Abstract

Predicted spectral linewidths have been computed as a function of the laser and physical parameters of a pulsed high-gain three-level multimode self-terminating laser. In particular, the values of the parameters that yield minimum widths have been obtained because of their applications in the fields of holography and lidar. The model previously developed by the author for the cuprous chloride laser and the approximate parametric values found are used as a basis for these computations, since this laser combines visible radiation, high average power, and intrinsically narrow hyperfine lines. It is found that a temporal minimum width occurs prior to termination of the laser pulse for all parameter combinations. This temporal minimum width increases with increased temperature and Cu density, decreases with increased electron-excitation pumping rate from the ground to the upper excited state, and is virtually independent of the homogeneous FWHM. Quantitative relations between the coherence length and the spectral linewidth are derived for several waveforms.

© 1984 Optical Society of America

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References

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  1. W. C. Kreye, F. L. Roesler, Appl. Opt. 22, 927 (1983).
    [CrossRef] [PubMed]
  2. A. A. Isaev, Sov. J. Quantum Electron. 10, 336 (1980).
    [CrossRef]
  3. M. C. Gokay, J. S. Harris, IEEE J. Quantum Electron. QE-18, 154 (1982); K. I. Zemskov et al.Sov. J. Quantum Electron. 8, 245 (1978).
    [CrossRef]
  4. E. W. Eloranta, F. L. Roesler, J. T. Sroga, “The High Spectral Resolution LIDAR,” in Optical and Laser Remote Sensing, D. K. Killinger, A. Mooradian, Eds. (Springer, Berlin, 1983).
  5. N. M. Nerheim, A. M. Bhanji, G. R. Russell, IEEE J. Quantum Electron. QE-14, 686 (1978).
    [CrossRef]
  6. L. W. Casperson, J. Appl. Phys. 47, 4563 (1976).
    [CrossRef]
  7. A. Ludmirsky, Laser Focus 19, 20 (1983).
  8. A. Bloom, Gas Lasers (Wiley, New York, 1968), p. 147.
  9. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), p. 192.
  10. H. H. Hopkins, “The Theory of Coherence and Its Applications,” in Advanced Optical Techniques, A. Van Heel, Ed. (North-Holland, Amsterdam, 1967).
  11. A. K. Ghatak, An Introduction to Modern Optics (McGraw-Hill, New York, 1972), p. 194.
  12. P. P. Gerke, Yu. N. Denisyuk, V. I. Lokshin, Sov. J. Opt. Technol. 35, 437 (1968).
  13. J. Ondra, Feingeraetetechnik 27, 106 (1978).
  14. L. Allen, Principles of Gas Lasers (Plenum, New York, 1967), pp. 119, 122; L. Mandel, in Progress in Optics, Vol. 2, E. Wolf, Ed. (North-Holland, Amsterdam, 1963), pp. 187–190.
    [CrossRef]
  15. H. C. Kuhn, Atomic Spectra (Academic, New York, 1969), p. 62.
  16. D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, N.J., 1951), p. 60.
  17. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), pp. 320–323.
  18. R. Chimenti, Appl. Opt. 7, 2142 (1968).
    [CrossRef] [PubMed]

1983 (2)

1982 (1)

M. C. Gokay, J. S. Harris, IEEE J. Quantum Electron. QE-18, 154 (1982); K. I. Zemskov et al.Sov. J. Quantum Electron. 8, 245 (1978).
[CrossRef]

1980 (1)

A. A. Isaev, Sov. J. Quantum Electron. 10, 336 (1980).
[CrossRef]

1978 (2)

J. Ondra, Feingeraetetechnik 27, 106 (1978).

N. M. Nerheim, A. M. Bhanji, G. R. Russell, IEEE J. Quantum Electron. QE-14, 686 (1978).
[CrossRef]

1976 (1)

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

1968 (2)

P. P. Gerke, Yu. N. Denisyuk, V. I. Lokshin, Sov. J. Opt. Technol. 35, 437 (1968).

R. Chimenti, Appl. Opt. 7, 2142 (1968).
[CrossRef] [PubMed]

Allen, L.

L. Allen, Principles of Gas Lasers (Plenum, New York, 1967), pp. 119, 122; L. Mandel, in Progress in Optics, Vol. 2, E. Wolf, Ed. (North-Holland, Amsterdam, 1963), pp. 187–190.
[CrossRef]

Bhanji, A. M.

N. M. Nerheim, A. M. Bhanji, G. R. Russell, IEEE J. Quantum Electron. QE-14, 686 (1978).
[CrossRef]

Bloom, A.

