Abstract

Time-averaged spectral line shapes of the a hyperfine component of the Cul 5782-Å line (2D3/22P1/2) from a pulsed high-gain cuprous chloride (CuCl) laser are measured with a high-resolution (±1 mK) Fabry-Perot interferometer. Four operational modes are studied: (1) high-power oscillator; (2) low-power oscillator; (3) oscillator–amplifier combination; and (4) spontaneous-emission source. Two models are used for the oscillator and amplifier: a quasi-steady-state approximation and a gain-switched pulsed model, respectively. The corresponding computed interferograms are fitted to the experimental ones by varying the unsaturated gain g0, saturation and spontaneous-emission parameters, and the temperature and homogeneous FWHM. Use of a common discharge tube enables us to achieve a one–one correspondence between experimental data and laser parameters, whose resulting values agree with those obtained by other methods. Typically, the total average spectral output of the high-power oscillator is ~6.7 W and its g0 value is 0.15 cm−1.

© 1983 Optical Society of America

Full Article  |  PDF Article

Corrections

W. C. Kreye and F. L. Roesler, "High-resolution line-shape analyses of the pulsed cuprous chloride-laser oscillator and amplifier: errata," Appl. Opt. 22, 2407-2407 (1983)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-22-16-2407

References

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  1. A. Szöke, A. Javan, Phys. Rev. Lett. 10, 521 (1963).
    [CrossRef]
  2. P. W. Smith, J. Appl. Phys. 37, 2089 (1966).
    [CrossRef]
  3. D. F. Hotz, Appl. Opt. 4, 527 (1965).
    [CrossRef]
  4. R. J. L. Chimenti, The Copper Vapor Laser, Ph.D. Thesis, Polytechnic Institute of New York, Brooklyn, N.Y. (1972).
  5. I. Smilanski, L. A. Levin, G. Erez, Opt. Lett. 5, 93 (1980).
    [CrossRef] [PubMed]
  6. E. A. Ballik, W. R. Bennett, G. N. Mercer, Appl. Phys. Lett. 8, 214 (1966).
    [CrossRef]
  7. J. D. Litke, J. Quant. Spectrosc. Radiat. Transfer. 17, 411 (1977).
    [CrossRef]
  8. N. M. Nerheim et al., IEEE J. Quantum Electron. QE-14, 686 (1978).
    [CrossRef]
  9. N. M. Nerheim, J. Appl. Phys. 48, 1186 (1977).
    [CrossRef]
  10. N. M. Nerheim, C. J. Chen, Visible Wavelength Laser Development Final Report, Phase I (Jet Propulsion Laboratory, for DARPA 2756, 1975).
  11. K. G. Harstad, IEEE J. Quantum Electron. QE-16, 550 (1980).
    [CrossRef]
  12. W. T. Walter, N. Solimene, G. M. Kull, in Proceedings, International Conference on Lasers, V. S. Corcoran, Ed. (STS, Mclean, Va., 1980), p. 148.
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    [CrossRef]
  14. E. I. Gordon et al., in Proceedings, Symposium on Optical Lasers (Polytechnic Press, Brooklyn, N.Y., 1963), pp. 309–319.
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    [CrossRef]
  16. L. W. Casperson, Appl. Opt. 14, 299 (1975).
    [CrossRef] [PubMed]
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    [CrossRef]
  18. A. Maitland, M. H. Dunn, Laser Physics (North-Holland, Amsterdam, 1969), Chap. 8.
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    [CrossRef]
  20. L. W. Casperson, J. Appl. Phys. 47, 4563 (1976).
    [CrossRef]
  21. A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (University P., New York, 1961), pp. 94 and 95.
  22. N. Kogelnik, A. Yariv, Proc. IEEE, 52, 165 (1964).
    [CrossRef]
  23. L. W. Casperson, J. Appl. Phys. 47, 4555 (1976).
    [CrossRef]
  24. G. P. Agrawal, M. Lax, J. Opt. Soc. Am. 71, 515 (1981).
    [CrossRef]
  25. W. W. Rigrod, J. Appl. Phys. 36, 2487 (1965).
    [CrossRef]
  26. W. Fischer, H. Huhnermann, K. J. Kollath, Z. Phys. 194, 417 (1966).
    [CrossRef]
  27. Yu. I. Malakhov, Opt. Spectrosc. (USSR) 44, 125 (1978).
  28. H. R. Griem, Plasma Spectroscopy (McGraw-Hill, New York, 1964).
  29. H. R. Griem, Spectral Line Broadening by Plasmas (Academic, New York, 1974).
  30. S. Trajmar et al., J. Phys. B 10, 3323 (1977).
    [CrossRef]
  31. E. Sovero et al., J. Appl. Phys. 47, 4538 (1976).
    [CrossRef]
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    [CrossRef]
  33. C. Corliss, W. R. Bozman, Experimental Transition Probabilities for Spectral Lines of Seventy Elements, Natl. Bur. Stand. (U.S.) Monogr. 53 (1962).
  34. E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (University P., Cambridge, 1964), p. 98.
  35. A. U. Hazi, in Proceedings, Thirty-Third Gaseous Electronics Conference, Norman, Okla., 1980.

