Abstract

A model for stimulated Raman scattering in the atmosphere is described for the pure rotational transitions in N2. This model accounts for the wavelength dependence of the N2 polarizability anisotropy, altitude and seasonal temperature variations in the atmosphere, and the O2 foreign-gas density broadening. This information is used to calculate the steady-state plane-wave Raman gain profile over the lower 100 km of the atmosphere. Over altitudes of 0–40 km, temperature variations produce 30% changes in the gain coefficients of 1 km−1 cm2 MW−1 for the strongest lines at Stokes wavelengths of 350 nm.

© 1987 Optical Society of America

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References

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  1. V. E. Zuev, Laser Beams in the Atmosphere (Consultants Bureau, New York, 1982).
    [CrossRef]
  2. M. A. Henesian, C. D. Swift, J. R. Murray, “Stimulated Rotational Raman Scattering in Long Air Paths,” Opt. Lett. 10, 565 (1985).
    [CrossRef] [PubMed]
  3. G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and Wavelength Dependence of the Rotational Raman Gain Coefficient in N2,” Opt. Lett. 11, 348 (1986).
    [CrossRef] [PubMed]
  4. M. Rokni, A. Flusberg, “Stimulated Rotational Raman Scattering in the Atmosphere,” IEEE. J. Quantum Electron. QE-22, 3671 (1986);see correction to be published in IEEE J. Quantum Electron.QE-23, 000 (July1987).
  5. P. M. Banks, G. Kockarts, Aeronomy (Academic, New York, 1973), Chap. 3.
  6. A. P. Hickman, J. A. Paisner, W. K. Bischel, “Theory of Multiwave Propagaton and Frequency Conversion in a Raman Medium,” Phys. Rev. A 33, 1788 (1986).
    [CrossRef] [PubMed]
  7. U.S. Standard Atmosphere, 1976, NOAA-S/T 76 1562 (National Oceanic and Atmospheric Administration, Washington DC, 1976).
  8. K. P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979), p. 420.
  9. P. L. Varghese, R. K. Hanson, “Collisional Narrowing Effects on Spectral Line Shapes Measured at High Resolution,” Appl. Opt. 23, 2376 (1984).
    [CrossRef] [PubMed]
  10. G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and Density Dependence of the Linewidths and Lineshifts of the Rotational Raman Lines in N2 and H2,” Phys. Rev. A 34, 1944 (1986).
    [CrossRef] [PubMed]
  11. A. Flusberg, “Stimulated Raman Scattering in the Presence of Strong Dispersion,” Opt. Commun. 38, 427 (1981).
    [CrossRef]
  12. E. A. Stappaerts, W. H. Long, H. Komine, “Gain Enhancement in Raman Amplifiers with Broadband Pumping,” Opt. Lett. 5, 4 (1980).
    [CrossRef] [PubMed]
  13. W. R. Trutna, Y. K. Park, R. L. Byer, “The Dependence of Raman Gain on Pump Laser Bandwidth,” IEEE J. Quantum Electron. QE-15, 648 (1979).
    [CrossRef]
  14. A. Flusberg, D. Kroff, C. Duzy, “The Effect of Weak Dispersion on Stimulated Raman Scattering,” IEEE J. Quantum Electron. QE-21, 232 (1985).
    [CrossRef]
  15. K. Jammu, G.St. John, H. Welsh, “Pressure Broadening of the Rotational Raman Lines of Some Simple Gases,” Can. J. Phys. 44, 797 (1966).
    [CrossRef]
  16. W. K. Bischel, G. Black, “Wavelength Dependence of Raman Scattering Cross Sections from 200-600 NM,” in AIP Conference Proceedings, No. 100, Subseries on Optical Science and Engineering, No. 3, Excimer Lasers-1983, C. K. Rhodes, H. Esser, H. Pummer, Eds.; (AIP, New York, 1983).

1986 (4)

G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and Wavelength Dependence of the Rotational Raman Gain Coefficient in N2,” Opt. Lett. 11, 348 (1986).
[CrossRef] [PubMed]

M. Rokni, A. Flusberg, “Stimulated Rotational Raman Scattering in the Atmosphere,” IEEE. J. Quantum Electron. QE-22, 3671 (1986);see correction to be published in IEEE J. Quantum Electron.QE-23, 000 (July1987).

