Abstract

The temperature, wavelength, and J dependence of the rotational Raman gain coefficient has been determined for the S-branch transitions in N2. First, the temperature dependence (80–300 K) of the density-broadening coefficients was measured using stimulated Raman spectroscopy. Second, the wavelength dependence (250–600 nm) of the polarizability anisotropy was empirically determined by fitting to the most recent experimental data. These two results were then used to calculate the rotational Raman gain coefficients with accuracies estimated at 5%. At room temperature, the high-density limit of the steady-state gain coefficient of the strongest line, S(10), is 4.8 × 10−12 cm/W for a Stokes wavelength of 568 nm.

© 1986 Optical Society of America

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  1. V. E. Zuev, Laser Beams in the Atmosphere (Consultants Bureau, New York, 1982), pp. 243–314.
    [CrossRef]
  2. M. Henesian, C. Swift, J. R. Murray, Opt. Lett. 10, 565 (1985).
    [CrossRef] [PubMed]
  3. V. S. Averbakh, A. I. Makarov, V. I. Talanov, Sov. J. Quantum Electron. 8, 472 (1978).
    [CrossRef]
  4. W. K. Bischel, M. J. Dyer, J. Opt. Soc. Am. B 3, 677 (1986).
    [CrossRef]
  5. P. Esherick, A. Owyoung, in Advances in Infrared and Raman Spectroscopy, R. J. H. Clark, R. E. Hestor, eds. (Heyden, London, 1983), pp. 130–187.
  6. G. R. Alms, A. K. Burnham, W. H. Flygare, J. Chem. Phys. 63, 3321 (1975).
    [CrossRef]
  7. P. W. Langhoff, J. Chem. Phys. 57, 2604 (1972).
    [CrossRef]
  8. M. P. Bogaard, A. D. Buckingham, R. K. Pierens, A. H. White, J. Chem. Soc. Faraday Trans. 1 74, 3008 (1978).
  9. N. J. Bridge, A. D. Buckingham, Proc. R. Soc. London Ser. A 295, 334 (1966).
    [CrossRef]
  10. J. R. Murray, J. Goldhar, D. Eimerl, A. Szoke, IEEE J. Quantum Electron. QE-15, 342 (1979).
    [CrossRef]
  11. D. A. Long, Raman Spectroscopy (McGraw-Hill, London, 1977).
  12. D. Robert, J. Bonomy, J. Phys. (Paris) 40, 923 (1978).
  13. H. G. M. Edwards, D. A. Long, S. W. Webb, “Self- and foreign-gas broadening of the pure rotational Raman line of oxygen and nitrogen,” presented at the IXth International Conference on Raman Spectroscopy, Tokyo, August 27–September 1, 1984.
  14. G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and density dependence of the linewidths and line-shifts of the rotational Raman lines in N2 and H2” (submitted to Phys. Rev. A).
  15. C. M. Penny, R. L. St. Peters, M. Lapp, J. Opt. Soc. Am. 64, 712 (1974).
    [CrossRef]
  16. W. R. Fenner, H. A. Hyatt, J. M. Kellam, S. P. S. Porto, J. Opt. Soc. Am. 63, 73, 1604 (1973).
    [CrossRef]
  17. C. Asawaroengchai, G. M. Rosenblatt, J. Chem. Phys. 72, 2664 (1979).
    [CrossRef]
  18. H. Hamaguchi, A. D. Buckingham, W. J. Jones, Mol. Phys. 43, 1311 (1981).
    [CrossRef]
  19. Landolt-Börnstein, Zahlenwerte und Funktionen. II Band, 8 Teil, Optische Konstanten (Springer-Verlag, Berlin, 1962).

1986

1985

1981

H. Hamaguchi, A. D. Buckingham, W. J. Jones, Mol. Phys. 43, 1311 (1981).
[CrossRef]

1979

C. Asawaroengchai, G. M. Rosenblatt, J. Chem. Phys. 72, 2664 (1979).
[CrossRef]

J. R. Murray, J. Goldhar, D. Eimerl, A. Szoke, IEEE J. Quantum Electron. QE-15, 342 (1979).
[CrossRef]

1978

D. Robert, J. Bonomy, J. Phys. (Paris) 40, 923 (1978).

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

M. P. Bogaard, A. D. Buckingham, R. K. Pierens, A. H. White, J. Chem. Soc. Faraday Trans. 1 74, 3008 (1978).

1975

G. R. Alms, A. K. Burnham, W. H. Flygare, J. Chem. Phys. 63, 3321 (1975).
[CrossRef]

1974

1973

1972

P. W. Langhoff, J. Chem. Phys. 57, 2604 (1972).
[CrossRef]

1966

N. J. Bridge, A. D. Buckingham, Proc. R. Soc. London Ser. A 295, 334 (1966).
[CrossRef]

Alms, G. R.

G. R. Alms, A. K. Burnham, W. H. Flygare, J. Chem. Phys. 63, 3321 (1975).
[CrossRef]

Asawaroengchai, C.