1981 (2)

M. J. Kushner, IEEE J. Quantum Electron. QE-17, 1555 (1981).
[CrossRef]

G. P. Agrawal, M. Lax, J. Opt. Soc. Am. 71, 515 (1981).
[CrossRef]

1980 (2)

K. G. Harstad, IEEE J. Quantum Electron. QE-16, 550 (1980).
[CrossRef]

I. Smilanski, L. A. Levin, G. Erez, Opt. Lett. 5, 93 (1980).
[CrossRef] [PubMed]

1978 (2)

N. M. Nerheim et al., IEEE J. Quantum Electron. QE-14, 686 (1978).
[CrossRef]

Yu. I. Malakhov, Opt. Spectrosc. (USSR) 44, 125 (1978).

1977 (4)

S. Trajmar et al., J. Phys. B 10, 3323 (1977).
[CrossRef]

C. S. Liu, D. W. Feldman, J. L. Pack, L. A. Weaver, IEEE J. Quantum Electron. QE-13, 744 (1977).
[CrossRef]

N. M. Nerheim, J. Appl. Phys. 48, 1186 (1977).
[CrossRef]

J. D. Litke, J. Quant. Spectrosc. Radiat. Transfer. 17, 411 (1977).
[CrossRef]

1976 (3)

L. W. Casperson, J. Appl. Phys. 47, 4563 (1976).
[CrossRef]

L. W. Casperson, J. Appl. Phys. 47, 4555 (1976).
[CrossRef]

E. Sovero et al., J. Appl. Phys. 47, 4538 (1976).
[CrossRef]

1975 (2)

L. W. Casperson, Appl. Opt. 14, 299 (1975).
[CrossRef] [PubMed]

L. W. Casperson, J. Appl. Phys. 46, 5194 (1975).
[CrossRef]

1972 (1)

L. W. Casperson, A. Yariv, IEEE J. Quantum Electron. QE-8, 80 (1972).
[CrossRef]

1970 (1)

1966 (3)

E. A. Ballik, W. R. Bennett, G. N. Mercer, Appl. Phys. Lett. 8, 214 (1966).
[CrossRef]

P. W. Smith, J. Appl. Phys. 37, 2089 (1966).
[CrossRef]

W. Fischer, H. Huhnermann, K. J. Kollath, Z. Phys. 194, 417 (1966).
[CrossRef]

1965 (2)

W. W. Rigrod, J. Appl. Phys. 36, 2487 (1965).
[CrossRef]

D. F. Hotz, Appl. Opt. 4, 527 (1965).
[CrossRef]

1964 (1)

N. Kogelnik, A. Yariv, Proc. IEEE, 52, 165 (1964).
[CrossRef]

1963 (1)

A. Szöke, A. Javan, Phys. Rev. Lett. 10, 521 (1963).
[CrossRef]

Agrawal, G. P.