A. P. Hickman, J. A. Paisner, W. K. Bischel, “Theory of Multiwave Propagaton and Frequency Conversion in a Raman Medium,” Phys. Rev. A 33, 1788 (1986).
[CrossRef] [PubMed]

G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and Density Dependence of the Linewidths and Lineshifts of the Rotational Raman Lines in N2 and H2,” Phys. Rev. A 34, 1944 (1986).
[CrossRef] [PubMed]

1985 (2)

A. Flusberg, D. Kroff, C. Duzy, “The Effect of Weak Dispersion on Stimulated Raman Scattering,” IEEE J. Quantum Electron. QE-21, 232 (1985).
[CrossRef]

M. A. Henesian, C. D. Swift, J. R. Murray, “Stimulated Rotational Raman Scattering in Long Air Paths,” Opt. Lett. 10, 565 (1985).
[CrossRef] [PubMed]

1984 (1)

1981 (1)

A. Flusberg, “Stimulated Raman Scattering in the Presence of Strong Dispersion,” Opt. Commun. 38, 427 (1981).
[CrossRef]

1980 (1)

1979 (1)

W. R. Trutna, Y. K. Park, R. L. Byer, “The Dependence of Raman Gain on Pump Laser Bandwidth,” IEEE J. Quantum Electron. QE-15, 648 (1979).
[CrossRef]

1966 (1)

K. Jammu, G.St. John, H. Welsh, “Pressure Broadening of the Rotational Raman Lines of Some Simple Gases,” Can. J. Phys. 44, 797 (1966).
[CrossRef]

Banks, P. M.

P. M. Banks, G. Kockarts, Aeronomy (Academic, New York, 1973), Chap. 3.

Bischel, W. K.

A. P. Hickman, J. A. Paisner, W. K. Bischel, “Theory of Multiwave Propagaton and Frequency Conversion in a Raman Medium,” Phys. Rev. A 33, 1788 (1986).
[CrossRef] [PubMed]

G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and Wavelength Dependence of the Rotational Raman Gain Coefficient in N2,” Opt. Lett. 11, 348 (1986).
[CrossRef] [PubMed]

G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and Density Dependence of the Linewidths and Lineshifts of the Rotational Raman Lines in N2 and H2,” Phys. Rev. A 34, 1944 (1986).
[CrossRef] [PubMed]

W. K. Bischel, G. Black, “Wavelength Dependence of Raman Scattering Cross Sections from 200-600 NM,” in AIP Conference Proceedings, No. 100, Subseries on Optical Science and Engineering, No. 3, Excimer Lasers-1983, C. K. Rhodes, H. Esser, H. Pummer, Eds.; (AIP, New York, 1983).

Black, G.

W. K. Bischel, G. Black, “Wavelength Dependence of Raman Scattering Cross Sections from 200-600 NM,” in AIP Conference Proceedings, No. 100, Subseries on Optical Science and Engineering, No. 3, Excimer Lasers-1983, C. K. Rhodes, H. Esser, H. Pummer, Eds.; (AIP, New York, 1983).

Byer, R. L.

W. R. Trutna, Y. K. Park, R. L. Byer, “The Dependence of Raman Gain on Pump Laser Bandwidth,” IEEE J. Quantum Electron. QE-15, 648 (1979).
[CrossRef]

Duzy, C.

A. Flusberg, D. Kroff, C. Duzy, “The Effect of Weak Dispersion on Stimulated Raman Scattering,” IEEE J. Quantum Electron. QE-21, 232 (1985).
[CrossRef]

Dyer, M. J.

G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and Density Dependence of the Linewidths and Lineshifts of the Rotational Raman Lines in N2 and H2,” Phys. Rev. A 34, 1944 (1986).
[CrossRef] [PubMed]

G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and Wavelength Dependence of the Rotational Raman Gain Coefficient in N2,” Opt. Lett. 11, 348 (1986).
[CrossRef] [PubMed]

Flusberg, A.

