Abstract

The output of a laser-diode-pumped Nd:YAG laser with an intravcavity-doubling crystal exhibits large-amplitude fluctuations and longitudinal-mode instabilities. The results of an experimental and theoretical investigation of these instabilities are described. The instabilities arise from coupling of the longitudinal modes of the laser oscillator by sum-frequency generation in the nonlinear crystal. A rate-equation theory of a multilongitudinal-mode laser oscillator with an intracavity-doubling crystal is presented that includes terms modeling the sum-frequency and frequency-doubling processes.

© 1986 Optical Society of America

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References

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  1. T. Baer and M. S. Keirstead, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1985), paper ThZ1.
  2. J. E. Geusic, H. J. Levinstein, S. Singh, R. G. Smith, and L. G. Van Uitert, Appl. Phys. Lett. 12, 306 (1968); Appl. Phys. Lett. 13, 395 (1968).
    [CrossRef]
  3. R. G. Smith, IEEE J. Quantum Electron. QE-6, 215 (1970).
    [CrossRef]
  4. W. C. Culshaw, J. Kannelaud, and J. E. Peterson, IEEE J. Quantum Electron. QE-10, 253 (1974).
    [CrossRef]
  5. C. J. Kennedy and J. D. Barry, IEEE J. Quantum Electron. QE-10, 596 (1974).
    [CrossRef]
  6. J. D. Barry and C. J. Kennedy, J. Appl. Phys. 48, 2518 (1977).
    [CrossRef]
  7. V. D. Volosov, S. G. Karpenko, N. E. Kornienko, V. N. Krylov, A. A. Man’ko, and V. L. Strizhevskii, Sov. J. Quantum Electron. 5, 500 (1975), and references therein.
    [CrossRef]
  8. R. R. Rice, J. R. Teague, and J. E. Jackson, J. Appl. Phys. 49, 5750 (1978).
    [CrossRef]
  9. C. B. Hitz and L. M. Osterink, Appl. Phys. Lett. 18, 378 (1971).
    [CrossRef]
  10. J. Falk, IEEE J. Quantum Electron. QE-11, 21 (1975).
    [CrossRef]
  11. T. R. Gurski, Appl. Phys. Lett. 15, 5 (1969).
    [CrossRef]
  12. M. A. Karr, J. Appl. Phys. 42, 4517 (1971).
    [CrossRef]
  13. Available from Spectra Diode Labs, 3333 N. First Street, San Jose, Calif. 95134; Model 2420.
  14. F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, J. Appl. Phys. 47, 4980 (1976).
    [CrossRef]
  15. Available from Airton Solid State Materials, 200 E. Hanover Avenue, Morris Plains, N.J. 07950.
  16. P. Mandel and T. Erneux, in Third New Zealand Symposium on Laser Physics, J. P. Harvey and D. F. Walls, eds. (Springer-Verlag, New York, 1983), p. 132; P. Mandel and X. G. Wu, J. Opt. Soc. Am. B (to be published).
  17. R. R. Rice, J. R. Teague, and J. E. Jackson, J. Appl. Phys. B 6, 2716 (1975).
  18. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  19. M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), Chap. 9, p. 115.
  20. W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1976), Chap. 8, p. 397.
    [CrossRef]
  21. N. B. Abraham, L. A. Lugiato, and L. M. Narducci, J. Opt. Soc. Am. B 2, 7 (1985).
    [CrossRef]
  22. P. A. Khandokin and Y. I. Khanin, J. Opt. Soc. Am. B 2, 226 (1985), and references therein.
    [CrossRef]

1985 (2)

1978 (1)

R. R. Rice, J. R. Teague, and J. E. Jackson, J. Appl. Phys. 49, 5750 (1978).
[CrossRef]

1977 (1)

J. D. Barry and C. J. Kennedy, J. Appl. Phys. 48, 2518 (1977).
[CrossRef]

1976 (1)

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

1975 (3)

R. R. Rice, J. R. Teague, and J. E. Jackson, J. Appl. Phys. B 6, 2716 (1975).

J. Falk, IEEE J. Quantum Electron. QE-11, 21 (1975).
[CrossRef]

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, V. N. Krylov, A. A. Man’ko, and V. L. Strizhevskii, Sov. J. Quantum Electron. 5, 500 (1975), and references therein.
[CrossRef]

1974 (2)

W. C. Culshaw, J. Kannelaud, and J. E. Peterson, IEEE J. Quantum Electron. QE-10, 253 (1974).
[CrossRef]

C. J. Kennedy and J. D. Barry, IEEE J. Quantum Electron. QE-10, 596 (1974).
[CrossRef]

1971 (2)

C. B. Hitz and L. M. Osterink, Appl. Phys. Lett. 18, 378 (1971).
[CrossRef]

M. A. Karr, J. Appl. Phys. 42, 4517 (1971).
[CrossRef]

1970 (1)

R. G. Smith, IEEE J. Quantum Electron. QE-6, 215 (1970).
[CrossRef]

1969 (1)

T. R. Gurski, Appl. Phys. Lett. 15, 5 (1969).
[CrossRef]

1968 (1)

J. E. Geusic, H. J. Levinstein, S. Singh, R. G. Smith, and L. G. Van Uitert, Appl. Phys. Lett. 12, 306 (1968); Appl. Phys. Lett. 13, 395 (1968).
[CrossRef]

Abraham, N. B.