Ballik, E. A.

E. A. Ballik, W. R. Bennett, G. N. Mercer, Appl. Phys. Lett. 8, 214 (1966).
[CrossRef]

Bennett, W. R.

E. A. Ballik, W. R. Bennett, G. N. Mercer, Appl. Phys. Lett. 8, 214 (1966).
[CrossRef]

Bozman, W. R.

C. Corliss, W. R. Bozman, Experimental Transition Probabilities for Spectral Lines of Seventy Elements, Natl. Bur. Stand. (U.S.) Monogr. 53 (1962).

Casperson, L. W.

L. W. Casperson, J. Appl. Phys. 47, 4563 (1976).
[CrossRef]

L. W. Casperson, J. Appl. Phys. 47, 4555 (1976).
[CrossRef]

L. W. Casperson, Appl. Opt. 14, 299 (1975).
[CrossRef] [PubMed]

L. W. Casperson, J. Appl. Phys. 46, 5194 (1975).
[CrossRef]

L. W. Casperson, A. Yariv, IEEE J. Quantum Electron. QE-8, 80 (1972).
[CrossRef]

Chen, C. J.

N. M. Nerheim, C. J. Chen, Visible Wavelength Laser Development Final Report, Phase I (Jet Propulsion Laboratory, for DARPA 2756, 1975).

Chimenti, R. J. L.

R. J. L. Chimenti, The Copper Vapor Laser, Ph.D. Thesis, Polytechnic Institute of New York, Brooklyn, N.Y. (1972).

Condon, E. U.

E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (University P., Cambridge, 1964), p. 98.

Corliss, C.

C. Corliss, W. R. Bozman, Experimental Transition Probabilities for Spectral Lines of Seventy Elements, Natl. Bur. Stand. (U.S.) Monogr. 53 (1962).

Dunn, M. H.

A. Maitland, M. H. Dunn, Laser Physics (North-Holland, Amsterdam, 1969), Chap. 8.

Erez, G.

Feldman, D. W.

C. S. Liu, D. W. Feldman, J. L. Pack, L. A. Weaver, IEEE J. Quantum Electron. QE-13, 744 (1977).
[CrossRef]

Fischer, W.

W. Fischer, H. Huhnermann, K. J. Kollath, Z. Phys. 194, 417 (1966).
[CrossRef]

Gordon, E. I.

E. I. Gordon et al., in Proceedings, Symposium on Optical Lasers (Polytechnic Press, Brooklyn, N.Y., 1963), pp. 309–319.

Griem, H. R.

H. R. Griem, Plasma Spectroscopy (McGraw-Hill, New York, 1964).

H. R. Griem, Spectral Line Broadening by Plasmas (Academic, New York, 1974).

Harstad, K. G.

K. G. Harstad, IEEE J. Quantum Electron. QE-16, 550 (1980).
[CrossRef]

Hazi, A. U.

A. U. Hazi, in Proceedings, Thirty-Third Gaseous Electronics Conference, Norman, Okla., 1980.

Hotz, D. F.

Huhnermann, H.

W. Fischer, H. Huhnermann, K. J. Kollath, Z. Phys. 194, 417 (1966).
[CrossRef]

Javan, A.

A. Szöke, A. Javan, Phys. Rev. Lett. 10, 521 (1963).
[CrossRef]

Kogelnik, N.

N. Kogelnik, A. Yariv, Proc. IEEE, 52, 165 (1964).
[CrossRef]

Kollath, K. J.

W. Fischer, H. Huhnermann, K. J. Kollath, Z. Phys. 194, 417 (1966).
[CrossRef]

Kreye, W. C.

Kull, G. M.