A. Bloom, Gas Lasers (Wiley, New York, 1968), p. 147.

Bohm, D.

D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, N.J., 1951), p. 60.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), pp. 320–323.

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), p. 192.

Casperson, L. W.

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

Chimenti, R.

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), p. 192.

Denisyuk, Yu. N.

P. P. Gerke, Yu. N. Denisyuk, V. I. Lokshin, Sov. J. Opt. Technol. 35, 437 (1968).

Eloranta, E. W.

E. W. Eloranta, F. L. Roesler, J. T. Sroga, “The High Spectral Resolution LIDAR,” in Optical and Laser Remote Sensing, D. K. Killinger, A. Mooradian, Eds. (Springer, Berlin, 1983).

Gerke, P. P.

P. P. Gerke, Yu. N. Denisyuk, V. I. Lokshin, Sov. J. Opt. Technol. 35, 437 (1968).

Ghatak, A. K.

A. K. Ghatak, An Introduction to Modern Optics (McGraw-Hill, New York, 1972), p. 194.

Gokay, M. C.

M. C. Gokay, J. S. Harris, IEEE J. Quantum Electron. QE-18, 154 (1982); K. I. Zemskov et al.Sov. J. Quantum Electron. 8, 245 (1978).
[CrossRef]

Harris, J. S.

M. C. Gokay, J. S. Harris, IEEE J. Quantum Electron. QE-18, 154 (1982); K. I. Zemskov et al.Sov. J. Quantum Electron. 8, 245 (1978).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, “The Theory of Coherence and Its Applications,” in Advanced Optical Techniques, A. Van Heel, Ed. (North-Holland, Amsterdam, 1967).

Isaev, A. A.

A. A. Isaev, Sov. J. Quantum Electron. 10, 336 (1980).
[CrossRef]

Kreye, W. C.

Kuhn, H. C.

H. C. Kuhn, Atomic Spectra (Academic, New York, 1969), p. 62.

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), p. 192.

Lokshin, V. I.

P. P. Gerke, Yu. N. Denisyuk, V. I. Lokshin, Sov. J. Opt. Technol. 35, 437 (1968).

Ludmirsky, A.

A. Ludmirsky, Laser Focus 19, 20 (1983).

Nerheim, N. M.

N. M. Nerheim, A. M. Bhanji, G. R. Russell, IEEE J. Quantum Electron. QE-14, 686 (1978).
[CrossRef]

Ondra, J.

J. Ondra, Feingeraetetechnik 27, 106 (1978).

Roesler, F. L.

W. C. Kreye, F. L. Roesler, Appl. Opt. 22, 927 (1983).
[CrossRef] [PubMed]

E. W. Eloranta, F. L. Roesler, J. T. Sroga, “The High Spectral Resolution LIDAR,” in Optical and Laser Remote Sensing, D. K. Killinger, A. Mooradian, Eds. (Springer, Berlin, 1983).

Russell, G. R.

N. M. Nerheim, A. M. Bhanji, G. R. Russell, IEEE J. Quantum Electron. QE-14, 686 (1978).
[CrossRef]

Sroga, J. T.

E. W. Eloranta, F. L. Roesler, J. T. Sroga, “The High Spectral Resolution LIDAR,” in Optical and Laser Remote Sensing, D. K. Killinger, A. Mooradian, Eds. (Springer, Berlin, 1983).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), pp. 320–323.

Appl. Opt. (2)

Feingeraetetechnik (1)

J. Ondra, Feingeraetetechnik 27, 106 (1978).

IEEE J. Quantum Electron. (2)

N. M. Nerheim, A. M. Bhanji, G. R. Russell, IEEE J. Quantum Electron. QE-14, 686 (1978).
[CrossRef]

M. C. Gokay, J. S. Harris, IEEE J. Quantum Electron. QE-18, 154 (1982); K. I. Zemskov et al.Sov. J. Quantum Electron. 8, 245 (1978).
[CrossRef]

J. Appl. Phys. (1)

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

Laser Focus (1)

A. Ludmirsky, Laser Focus 19, 20 (1983).

Sov. J. Opt. Technol. (1)

P. P. Gerke, Yu. N. Denisyuk, V. I. Lokshin, Sov. J. Opt. Technol. 35, 437 (1968).

Sov. J. Quantum Electron. (1)

A. A. Isaev, Sov. J. Quantum Electron. 10, 336 (1980).
[CrossRef]

Other (9)

E. W. Eloranta, F. L. Roesler, J. T. Sroga, “The High Spectral Resolution LIDAR,” in Optical and Laser Remote Sensing, D. K. Killinger, A. Mooradian, Eds. (Springer, Berlin, 1983).

