (1966).
[CrossRef]

1965 (1)

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, R. V. Khokhlov, and A. P. Sukhorukov in Laser Handbook, F. T. Arecchi and E. O. Schulz-Du Bois, eds. (North-Holland, Amsterdam, 1972), p. 1151.

Averbakh, V. S.

V. S. Averbakh, A. I. Makarov, and V. I. Talanov, Sov. J. Quantum Electron. 8, 472 (1978).
[CrossRef]

Bischel, W. K.

Bloembergen, N.

N. Bloembergen and P. Lallemand, Phys. Rev. Lett. 16, 81 (1966).
[CrossRef]

Dawes, E. L.

E. L. Dawes, Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1969).

DeShazer, L. G.

G. L. McAllister, J. H. Marburger, and L. G. DeShazer, Phys. Rev. Lett. 21, 1648 (1968).
[CrossRef]

Dyer, M. J.

Garaev, R. A.

D. V. Vlasov, R. A. Garaev, V. V. Korobkin, and R. V. Serov, Sov. Phys. JETP 49, 1033 (1979).

George, N.

R. W. Hellwarth, A. Owyoung, and N. George, Phys. Rev. A 4, 2342 (1971).
[CrossRef]

Hagenlocker, E. E.

E. E. Hagenlocker, R. W. Minck, and W. G. Rado, Phys. Rev. 154, 226 (1967).
[CrossRef]

Hellwarth, R. W.

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, Phys. Rev. A 39, 3003 (1989);M. A. Henesian, D. M. Pennington, C. D. Swift, and R. W. Hellwarth, 1986 Laser Program Annual Rep. UCRL-50021-86 (Lawrence Livermore National Laboratory, Livermore, Calif., 1987), pp. 4–71.
[CrossRef] [PubMed]

R. W. Hellwarth, A. Owyoung, and N. George, Phys. Rev. A 4, 2342 (1971).
[CrossRef]

Henesian, M. A.

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, Phys. Rev. A 39, 3003 (1989);M. A. Henesian, D. M. Pennington, C. D. Swift, and R. W. Hellwarth, 1986 Laser Program Annual Rep. UCRL-50021-86 (Lawrence Livermore National Laboratory, Livermore, Calif., 1987), pp. 4–71.
[CrossRef] [PubMed]

Herring, G. C.

Kelley, P. L.

Khokhlov, R. V.

S. A. Akhmanov, R. V. Khokhlov, and A. P. Sukhorukov in Laser Handbook, F. T. Arecchi and E. O. Schulz-Du Bois, eds. (North-Holland, Amsterdam, 1972), p. 1151.

Korobkin, V. V.

D. V. Vlasov, R. A. Garaev, V. V. Korobkin, and R. V. Serov, Sov. Phys. JETP 49, 1033 (1979).

Lallemand, P.

N. Bloembergen and P. Lallemand, Phys. Rev. Lett. 16, 81 (1966).
[CrossRef]

Lapp, M.

Littman, M. G.

Makarov, A. I.

V. S. Averbakh, A. I. Makarov, and V. I. Talanov, Sov. J. Quantum Electron. 8, 472 (1978).
[CrossRef]

Marburger, J. H.

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

G. L. McAllister, J. H. Marburger, and L. G. DeShazer, Phys. Rev. Lett. 21, 1648 (1968).
[CrossRef]

Martin, W. E.

McAllister, G. L.

G. L. McAllister, J. H. Marburger, and L. G. DeShazer, Phys. Rev. Lett. 21, 1648 (1968).
[CrossRef]

Minck, R. W.

E. E. Hagenlocker, R. W. Minck, and W. G. Rado, Phys. Rev. 154, 226 (1967).
[CrossRef]

Mizrahi, V.

V. Mizrahi and D. P. Shelton, Phys. Rev. Lett. 55, 696 (1985).
[CrossRef] [PubMed]

Owyoung, A.

R. W. Hellwarth, A. Owyoung, and N. George, Phys. Rev. A 4, 2342 (1971).
[CrossRef]

A. Owyoung, Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1972).

Penney, C. M.

Pennington, D. M.

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, Phys. Rev. A 39, 3003 (1989);M. A. Henesian, D. M. Pennington, C. D. Swift, and R. W. Hellwarth, 1986 Laser Program Annual Rep. UCRL-50021-86 (Lawrence Livermore National Laboratory, Livermore, Calif., 1987), pp. 4–71.
[CrossRef] [PubMed]

Rado, W. G.

E. E. Hagenlocker, R. W. Minck, and W. G. Rado, Phys. Rev. 154, 226 (1967).
[CrossRef]

Saulyev, V. K.

V. K. Saulyev, Integration of Equations of Parabolic Type by the Method of Nets (Macmillan, New York, 1964).

Serov, R. V.

D. V. Vlasov, R. A. Garaev, V. V. Korobkin, and R. V. Serov, Sov. Phys. JETP 49, 1033 (1979).

Shelton, D. P.

V. Mizrahi and D. P. Shelton, Phys. Rev. Lett. 55, 696 (1985).
[CrossRef] [PubMed]

Shen, Y. R.

Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975).
[CrossRef]

Sitz, P.