M. Rokni, A. Flusberg, “Stimulated Rotational Raman Scattering in the Atmosphere,” IEEE. J. Quantum Electron. QE-22, 3671 (1986);see correction to be published in IEEE J. Quantum Electron.QE-23, 000 (July1987).

A. Flusberg, D. Kroff, C. Duzy, “The Effect of Weak Dispersion on Stimulated Raman Scattering,” IEEE J. Quantum Electron. QE-21, 232 (1985).
[CrossRef]

A. Flusberg, “Stimulated Raman Scattering in the Presence of Strong Dispersion,” Opt. Commun. 38, 427 (1981).
[CrossRef]

Hanson, R. K.

Henesian, M. A.

Herring, G. C.

G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and Wavelength Dependence of the Rotational Raman Gain Coefficient in N2,” Opt. Lett. 11, 348 (1986).
[CrossRef] [PubMed]

G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and Density Dependence of the Linewidths and Lineshifts of the Rotational Raman Lines in N2 and H2,” Phys. Rev. A 34, 1944 (1986).
[CrossRef] [PubMed]

Herzberg, G.

K. P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979), p. 420.

Hickman, A. P.

A. P. Hickman, J. A. Paisner, W. K. Bischel, “Theory of Multiwave Propagaton and Frequency Conversion in a Raman Medium,” Phys. Rev. A 33, 1788 (1986).
[CrossRef] [PubMed]

Huber, K. P.

K. P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979), p. 420.

Jammu, K.

K. Jammu, G.St. John, H. Welsh, “Pressure Broadening of the Rotational Raman Lines of Some Simple Gases,” Can. J. Phys. 44, 797 (1966).
[CrossRef]

John, G.St.

K. Jammu, G.St. John, H. Welsh, “Pressure Broadening of the Rotational Raman Lines of Some Simple Gases,” Can. J. Phys. 44, 797 (1966).
[CrossRef]

Kockarts, G.

P. M. Banks, G. Kockarts, Aeronomy (Academic, New York, 1973), Chap. 3.

Komine, H.

Kroff, D.

A. Flusberg, D. Kroff, C. Duzy, “The Effect of Weak Dispersion on Stimulated Raman Scattering,” IEEE J. Quantum Electron. QE-21, 232 (1985).
[CrossRef]

Long, W. H.

Murray, J. R.

Paisner, J. A.

A. P. Hickman, J. A. Paisner, W. K. Bischel, “Theory of Multiwave Propagaton and Frequency Conversion in a Raman Medium,” Phys. Rev. A 33, 1788 (1986).
[CrossRef] [PubMed]

Park, Y. K.

W. R. Trutna, Y. K. Park, R. L. Byer, “The Dependence of Raman Gain on Pump Laser Bandwidth,” IEEE J. Quantum Electron. QE-15, 648 (1979).
[CrossRef]

Rokni, M.

M. Rokni, A. Flusberg, “Stimulated Rotational Raman Scattering in the Atmosphere,” IEEE. J. Quantum Electron. QE-22, 3671 (1986);see correction to be published in IEEE J. Quantum Electron.QE-23, 000 (July1987).

Stappaerts, E. A.

Swift, C. D.

Trutna, W. R.

W. R. Trutna, Y. K. Park, R. L. Byer, “The Dependence of Raman Gain on Pump Laser Bandwidth,” IEEE J. Quantum Electron. QE-15, 648 (1979).
[CrossRef]

Varghese, P. L.

Welsh, H.

K. Jammu, G.St. John, H. Welsh, “Pressure Broadening of the Rotational Raman Lines of Some Simple Gases,” Can. J. Phys. 44, 797 (1966).
[CrossRef]

Zuev, V. E.

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

Appl. Opt. (1)

Can. J. Phys. (1)

K. Jammu, G.St. John, H. Welsh, “Pressure Broadening of the Rotational Raman Lines of Some Simple Gases,” Can. J. Phys. 44, 797 (1966).
[CrossRef]

IEEE J. Quantum Electron. (2)

W. R. Trutna, Y. K. Park, R. L. Byer, “The Dependence of Raman Gain on Pump Laser Bandwidth,” IEEE J. Quantum Electron. QE-15, 648 (1979).
[CrossRef]

A. Flusberg, D. Kroff, C. Duzy, “The Effect of Weak Dispersion on Stimulated Raman Scattering,” IEEE J. Quantum Electron. QE-21, 232 (1985).
[CrossRef]

IEEE. J. Quantum Electron. (1)

M. Rokni, A. Flusberg, “Stimulated Rotational Raman Scattering in the Atmosphere,” IEEE. J. Quantum Electron. QE-22, 3671 (1986);see correction to be published in IEEE J. Quantum Electron.QE-23, 000 (July1987).