W. T. Walter, N. Solimene, G. M. Kull, in Proceedings, International Conference on Lasers, V. S. Corcoran, Ed. (STS, Mclean, Va., 1980), p. 148.

Kushner, M. J.

M. J. Kushner, IEEE J. Quantum Electron. QE-17, 1555 (1981).
[CrossRef]

Lax, M.

Levin, L. A.

Litke, J. D.

J. D. Litke, J. Quant. Spectrosc. Radiat. Transfer. 17, 411 (1977).
[CrossRef]

Liu, C. S.

C. S. Liu, D. W. Feldman, J. L. Pack, L. A. Weaver, IEEE J. Quantum Electron. QE-13, 744 (1977).
[CrossRef]

Maitland, A.

A. Maitland, M. H. Dunn, Laser Physics (North-Holland, Amsterdam, 1969), Chap. 8.

Malakhov, Yu. I.

Yu. I. Malakhov, Opt. Spectrosc. (USSR) 44, 125 (1978).

Mercer, G. N.

E. A. Ballik, W. R. Bennett, G. N. Mercer, Appl. Phys. Lett. 8, 214 (1966).
[CrossRef]

Mitchell, A. C. G.

A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (University P., New York, 1961), pp. 94 and 95.

Nerheim, N. M.

N. M. Nerheim et al., IEEE J. Quantum Electron. QE-14, 686 (1978).
[CrossRef]

N. M. Nerheim, J. Appl. Phys. 48, 1186 (1977).
[CrossRef]

N. M. Nerheim, C. J. Chen, Visible Wavelength Laser Development Final Report, Phase I (Jet Propulsion Laboratory, for DARPA 2756, 1975).

Pack, J. L.

C. S. Liu, D. W. Feldman, J. L. Pack, L. A. Weaver, IEEE J. Quantum Electron. QE-13, 744 (1977).
[CrossRef]

Rigrod, W. W.

W. W. Rigrod, J. Appl. Phys. 36, 2487 (1965).
[CrossRef]

Roesler, F. L.

Shortley, G. H.

E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (University P., Cambridge, 1964), p. 98.

Smilanski, I.

Smith, P. W.

P. W. Smith, J. Appl. Phys. 37, 2089 (1966).
[CrossRef]

Solimene, N.

W. T. Walter, N. Solimene, G. M. Kull, in Proceedings, International Conference on Lasers, V. S. Corcoran, Ed. (STS, Mclean, Va., 1980), p. 148.

Sovero, E.

E. Sovero et al., J. Appl. Phys. 47, 4538 (1976).
[CrossRef]

Szöke, A.

A. Szöke, A. Javan, Phys. Rev. Lett. 10, 521 (1963).
[CrossRef]

Trajmar, S.

S. Trajmar et al., J. Phys. B 10, 3323 (1977).
[CrossRef]

Walter, W. T.

W. T. Walter, N. Solimene, G. M. Kull, in Proceedings, International Conference on Lasers, V. S. Corcoran, Ed. (STS, Mclean, Va., 1980), p. 148.

Weaver, L. A.

C. S. Liu, D. W. Feldman, J. L. Pack, L. A. Weaver, IEEE J. Quantum Electron. QE-13, 744 (1977).
[CrossRef]

Yariv, A.

L. W. Casperson, A. Yariv, IEEE J. Quantum Electron. QE-8, 80 (1972).
[CrossRef]

N. Kogelnik, A. Yariv, Proc. IEEE, 52, 165 (1964).
[CrossRef]

Zemansky, M. W.