Baer, T.

T. Baer and M. S. Keirstead, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1985), paper ThZ1.

Barry, J. D.

J. D. Barry and C. J. Kennedy, J. Appl. Phys. 48, 2518 (1977).
[CrossRef]

C. J. Kennedy and J. D. Barry, IEEE J. Quantum Electron. QE-10, 596 (1974).
[CrossRef]

Bierlein, J. D.

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

Culshaw, W. C.

W. C. Culshaw, J. Kannelaud, and J. E. Peterson, IEEE J. Quantum Electron. QE-10, 253 (1974).
[CrossRef]

Erneux, T.

P. Mandel and T. Erneux, in Third New Zealand Symposium on Laser Physics, J. P. Harvey and D. F. Walls, eds. (Springer-Verlag, New York, 1983), p. 132; P. Mandel and X. G. Wu, J. Opt. Soc. Am. B (to be published).

Falk, J.

J. Falk, IEEE J. Quantum Electron. QE-11, 21 (1975).
[CrossRef]

Geusic, J. E.

J. E. Geusic, H. J. Levinstein, S. Singh, R. G. Smith, and L. G. Van Uitert, Appl. Phys. Lett. 12, 306 (1968); Appl. Phys. Lett. 13, 395 (1968).
[CrossRef]

Gier, T. E.

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

Gurski, T. R.

T. R. Gurski, Appl. Phys. Lett. 15, 5 (1969).
[CrossRef]

Hitz, C. B.

C. B. Hitz and L. M. Osterink, Appl. Phys. Lett. 18, 378 (1971).
[CrossRef]

Jackson, J. E.

R. R. Rice, J. R. Teague, and J. E. Jackson, J. Appl. Phys. 49, 5750 (1978).
[CrossRef]

R. R. Rice, J. R. Teague, and J. E. Jackson, J. Appl. Phys. B 6, 2716 (1975).

Kannelaud, J.

W. C. Culshaw, J. Kannelaud, and J. E. Peterson, IEEE J. Quantum Electron. QE-10, 253 (1974).
[CrossRef]

Karpenko, S. G.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, V. N. Krylov, A. A. Man’ko, and V. L. Strizhevskii, Sov. J. Quantum Electron. 5, 500 (1975), and references therein.
[CrossRef]

Karr, M. A.

M. A. Karr, J. Appl. Phys. 42, 4517 (1971).
[CrossRef]

Keirstead, M. S.

T. Baer and M. S. Keirstead, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1985), paper ThZ1.

Kennedy, C. J.

J. D. Barry and C. J. Kennedy, J. Appl. Phys. 48, 2518 (1977).
[CrossRef]

C. J. Kennedy and J. D. Barry, IEEE J. Quantum Electron. QE-10, 596 (1974).
[CrossRef]

Khandokin, P. A.

Khanin, Y. I.

Koechner, W.

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1976), Chap. 8, p. 397.
[CrossRef]

Kornienko, N. E.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, V. N. Krylov, A. A. Man’ko, and V. L. Strizhevskii, Sov. J. Quantum Electron. 5, 500 (1975), and references therein.
[CrossRef]

Krylov, V. N.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, V. N. Krylov, A. A. Man’ko, and V. L. Strizhevskii, Sov. J. Quantum Electron. 5, 500 (1975), and references therein.
[CrossRef]

Lamb, W. E.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), Chap. 9, p. 115.

Levinstein, H. J.

J. E. Geusic, H. J. Levinstein, S. Singh, R. G. Smith, and L. G. Van Uitert, Appl. Phys. Lett. 12, 306 (1968); Appl. Phys. Lett. 13, 395 (1968).
[CrossRef]

Lugiato, L. A.

Man’ko, A. A.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, V. N. Krylov, A. A. Man’ko, and V. L. Strizhevskii, Sov. J. Quantum Electron. 5, 500 (1975), and references therein.
[CrossRef]

Mandel, P.

P. Mandel and T. Erneux, in Third New Zealand Symposium on Laser Physics, J. P. Harvey and D. F. Walls, eds. (Springer-Verlag, New York, 1983), p. 132; P. Mandel and X. G. Wu, J. Opt. Soc. Am. B (to be published).

Narducci, L. M.

Osterink, L. M.

C. B. Hitz and L. M. Osterink, Appl. Phys. Lett. 18, 378 (1971).
[CrossRef]

Peterson, J. E.

W. C. Culshaw, J. Kannelaud, and J. E. Peterson, IEEE J. Quantum Electron. QE-10, 253 (1974).
[CrossRef]

Rice, R. R.