P. Sitz and R. Yaris, J.Chem. Phys. 49, 3546 (1968).
[CrossRef]

St. Peters, R. L.

Sukhorukov, A. P.

S. A. Akhmanov, R. V. Khokhlov, and A. P. Sukhorukov in Laser Handbook, F. T. Arecchi and E. O. Schulz-Du Bois, eds. (North-Holland, Amsterdam, 1972), p. 1151.

Talanov, V. I.

V. S. Averbakh, A. I. Makarov, and V. I. Talanov, Sov. J. Quantum Electron. 8, 472 (1978).
[CrossRef]

Taran, J. P. E.

Vlasov, D. V.

D. V. Vlasov, R. A. Garaev, V. V. Korobkin, and R. V. Serov, Sov. Phys. JETP 49, 1033 (1979).

Winfield, R. T.

Yaris, R.

P. Sitz and R. Yaris, J.Chem. Phys. 49, 3546 (1968).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

J.Chem. Phys. (1)

P. Sitz and R. Yaris, J.Chem. Phys. 49, 3546 (1968).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

E. E. Hagenlocker, R. W. Minck, and W. G. Rado, Phys. Rev. 154, 226 (1967).
[CrossRef]

Phys. Rev. A (2)

R. W. Hellwarth, A. Owyoung, and N. George, Phys. Rev. A 4, 2342 (1971).
[CrossRef]

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, Phys. Rev. A 39, 3003 (1989);M. A. Henesian, D. M. Pennington, C. D. Swift, and R. W. Hellwarth, 1986 Laser Program Annual Rep. UCRL-50021-86 (Lawrence Livermore National Laboratory, Livermore, Calif., 1987), pp. 4–71.
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

G. L. McAllister, J. H. Marburger, and L. G. DeShazer, Phys. Rev. Lett. 21, 1648 (1968).
[CrossRef]

N. Bloembergen and P. Lallemand, Phys. Rev. Lett. 16, 81 (1966).
[CrossRef]

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

V. Mizrahi and D. P. Shelton, Phys. Rev. Lett. 55, 696 (1985).
[CrossRef] [PubMed]

Prog. Quantum Electron. (2)

Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975).
[CrossRef]

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Sov. J. Quantum Electron. (1)

V. S. Averbakh, A. I. Makarov, and V. I. Talanov, Sov. J. Quantum Electron. 8, 472 (1978).
[CrossRef]

Sov. Phys. JETP (1)

D. V. Vlasov, R. A. Garaev, V. V. Korobkin, and R. V. Serov, Sov. Phys. JETP 49, 1033 (1979).

Other (4)

S. A. Akhmanov, R. V. Khokhlov, and A. P. Sukhorukov in Laser Handbook, F. T. Arecchi and E. O. Schulz-Du Bois, eds. (North-Holland, Amsterdam, 1972), p. 1151.

V. K. Saulyev, Integration of Equations of Parabolic Type by the Method of Nets (Macmillan, New York, 1964).

E. L. Dawes, Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1969).

A. Owyoung, Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1972).

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Figures (7)

Fig. 1
Fig. 1

Schematic of the experimental arrangement used for the self-focusing measurements.

Fig. 2
Fig. 2

Profile of the laser beam as measured by a diode array directly in front of the entrance window of the propagation cell. The curve represents the best Gaussian fit.

Fig. 3
Fig. 3

Time dependence of the laser pulse: A, as measured by the photodiode and B, after correction for detection system response.

Fig. 4
Fig. 4

Fluence profile of the beam emerging from the propagation cell for input energy of A, 0.95 mJ and B, 2.7 mJ. The signal in B was 10 times attenuated and recorded with half the sensitivity as for A, so that its peak fluence is approximately 40 times that of A. Pressure was 37 atm.

Fig. 5
Fig. 5

On-axis intensity as a function of propagation distance relative to the on-axis intensity in the entrance plane for several incident power levels. Distance is normalized to the Rayleigh range z0 = πω02/λ, where ω0 is the beam radius at the waist (entrance plane).

Fig. 6
Fig. 6

Calculated on-axis intensity in the exit plane (z = 1.1z0) relative to the on-axis intensity in the entrance plane as a function of input power normalized to the critical power Pc.

Fig. 7
Fig. 7

Experimentally determined nonlinear refractive index of air at six different pressures and the best straight-line fit to the data.

Equations (9)

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n = n 0 + n 2 | E | 2 + ,
E = ½ E exp [ i ( k z ω t ) ] + c . c . ,
2 i k E z + i k α E + T 2 E + n 2 k 2 n 0 | E | 2 E = 0 ,
P c = ( 1.22 λ ) 2 c 128 n 2 .
n 2 = 12 π N n χ 1111 ( 3 ) ( ω ; ω , ω , ω ) ,
χ 1111 ( 3 ) ( ω ; ω , ω , ω ) = σ 8 + a + b 6 ,
χ 1111 ( 3 ) ( ω ; ω , ω , ω ) = σ 8 + b 9 .
χ 1111 ( 3 ) ( 2 ω ; ω , ω , 0 ) = σ 8 .
b = γ 2 15 kT .

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