A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (University P., New York, 1961), pp. 94 and 95.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

E. A. Ballik, W. R. Bennett, G. N. Mercer, Appl. Phys. Lett. 8, 214 (1966).
[CrossRef]

IEEE J. Quantum Electron. (5)

N. M. Nerheim et al., IEEE J. Quantum Electron. QE-14, 686 (1978).
[CrossRef]

L. W. Casperson, A. Yariv, IEEE J. Quantum Electron. QE-8, 80 (1972).
[CrossRef]

K. G. Harstad, IEEE J. Quantum Electron. QE-16, 550 (1980).
[CrossRef]

M. J. Kushner, IEEE J. Quantum Electron. QE-17, 1555 (1981).
[CrossRef]

C. S. Liu, D. W. Feldman, J. L. Pack, L. A. Weaver, IEEE J. Quantum Electron. QE-13, 744 (1977).
[CrossRef]

J. Appl. Phys. (7)

E. Sovero et al., J. Appl. Phys. 47, 4538 (1976).
[CrossRef]

L. W. Casperson, J. Appl. Phys. 47, 4563 (1976).
[CrossRef]

L. W. Casperson, J. Appl. Phys. 47, 4555 (1976).
[CrossRef]

W. W. Rigrod, J. Appl. Phys. 36, 2487 (1965).
[CrossRef]

L. W. Casperson, J. Appl. Phys. 46, 5194 (1975).
[CrossRef]

N. M. Nerheim, J. Appl. Phys. 48, 1186 (1977).
[CrossRef]

P. W. Smith, J. Appl. Phys. 37, 2089 (1966).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. B (1)

S. Trajmar et al., J. Phys. B 10, 3323 (1977).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer. (1)

J. D. Litke, J. Quant. Spectrosc. Radiat. Transfer. 17, 411 (1977).
[CrossRef]

Opt. Lett. (1)

Opt. Spectrosc. (USSR) (1)

Yu. I. Malakhov, Opt. Spectrosc. (USSR) 44, 125 (1978).

Phys. Rev. Lett. (1)

A. Szöke, A. Javan, Phys. Rev. Lett. 10, 521 (1963).
[CrossRef]

Proc. IEEE (1)

N. Kogelnik, A. Yariv, Proc. IEEE, 52, 165 (1964).
[CrossRef]

Z. Phys. (1)

W. Fischer, H. Huhnermann, K. J. Kollath, Z. Phys. 194, 417 (1966).
[CrossRef]

Other (11)

H. R. Griem, Plasma Spectroscopy (McGraw-Hill, New York, 1964).

H. R. Griem, Spectral Line Broadening by Plasmas (Academic, New York, 1974).

A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (University P., New York, 1961), pp. 94 and 95.

C. Corliss, W. R. Bozman, Experimental Transition Probabilities for Spectral Lines of Seventy Elements, Natl. Bur. Stand. (U.S.) Monogr. 53 (1962).

E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (University P., Cambridge, 1964), p. 98.

A. U. Hazi, in Proceedings, Thirty-Third Gaseous Electronics Conference, Norman, Okla., 1980.

R. J. L. Chimenti, The Copper Vapor Laser, Ph.D. Thesis, Polytechnic Institute of New York, Brooklyn, N.Y. (1972).

N. M. Nerheim, C. J. Chen, Visible Wavelength Laser Development Final Report, Phase I (Jet Propulsion Laboratory, for DARPA 2756, 1975).

A. Maitland, M. H. Dunn, Laser Physics (North-Holland, Amsterdam, 1969), Chap. 8.

E. I. Gordon et al., in Proceedings, Symposium on Optical Lasers (Polytechnic Press, Brooklyn, N.Y., 1963), pp. 309–319.

W. T. Walter, N. Solimene, G. M. Kull, in Proceedings, International Conference on Lasers, V. S. Corcoran, Ed. (STS, Mclean, Va., 1980), p. 148.

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Figures (8)

Fig. 1
Fig. 1

Schematic drawing of the oscillator geometry for two RT oscillations, with the left-hand and right-hand mirrors designated by Rl and Rr, respectively. The detection system is on the right. The initiating incoherent and partially coherent parts of the ASE radiation are indicated by IASE,1(σ,l) and IASE,2(σ,z), respectively; the first coherent pass is I(1)(σ,z), etc., and the output from the second pass after the first amplified RT is I(2)(σ,0). The transmitted intensities which pass through the right-hand mirror after each even-numbered pass are listed on the right. Their sum, for this example, is the total transmitted intensity I t r ( 2 ) ( σ ).