C. Asawaroengchai, G. M. Rosenblatt, J. Chem. Phys. 72, 2664 (1979).
[CrossRef]

Averbakh, V. S.

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

Bischel, W. K.

W. K. Bischel, M. J. Dyer, J. Opt. Soc. Am. B 3, 677 (1986).
[CrossRef]

G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and density dependence of the linewidths and line-shifts of the rotational Raman lines in N2 and H2” (submitted to Phys. Rev. A).

Bogaard, M. P.

M. P. Bogaard, A. D. Buckingham, R. K. Pierens, A. H. White, J. Chem. Soc. Faraday Trans. 1 74, 3008 (1978).

Bonomy, J.

D. Robert, J. Bonomy, J. Phys. (Paris) 40, 923 (1978).

Bridge, N. J.

N. J. Bridge, A. D. Buckingham, Proc. R. Soc. London Ser. A 295, 334 (1966).
[CrossRef]

Buckingham, A. D.

H. Hamaguchi, A. D. Buckingham, W. J. Jones, Mol. Phys. 43, 1311 (1981).
[CrossRef]

M. P. Bogaard, A. D. Buckingham, R. K. Pierens, A. H. White, J. Chem. Soc. Faraday Trans. 1 74, 3008 (1978).

N. J. Bridge, A. D. Buckingham, Proc. R. Soc. London Ser. A 295, 334 (1966).
[CrossRef]

Burnham, A. K.

G. R. Alms, A. K. Burnham, W. H. Flygare, J. Chem. Phys. 63, 3321 (1975).
[CrossRef]

Dyer, M. J.

W. K. Bischel, M. J. Dyer, J. Opt. Soc. Am. B 3, 677 (1986).
[CrossRef]

G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and density dependence of the linewidths and line-shifts of the rotational Raman lines in N2 and H2” (submitted to Phys. Rev. A).

Edwards, H. G. M.

H. G. M. Edwards, D. A. Long, S. W. Webb, “Self- and foreign-gas broadening of the pure rotational Raman line of oxygen and nitrogen,” presented at the IXth International Conference on Raman Spectroscopy, Tokyo, August 27–September 1, 1984.

Eimerl, D.

J. R. Murray, J. Goldhar, D. Eimerl, A. Szoke, IEEE J. Quantum Electron. QE-15, 342 (1979).
[CrossRef]

Esherick, P.

P. Esherick, A. Owyoung, in Advances in Infrared and Raman Spectroscopy, R. J. H. Clark, R. E. Hestor, eds. (Heyden, London, 1983), pp. 130–187.

Fenner, W. R.

Flygare, W. H.

G. R. Alms, A. K. Burnham, W. H. Flygare, J. Chem. Phys. 63, 3321 (1975).
[CrossRef]

Goldhar, J.

J. R. Murray, J. Goldhar, D. Eimerl, A. Szoke, IEEE J. Quantum Electron. QE-15, 342 (1979).
[CrossRef]

Hamaguchi, H.

H. Hamaguchi, A. D. Buckingham, W. J. Jones, Mol. Phys. 43, 1311 (1981).
[CrossRef]

Henesian, M.

Herring, G. C.

G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and density dependence of the linewidths and line-shifts of the rotational Raman lines in N2 and H2” (submitted to Phys. Rev. A).

Hyatt, H. A.

Jones, W. J.

H. Hamaguchi, A. D. Buckingham, W. J. Jones, Mol. Phys. 43, 1311 (1981).
[CrossRef]

Kellam, J. M.

Landolt-Börnstein,

Landolt-Börnstein, Zahlenwerte und Funktionen. II Band, 8 Teil, Optische Konstanten (Springer-Verlag, Berlin, 1962).

Langhoff, P. W.

P. W. Langhoff, J. Chem. Phys. 57, 2604 (1972).
[CrossRef]

Lapp, M.

Long, D. A.

D. A. Long, Raman Spectroscopy (McGraw-Hill, London, 1977).

H. G. M. Edwards, D. A. Long, S. W. Webb, “Self- and foreign-gas broadening of the pure rotational Raman line of oxygen and nitrogen,” presented at the IXth International Conference on Raman Spectroscopy, Tokyo, August 27–September 1, 1984.

Makarov, A. I.

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

Murray, J. R.

M. Henesian, C. Swift, J. R. Murray, Opt. Lett. 10, 565 (1985).
[CrossRef] [PubMed]

J. R. Murray, J. Goldhar, D. Eimerl, A. Szoke, IEEE J. Quantum Electron. QE-15, 342 (1979).
[CrossRef]

Owyoung, A.

P. Esherick, A. Owyoung, in Advances in Infrared and Raman Spectroscopy, R. J. H. Clark, R. E. Hestor, eds. (Heyden, London, 1983), pp. 130–187.

Penny, C. M.

Peters, R. L. St.

Pierens, R. K.

M. P. Bogaard, A. D. Buckingham, R. K. Pierens, A. H. White, J. Chem. Soc. Faraday Trans. 1 74, 3008 (1978).

Porto, S. P. S.

Robert, D.

