Abstract

The dynamics of transverse mode formation time in positive-branch unstable resonators with low magnification (M = 1.32) and typical Fresnel numbers (279 < NT < 2700) used in high-energy lasers has been investigated. The objective was to observe the far-field intensity distribution from the onset of pumping to the settled steady-state diffraction-limited pattern. The research consisted of an experimental and numerical analysis. The experimental measurements of mode formation time were with a pulsed XeF laser having centered resonator optics. Mode formation was deduced from observation of the far field. The analytical effort consisted of a fast Fourier transform wave optics code which modeled the far-field pattern evolution. Results agree with temporal mode formation geometrical predictions of Ananev when laser saturation is achieved around this time.

© 1984 Optical Society of America

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References

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  1. K. I. Zemskov et al., Sov. J. Quantum Electron. 4, 474 (1974).
    [CrossRef]
  2. B. K. Deka, P. E. Dyer, Opt. Commun. 18, 462 (1976).
    [CrossRef]
  3. R. S. Hargrove, R. Grove, T. Kan, IEEE J. Quantum Electron. QE-15, 1228 (1979).
    [CrossRef]
  4. Y. A. Ananev, Sov. J. Quantum Electron. 5, 615 (1975).
    [CrossRef]
  5. J. Goldhar, W. R. Rapoport, J. R. Murray, IEEE J. Quantum Electron. QE-16, 235 (1980).
    [CrossRef]
  6. B. K. Deka, P. E. Dyer, IEEE J. Quantum Electron. QE-14, 661 (1978).
    [CrossRef]
  7. R. W. Jones, “Transverse Mode Formation in Positive Branch Unstable Resonators,” Dissertation published at the University of Alabama in Hunstville (1983).
  8. R. W. Jones, Phys. Lett. A 93, 472 (1983).
    [CrossRef]
  9. A. E. Siegman, Appl. Opt. 13, 353 (1974).
    [CrossRef] [PubMed]
  10. W. W. Rigrod, J. Appl. Phys. 34, 2602 (1963).
    [CrossRef]
  11. J. F. Perkins, R. A. Shatas, Appl. Phys. 9, 343 (1976).
    [CrossRef]
  12. P. Horwitz, J. Opt. Soc. Am. 63, 1528 (1973).
    [CrossRef]
  13. R. W. Jones, J. F. Perkins, C. C. Shih, “Wave Optics Investigations of Transverse Mode Formation,” Report TR-RH-82-4, U.S. Army Missile Command (Mar.1982).

1983 (1)

R. W. Jones, Phys. Lett. A 93, 472 (1983).
[CrossRef]

1980 (1)

J. Goldhar, W. R. Rapoport, J. R. Murray, IEEE J. Quantum Electron. QE-16, 235 (1980).
[CrossRef]

1979 (1)

R. S. Hargrove, R. Grove, T. Kan, IEEE J. Quantum Electron. QE-15, 1228 (1979).
[CrossRef]

1978 (1)

B. K. Deka, P. E. Dyer, IEEE J. Quantum Electron. QE-14, 661 (1978).
[CrossRef]

1976 (2)

B. K. Deka, P. E. Dyer, Opt. Commun. 18, 462 (1976).
[CrossRef]

J. F. Perkins, R. A. Shatas, Appl. Phys. 9, 343 (1976).
[CrossRef]

1975 (1)

Y. A. Ananev, Sov. J. Quantum Electron. 5, 615 (1975).
[CrossRef]

1974 (2)

K. I. Zemskov et al., Sov. J. Quantum Electron. 4, 474 (1974).
[CrossRef]

A. E. Siegman, Appl. Opt. 13, 353 (1974).
[CrossRef] [PubMed]

1973 (1)

1963 (1)

W. W. Rigrod, J. Appl. Phys. 34, 2602 (1963).
[CrossRef]

Ananev, Y. A.

Y. A. Ananev, Sov. J. Quantum Electron. 5, 615 (1975).
[CrossRef]

Deka, B. K.

B. K. Deka, P. E. Dyer, IEEE J. Quantum Electron. QE-14, 661 (1978).
[CrossRef]

B. K. Deka, P. E. Dyer, Opt. Commun. 18, 462 (1976).
[CrossRef]

Dyer, P. E.

B. K. Deka, P. E. Dyer, IEEE J. Quantum Electron. QE-14, 661 (1978).
[CrossRef]

B. K. Deka, P. E. Dyer, Opt. Commun. 18, 462 (1976).
[CrossRef]

Goldhar, J.

J. Goldhar, W. R. Rapoport, J. R. Murray, IEEE J. Quantum Electron. QE-16, 235 (1980).
[CrossRef]

Grove, R.

R. S. Hargrove, R. Grove, T. Kan, IEEE J. Quantum Electron. QE-15, 1228 (1979).
[CrossRef]

Hargrove, R. S.