Fig. 2
Fig. 2

Four peak-normalized interferograms of the hyperfine a component of the Cul 5782-Å line are plotted against wave number, where the circles are the experimental points from the red wings, and the solid lines are the computed modeled interferograms. The four operational modes are (1) spontaneous emission, (2) low-power oscillator, (3) high-power oscillator, and (4) low-power oscillator/high-power amplifier. The blue wings of the spontaneous-emission and high-power-oscillator interferograms exhibit isotope and hyperfine component overlapping, but the red wings are completely isolated. Also, the interferograms for the other two modes are completely symmetrical and isolated.

Fig. 3
Fig. 3

Normalized reduced tracing of the full hyperfine structure of the Cul 5782-Å line from the high-power oscillator for which natural Cu was used. However, even though the relative abundance of 63Cu is only 68%, this isotope forms the main contributions to the lasing components. The hyperfine component designation is taken from Ref. 26. The 65Cu a component is only measurable as a slight shoulder on the 63Cu line. For the low-power oscillator, only the a component from the 63Cu isotope is observed; and for the spontaneous-emission source, all the components from both isotopes are observed as overlapping lines (with the exception of the red wing of the 63Cu a component).

Fig. 4
Fig. 4

Four derived computed line shapes of the CuI 5782-Å (a) component are plotted as functions of the wave number. The sources are designated under Fig. 2. Two effects are illustrated here: (1) although the power outputs associated with the high-power oscillator and the oscillator–amplifier line shapes are about the same, the latter line shape is much narrower by ~9 mK: this indicates the effectiveness of the low-power oscillator/high-power amplifier combination in producing high spectral-density radiation; (2) a strong satellite appears on the oscillator–amplifier line shape which is not present on the low-power oscillator input; this is a real effect in the sense that Eq. (6) produces it. The lasing line shapes correspond to the transmitted signal of the fourth RT I t r ( 4 ) ( σ ) for the low-power oscillator, and I t r ( 3 ) ( σ ) for the high-power oscillator.

Fig. 5
Fig. 5

Plots of the estimated density distributions of n ˜ 3 / n ˜ 1 0 ( P 2 ) and ( n ˜ 2 / n ˜ 1 0 ) 5 / 7 ( D 2 ) as a function of time, where n ˜ 1 0 is the initial density of the Cu0 atoms. These densities are the values at the leading edge of wave, and they are obtained by numerical solutions of the rate Eqs. (B1)(B4) on the basis of the QSS approximation. The time origin corresponds to the onset of the power pulse. The curves have been smoothed to compensate for the somewhat artificial assumption that the formal oscillation begins abruptly at 12 nsec. The fitted parametric values are S12 = 0.0019 nsec−1 and S13 = 0.0152 nsec−1. These data correspond to the low-power oscillator. The plot of the total radiation field ΣI(n)(σ,t) is oscillatory because of the repeated large transmitted losses at the right-hand mirror. For these curves, σ = 0.

Fig. 6
Fig. 6

Plots of n ˜ 3 / n ˜ 1 0 , ( n ˜ 2 / n ˜ 1 0 ) 5 / 7, and peak-intensity sum against time for the high-power oscillator, where the definitions and assumptions are the same as for Fig. 5. We assume that after about three RTs, the depicted small approximate population inversion corresponds to the approach of the exact population inversion towards zero. Hence, the oscillation and lasing is assumed to terminate after three RTs. Note that considerable intensity is developed in the amplified spontaneous-emission phase before 12 nsec. S12 = 0.0006 nsec−1 and S13 = 0.0051 nsec−1. It is not certain whether the difference between the two S13 values for the two oscillators is real or due to the appoximations that are employed.