A. Bloom, Gas Lasers (Wiley, New York, 1968), p. 147.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), p. 192.

H. H. Hopkins, “The Theory of Coherence and Its Applications,” in Advanced Optical Techniques, A. Van Heel, Ed. (North-Holland, Amsterdam, 1967).

A. K. Ghatak, An Introduction to Modern Optics (McGraw-Hill, New York, 1972), p. 194.

L. Allen, Principles of Gas Lasers (Plenum, New York, 1967), pp. 119, 122; L. Mandel, in Progress in Optics, Vol. 2, E. Wolf, Ed. (North-Holland, Amsterdam, 1963), pp. 187–190.
[CrossRef]

H. C. Kuhn, Atomic Spectra (Academic, New York, 1969), p. 62.

D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, N.J., 1951), p. 60.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), pp. 320–323.

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Figures (4)

Fig. 1
Fig. 1

Computed spectral-line shapes I t r ( n ) ( σ ) transmitted by the modeled CuCl oscillator (from Ref. 1). Each curve corresponds to an increasing number n of fully amplified RTs made by the leading edge. The interval between each curve is 12 nsec, which represents one RT between the 180-cm spaced mirrors. The laser parameters are given under Fig. 2, except that T = 660 K.

Fig. 2
Fig. 2

Curves showing the variation of the HWHM(min) with temperature ⊙ and the Doppler width ⊡. The following CuCl laser parameters hold: g0 = 0.0435 cm−1; Δσh = 10.08 mK; l = 100 cm; s = 1 × 10−6 AIU−1; ψ = 7 AIU.

Fig. 3
Fig. 3

Curves depicting the variations of the HWHM(min) with the unsaturated gain g0 (—) and the dimensionless parameter (g0l) (- - - -), where the values of S13, A32, and S34 are invariant along each curve. The three upper solid curves correspond to three different values of S13 (nsec−1) given to the right of the curves, and for all three curves l = 100 cm. The values of s and ψ used in the computations are based upon the value of S13 and the assumptions that S13S34 and A32 = 0.0018 nsec−1. For the dotted curve, S13 = 0.010 nsec−1. For the upper four curves, T = 660 K. Each plotted HWHM(min) is obtained by a quadratic fitting of the three HWHM(n) values, which correspond to the three discrete number of RTs producing the smallest values of the HWHM. The numbers in parentheses refer to the nearest number of whole RTs, where (0) corresponds to amplified spontaneous-emission radiation whose leading edge has not made a full RT. The lowest curve represents the dependence of the HWHM(min) upon g0 for T = 150 K and l = 100 cm.

Fig. 4
Fig. 4

Computed variations of the HWHM(min) (—) and the corresponding peak transmitted intensity I t r ( n ) ( 0 ) (- - - -) with the excitation pumping rate S13. The dimensionless ratio S13/A32 provides a generalized coordinate system. The quantities to the right of the curves equal the value of the term Ω n ˜ 1 0 A 32 λ 2 / ( 2 c 8 π ). Thus each curve is an isodensity plot for a fixed A32. For these computations (r/L)2 = 1.15 × 10−4. The lowest value of Ω corresponds to the parameters associated with the low-power CuCl oscillator.

Equations (11)

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g 0 = 1 ( 2 + A 32 / S 13 ) · n ˜ 1 0 A 32 λ 2 2 c 8 π ,
Ω n ˜ 1 0 A 32 λ 2 / ( 2 c 8 π )
s · ψ = A 32 S 13 ( r L ) 2 8 π ,
L S = c T = c / Δ ν S .
Δ ν G = 2 1 / 2 4 ln 2 / ( 2 π Δ τ ) .
L G = c T = 3 c 2 1 / 2 4 ln 2 / ( 2 π Δ ν G ) = 1.87 c / Δ ν G .
L L = c T = ( 1 / 2 π ) / Δ ν L = 0.159 / Δ ν L .
R [ E ( t ) ] sin [ Δ ν B π ( t - t 0 ) ] t - t 0 cos [ ν 0 2 π ( t - t 0 ) ] .
L B = c T = 2 c / Δ ν B .
V ( p , Δ σ ) - I ( σ , Δ σ ) cos ( 2 π σ p ) d σ ,
V ( p , L ) = exp ( - 18 · ln 2 p 2 / L 2 ) .

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