D. Robert, J. Bonomy, J. Phys. (Paris) 40, 923 (1978).

Rosenblatt, G. M.

C. Asawaroengchai, G. M. Rosenblatt, J. Chem. Phys. 72, 2664 (1979).
[CrossRef]

Swift, C.

Szoke, A.

J. R. Murray, J. Goldhar, D. Eimerl, A. Szoke, IEEE J. Quantum Electron. QE-15, 342 (1979).
[CrossRef]

Talanov, V. I.

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

Webb, S. W.

H. G. M. Edwards, D. A. Long, S. W. Webb, “Self- and foreign-gas broadening of the pure rotational Raman line of oxygen and nitrogen,” presented at the IXth International Conference on Raman Spectroscopy, Tokyo, August 27–September 1, 1984.

White, A. H.

M. P. Bogaard, A. D. Buckingham, R. K. Pierens, A. H. White, J. Chem. Soc. Faraday Trans. 1 74, 3008 (1978).

Zuev, V. E.

V. E. Zuev, Laser Beams in the Atmosphere (Consultants Bureau, New York, 1982), pp. 243–314.
[CrossRef]

IEEE J. Quantum Electron.

J. R. Murray, J. Goldhar, D. Eimerl, A. Szoke, IEEE J. Quantum Electron. QE-15, 342 (1979).
[CrossRef]

J. Chem. Phys.

C. Asawaroengchai, G. M. Rosenblatt, J. Chem. Phys. 72, 2664 (1979).
[CrossRef]

G. R. Alms, A. K. Burnham, W. H. Flygare, J. Chem. Phys. 63, 3321 (1975).
[CrossRef]

P. W. Langhoff, J. Chem. Phys. 57, 2604 (1972).
[CrossRef]

J. Chem. Soc. Faraday Trans. 1

M. P. Bogaard, A. D. Buckingham, R. K. Pierens, A. H. White, J. Chem. Soc. Faraday Trans. 1 74, 3008 (1978).

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

J. Phys. (Paris)

D. Robert, J. Bonomy, J. Phys. (Paris) 40, 923 (1978).

Mol. Phys.

H. Hamaguchi, A. D. Buckingham, W. J. Jones, Mol. Phys. 43, 1311 (1981).
[CrossRef]

Opt. Lett.

Proc. R. Soc. London Ser. A

N. J. Bridge, A. D. Buckingham, Proc. R. Soc. London Ser. A 295, 334 (1966).
[CrossRef]

Sov. J. Quantum Electron.

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

Other

P. Esherick, A. Owyoung, in Advances in Infrared and Raman Spectroscopy, R. J. H. Clark, R. E. Hestor, eds. (Heyden, London, 1983), pp. 130–187.

D. A. Long, Raman Spectroscopy (McGraw-Hill, London, 1977).

Landolt-Börnstein, Zahlenwerte und Funktionen. II Band, 8 Teil, Optische Konstanten (Springer-Verlag, Berlin, 1962).

H. G. M. Edwards, D. A. Long, S. W. Webb, “Self- and foreign-gas broadening of the pure rotational Raman line of oxygen and nitrogen,” presented at the IXth International Conference on Raman Spectroscopy, Tokyo, August 27–September 1, 1984.

G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and density dependence of the linewidths and line-shifts of the rotational Raman lines in N2 and H2” (submitted to Phys. Rev. A).

V. E. Zuev, Laser Beams in the Atmosphere (Consultants Bureau, New York, 1982), pp. 243–314.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Measured temperature dependence of the density-broadening coefficient for Stokes-branch rotational Raman transitions in N2. The solid line indicates the most recent room-temperature ab initio calculations given in Ref. 12.

Fig. 2
Fig. 2

Wavelength dependence of the N2 polarizability anisotropy. Solid line is given by Eq. (3), which was derived with a fit to the data of Refs. 6, 8, and 9. Data of Refs. 2 and 15 were not used in the fit but are shown for comparison.

Fig. 3
Fig. 3

Temperature dependence of the plane-wave, steady-state Raman gain in N2 calculated from Eq. (1) for the high-density limit (ρ > 0.01 amagat). The pump and Stokes polarizations are linear and parallel.

Tables (1)

Tables Icon

Table 1 Temperature Dependence of Rotational Raman Linewidths, Fractional Population Differences, and Gain Coefficients for S Branch in N2a

Equations (4)

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g = 2 λ s 2 Δ N h ν s π Δ ν σ Ω ,
σ Ω = 2 15 ( 2 π ν s c ) 2 ( J + 1 ) ( J + 2 ) ( 2 J + 1 ) ( 2 J + 3 ) γ 2 ,
γ ( ν ) = α s | | ( ν i | | 2 ν i | | 2 - ν 2 ) - α s ( ν i 2 ν i 2 - ν 2 ) ,
2 3 ( n - 1 ) n 2 - 1 n 2 + 2 = 4 π N 9 × [ α s ( 2 ν i 2 ν i 2 - ν 2 ) + α s | | ( ν i | | 2 ν i | | 2 - ν 2 ) ] ,

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