Fig. 7
Fig. 7

Plots of the computed 5782-Å (a) line shape which is transmitted from the low-power oscillator after each RT interval. The lowest curve corresponds to the ASE. The second curve corresponds to the transmission after one RT of full amplification, namely, I t r ( 1 ) ( σ ), etc These curves show the effects of the increased gain due to the increase in number of RTs on the intensity peak, the HWHM, and the X0.15 ratio.

Fig. 8
Fig. 8

Plots of the incremental gain g(0,z) and the peak intensity IASE,2(0,z) against z for the high- power oscillator, where g(0,z) is given by Eq (18) These curves demonstrate the strong general decrease of g(σ,z) with increasing gain distance (in the beam direction) and the corresponding cause, namely, the increase in the gain-saturation factor s·IASE,2(σ,z). The laser parameters differ slightly from those in Table II.

Tables (5)

Tables Icon

Table I Physical, Electric, and Optical Properties of the CuCl Oscillator and Amplifier Lasers

Tables Icon

Table II Parametric Values Which Yield the Computed Interferograms, Whose Relative Intensities, HWHM and X0.15 Best Fit the Corresponding Experimental Values, are Listed in Columns 2–4

Tables Icon

Table III Values of the Widths and X0.15 Ratios for the Computed Line Shapes Which are Based On the Best-Fit Parameters in Table IIa

Tables Icon

Table IV Summary of the Values of the Optical, Electronic, and Atomic Parameters for the Pulsed CuCl Laser Oscillator and Amplifier

Tables Icon

Table V Comparison of Experimental Values of the Fitted Parameters and Parameter Combinations With Corresponding Derived Values

Equations (31)