R. S. Hargrove, R. Grove, T. Kan, IEEE J. Quantum Electron. QE-15, 1228 (1979).
[CrossRef]

Horwitz, P.

Jones, R. W.

R. W. Jones, Phys. Lett. A 93, 472 (1983).
[CrossRef]

R. W. Jones, “Transverse Mode Formation in Positive Branch Unstable Resonators,” Dissertation published at the University of Alabama in Hunstville (1983).

R. W. Jones, J. F. Perkins, C. C. Shih, “Wave Optics Investigations of Transverse Mode Formation,” Report TR-RH-82-4, U.S. Army Missile Command (Mar.1982).

Kan, T.

R. S. Hargrove, R. Grove, T. Kan, IEEE J. Quantum Electron. QE-15, 1228 (1979).
[CrossRef]

Murray, J. R.

J. Goldhar, W. R. Rapoport, J. R. Murray, IEEE J. Quantum Electron. QE-16, 235 (1980).
[CrossRef]

Perkins, J. F.

J. F. Perkins, R. A. Shatas, Appl. Phys. 9, 343 (1976).
[CrossRef]

R. W. Jones, J. F. Perkins, C. C. Shih, “Wave Optics Investigations of Transverse Mode Formation,” Report TR-RH-82-4, U.S. Army Missile Command (Mar.1982).

Rapoport, W. R.

J. Goldhar, W. R. Rapoport, J. R. Murray, IEEE J. Quantum Electron. QE-16, 235 (1980).
[CrossRef]

Rigrod, W. W.

W. W. Rigrod, J. Appl. Phys. 34, 2602 (1963).
[CrossRef]

Shatas, R. A.

J. F. Perkins, R. A. Shatas, Appl. Phys. 9, 343 (1976).
[CrossRef]

Shih, C. C.

R. W. Jones, J. F. Perkins, C. C. Shih, “Wave Optics Investigations of Transverse Mode Formation,” Report TR-RH-82-4, U.S. Army Missile Command (Mar.1982).

Siegman, A. E.

Zemskov, K. I.

K. I. Zemskov et al., Sov. J. Quantum Electron. 4, 474 (1974).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. (1)

J. F. Perkins, R. A. Shatas, Appl. Phys. 9, 343 (1976).
[CrossRef]

IEEE J. Quantum Electron. (3)

R. S. Hargrove, R. Grove, T. Kan, IEEE J. Quantum Electron. QE-15, 1228 (1979).
[CrossRef]

J. Goldhar, W. R. Rapoport, J. R. Murray, IEEE J. Quantum Electron. QE-16, 235 (1980).
[CrossRef]

B. K. Deka, P. E. Dyer, IEEE J. Quantum Electron. QE-14, 661 (1978).
[CrossRef]

J. Appl. Phys. (1)

W. W. Rigrod, J. Appl. Phys. 34, 2602 (1963).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

B. K. Deka, P. E. Dyer, Opt. Commun. 18, 462 (1976).
[CrossRef]

Phys. Lett. A (1)

R. W. Jones, Phys. Lett. A 93, 472 (1983).
[CrossRef]

Sov. J. Quantum Electron. (2)

K. I. Zemskov et al., Sov. J. Quantum Electron. 4, 474 (1974).
[CrossRef]

Y. A. Ananev, Sov. J. Quantum Electron. 5, 615 (1975).
[CrossRef]

Other (2)

R. W. Jones, “Transverse Mode Formation in Positive Branch Unstable Resonators,” Dissertation published at the University of Alabama in Hunstville (1983).

R. W. Jones, J. F. Perkins, C. C. Shih, “Wave Optics Investigations of Transverse Mode Formation,” Report TR-RH-82-4, U.S. Army Missile Command (Mar.1982).

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Figures (7)

Fig. 1
Fig. 1

Experimental XeF far-field mode formation configuration.

Fig. 2
Fig. 2

Selected mode formation run (shot number 3/5–1).

Fig. 3
Fig. 3

Summary of runs for the XeF resonator.

Fig. 4
Fig. 4

I/I0 statistics of 20 runs for CO2 with loaded cavity, M = 1.32, NT = 279.

Fig. 5
Fig. 5

(θD)/λ statistics of 20 runs for CO2 with loaded cavity, M = 1.32, NT = 279.

Fig. 6
Fig. 6

I/I0 statistics of 15 runs for XeF with loaded cavity and vignetting, M = 1.32, NT = 2700.

Fig. 7
Fig. 7

(θD)/λ statistics of 15 runs for XeF with loaded cavity and vignetting M = 1.32, NT = 2700.

Tables (1)

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Table I Laser System Parameters

Equations (2)

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n = ln ( a 2 / λ f 1 ) ln ( M ) ,
τ = 2 n L c = 2 L ln ( a 2 / λ f 1 ) c ln ( M ) ,

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