Opt. Commun. (1)

A. Flusberg, “Stimulated Raman Scattering in the Presence of Strong Dispersion,” Opt. Commun. 38, 427 (1981).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (2)

G. C. Herring, M. J. Dyer, W. K. Bischel, “Temperature and Density Dependence of the Linewidths and Lineshifts of the Rotational Raman Lines in N2 and H2,” Phys. Rev. A 34, 1944 (1986).
[CrossRef] [PubMed]

A. P. Hickman, J. A. Paisner, W. K. Bischel, “Theory of Multiwave Propagaton and Frequency Conversion in a Raman Medium,” Phys. Rev. A 33, 1788 (1986).
[CrossRef] [PubMed]

Other (5)

U.S. Standard Atmosphere, 1976, NOAA-S/T 76 1562 (National Oceanic and Atmospheric Administration, Washington DC, 1976).

K. P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979), p. 420.

P. M. Banks, G. Kockarts, Aeronomy (Academic, New York, 1973), Chap. 3.

W. K. Bischel, G. Black, “Wavelength Dependence of Raman Scattering Cross Sections from 200-600 NM,” in AIP Conference Proceedings, No. 100, Subseries on Optical Science and Engineering, No. 3, Excimer Lasers-1983, C. K. Rhodes, H. Esser, H. Pummer, Eds.; (AIP, New York, 1983).

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

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Figures (6)

Fig. 1
Fig. 1

Temperature profiles used in the Raman gain calculations. Maximum variations are indicated by horizontal bars for summer and by shading for winter (from Ref. 5).

Fig. 2
Fig. 2

Raman gain vs altitude. The solid curves show (a) the peak, steady-state plane-wave Raman gain coefficient; (b) the population difference ΔN, and (c) the Raman linewidth (Voigt FWHM) as a function of altitude for S(8) in N2. The dashed curve in (a) shows the gain if the approximation, Δ ν T 2 = Δ ν G 2 + Δ ν L 2, is used in place of the Voigt calculation of (c). ΔνT, ΔνG, and ΔνL are the total, Gaussian, and Lorentzian linewidths, respectively.

Fig. 3
Fig. 3

Peak Raman gain coefficients for (a) the strongest transitions and (b) some of the weaker transitions as a function of altitude.

Fig. 4
Fig. 4

S(8) Raman gain coefficient (a) as a function of altitude for detunings of 0,10,100, and 800 MHz from the line center and (b) integrated (from 0 to 100 km in altitude) gain coefficient as a function of detuning.

Fig. 5
Fig. 5

S(8) peak Raman gain variations for typical variations in atmospheric temperatures.

Fig. 6
Fig. 6

Comparison of the temperature-independent model of Ref. 4 and the present temperature-dependent model of the atmospheric Raman gain coefficient for S(8).

Tables (3)

Tables Icon

Table I Parameters Used in the S(8) Gain Calculation for λS = 350 nm

Tables Icon

Table II Peak Raman Gain Coefficients (Integrated from Sea Level to 100 km) for Stokes Rotational Transitions of N2

Tables Icon

Table III Atmospheric Rotational Raman Gain Coefficient and Associated Parameters for the S(8) Line in N2 at λS = 350 nm

Equations (5)

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g = λ S 2 Δ N h ν S δ σ δ Ω f ( δ ν ) ,
σ Ω = 2 15 ( 2 π ν S c ) 4 ( J + 1 ) ( 2 J + 1 ) J + 2 ) ( 2 J + 3 ) γ 2
Δ N = N ( J ) ( 2 J + 1 2 J + 1 ) N ( J ) .
Δ ν T = ( Δ ν L 2 + Δ ν G 2 ) 1 / 2 .
I s = I N exp ( I p g ( z ) dz ) ,

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