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

g ( σ , z , t ) 1 I ( σ , z , t ) d I ( σ , z , t ) d z = h ν 8 π [ B 32 ( σ , σ ) n ˜ 3 ( σ , z , t ) B 23 ( σ , σ ) n ˜ 2 ( σ , z , t ) ] d σ ,
d I ( σ , z , t ) d z I ( σ , z , t ) h ν 8 π s N ( σ , z , t ) 2 F ( σ ) / ( π Δ σ h ) , F ( σ ) exp ( σ 2 4 ln 2 / Δ σ D 2 ) 1 + ( σ σ ) 2 4 / Δ σ h 2 d σ ,
N ˜ ( σ , z , t ) N ( σ , z , t ) exp ( σ 2 4 ln 2 / Δ σ D 2 ) , S ( σ , z , t ) S ( z , t ) exp ( σ 2 4 ln 2 / Δ σ D 2 ) ,
N ( σ , z , t ) t S ( z , t ) 12 7 s N ( σ , z , t ) I ( σ , z , t ) ,
S ( z , τ ) = { N ˜ ( τ = 0 ) τ 3 exp ( τ τ 3 z c τ 3 + t ρ τ 3 ) , τ > t ρ z / c 0 , t ρ z / c > τ ,
I ( p ) ( σ , l , τ ) = I inp ( p ) ( σ ) exp [ 12 7 s I inp ( p ) ( σ ) · τ ] exp [ 12 7 s I inp ( p ) ( σ ) · τ ] + exp [ g 0 l 2 F ( σ ) / ( π Δ σ h ) ] 1 ,
I inp ( p ) ( σ ) = α · I t r ( p ) ( σ ) ,
n ˜ 3 ( σ , z ) = S 13 [ n ˜ 1 0 ( σ ) n ˜ 3 ( σ , z ) n ˜ 2 ( σ , z ) ] n ˜ 3 ( σ , z ) [ A 32 + S 34 + d σ B 32 ( σ , σ ) × I ( σ , z ) 8 π ] + n ˜ 2 ( σ , z ) [ d σ B 23 ( σ , σ ) I ( σ , z ) 8 π ] ,
[ n ˜ 3 ( σ , z ) n ˜ 2 ( σ , z ) 5 7 ] QSS S 13 n ˜ 1 0 exp ( σ 2 4 ln 2 / Δ σ D 2 ) ( A 32 + S 13 + S 34 ) + d σ B 32 ( σ , σ ) I ( σ , z ) / 8 π ,
d I ( σ , z ) d z g 0 I ( σ , z ) 2 F ( σ ) / ( π Δ σ h ) 1 + s I ( σ , z ) .
I ( σ , z ) = I ( σ , z 0 ) + 1 s { g 0 z · 2 F ( σ ) π Δ σ h ln [ I ( σ , z ) I ( σ , z 0 ) ] } ,
I ASE , 1 , exact ( σ , l ) = η 0 0 l d z · exp [ 0 l z g ( σ , z ) d z ] ,
I ASE , 1 , approx . ( σ , l ) = ψ 0 B { exp [ 0 l g ( σ , z ) d z ] 1 } ,
I ASE , 1 ( σ , l ) 1 s { g 0 l · 2 F ( σ ) π Δ σ h ( 1 s ψ 0 B ) · ln [ I ASE , 1 ( σ , l ) + ψ 0 B ψ 0 B ] } .
d I ( m ) ( σ , z ) d z = g 0 I ( m ) ( σ , z ) · 2 F ( σ ) / ( π Δ σ h ) 1 + s n = 0 m I ( n ) ( σ , z ) , m 0 , BC { I ( m ) ( σ , 0 ) = R r , eff · I ( m 1 ) ( σ , 0 ) m odd I ( m ) ( σ , l ) = R l · I ( m 1 ) ( σ , l ) , m even ,
I t r ( p ) ( σ ) = ( 1 R r ) · Σ m = 0,2 , 2 p I ( m ) ( σ , 0 ) , p = 0,1 .
I resp ( σ ) = p = 0,1 p upper I t r ( p ) ( σ ) ,
lim σ I ( p ) ( σ , l , τ ) | modif = 7 / ( 12 s τ ) .
η 0 s g 0 | theor = A 32 S ¯ 13 ( r L ) 2 2 F ( σ ) π Δ σ h .
S ¯ 13 | spectr = 0.010 ± 0.008 nsec 1 .
S ¯ 13 | kinet = 0.011 ± 0.006 nsec 1 .
B 32 A 32 10 9 λ 3 2 h c 2 ,
g 0 | theor = 1 8 π · S 13 n ˜ 1 0 ( A 32 + S 13 + S 34 ) · A 32 10 9 λ 2 2 c .
0.2 < g 0 | theor < 200 cm 1 .
g 0 | expt = 0.15 ± 0.04 cm 1 .
g 0 g 0 = N ˜ ( τ = 0 ) n ˜ 1 0 · A 32 + S 13 + S 34 S 13 .
g ( 0 , z ) = g 0 2 F ( 0 ) / ( π Δ σ h ) 1 + s I ASE , 2 ( 0 , z ) .
n ˜ 3 ( 0 , t ) = n ˜ 1 ( 0 , t ) S 13 + n ˜ 2 ( 0 , t ) [ B 23 8 π m I ( m ) ( 0 , t ) ] n ˜ 3 ( 0 , t ) [ A 32 + S 34 + B 32 8 π m I ( m ) ( 0 , t ) ] ,
n ˜ 2 ( 0 , t ) = n ˜ 1 ( 0 , t ) S 12 n ˜ 2 ( 0 , t ) [ B 23 8 π m I ( m ) ( 0 , t ) ] + n ˜ 3 ( 0 , t ) [ A 32 + B 32 8 π m I ( m ) ( 0 , t ) ] ,
n ˜ 1 ( 0 , t ) = n ˜ 1 ( 0 , t ) ( S 12 + S 13 ) ,
n ˜ 1 ( 0 , t ) n ˜ 1 0 exp ( S 13 t ) .

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