R. R. Rice, J. R. Teague, and J. E. Jackson, J. Appl. Phys. 49, 5750 (1978).
[CrossRef]

R. R. Rice, J. R. Teague, and J. E. Jackson, J. Appl. Phys. B 6, 2716 (1975).

Sargent, M.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), Chap. 9, p. 115.

Scully, M. O.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), Chap. 9, p. 115.

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

Singh, S.

J. E. Geusic, H. J. Levinstein, S. Singh, R. G. Smith, and L. G. Van Uitert, Appl. Phys. Lett. 12, 306 (1968); Appl. Phys. Lett. 13, 395 (1968).
[CrossRef]

Smith, R. G.

R. G. Smith, IEEE J. Quantum Electron. QE-6, 215 (1970).
[CrossRef]

J. E. Geusic, H. J. Levinstein, S. Singh, R. G. Smith, and L. G. Van Uitert, Appl. Phys. Lett. 12, 306 (1968); Appl. Phys. Lett. 13, 395 (1968).
[CrossRef]

Strizhevskii, V. L.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, V. N. Krylov, A. A. Man’ko, and V. L. Strizhevskii, Sov. J. Quantum Electron. 5, 500 (1975), and references therein.
[CrossRef]

Teague, J. R.

R. R. Rice, J. R. Teague, and J. E. Jackson, J. Appl. Phys. 49, 5750 (1978).
[CrossRef]

R. R. Rice, J. R. Teague, and J. E. Jackson, J. Appl. Phys. B 6, 2716 (1975).

Van Uitert, L. G.

J. E. Geusic, H. J. Levinstein, S. Singh, R. G. Smith, and L. G. Van Uitert, Appl. Phys. Lett. 12, 306 (1968); Appl. Phys. Lett. 13, 395 (1968).
[CrossRef]

Volosov, V. D.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, V. N. Krylov, A. A. Man’ko, and V. L. Strizhevskii, Sov. J. Quantum Electron. 5, 500 (1975), and references therein.
[CrossRef]

Zumsteg, F. C.

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

Appl. Phys. Lett. (3)

J. E. Geusic, H. J. Levinstein, S. Singh, R. G. Smith, and L. G. Van Uitert, Appl. Phys. Lett. 12, 306 (1968); Appl. Phys. Lett. 13, 395 (1968).
[CrossRef]

C. B. Hitz and L. M. Osterink, Appl. Phys. Lett. 18, 378 (1971).
[CrossRef]

T. R. Gurski, Appl. Phys. Lett. 15, 5 (1969).
[CrossRef]

IEEE J. Quantum Electron. (4)

J. Falk, IEEE J. Quantum Electron. QE-11, 21 (1975).
[CrossRef]

R. G. Smith, IEEE J. Quantum Electron. QE-6, 215 (1970).
[CrossRef]

W. C. Culshaw, J. Kannelaud, and J. E. Peterson, IEEE J. Quantum Electron. QE-10, 253 (1974).
[CrossRef]

C. J. Kennedy and J. D. Barry, IEEE J. Quantum Electron. QE-10, 596 (1974).
[CrossRef]

J. Appl. Phys. (4)

J. D. Barry and C. J. Kennedy, J. Appl. Phys. 48, 2518 (1977).
[CrossRef]

R. R. Rice, J. R. Teague, and J. E. Jackson, J. Appl. Phys. 49, 5750 (1978).
[CrossRef]

M. A. Karr, J. Appl. Phys. 42, 4517 (1971).
[CrossRef]

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

J. Appl. Phys. B (1)

R. R. Rice, J. R. Teague, and J. E. Jackson, J. Appl. Phys. B 6, 2716 (1975).

J. Opt. Soc. Am. B (2)

Sov. J. Quantum Electron. (1)

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, V. N. Krylov, A. A. Man’ko, and V. L. Strizhevskii, Sov. J. Quantum Electron. 5, 500 (1975), and references therein.
[CrossRef]

Other (7)

T. Baer and M. S. Keirstead, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1985), paper ThZ1.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), Chap. 9, p. 115.

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1976), Chap. 8, p. 397.
[CrossRef]

Available from Airton Solid State Materials, 200 E. Hanover Avenue, Morris Plains, N.J. 07950.

P. Mandel and T. Erneux, in Third New Zealand Symposium on Laser Physics, J. P. Harvey and D. F. Walls, eds. (Springer-Verlag, New York, 1983), p. 132; P. Mandel and X. G. Wu, J. Opt. Soc. Am. B (to be published).

Available from Spectra Diode Labs, 3333 N. First Street, San Jose, Calif. 95134; Model 2420.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the laser-diode-array-pumped Nd:YAG laser with an intracavity-doubling crystal. The separation between the output coupler and the high reflector on the end of the laser rod is 6 cm.

Fig. 2
Fig. 2

The amplitude noise of the 532-nm output from the intracavity-doubled system.

Fig. 3
Fig. 3

The amplitude fluctuations at 1064 nm of each longitudinal mode when only two modes are oscillating.

Fig. 4
Fig. 4

The calculated mode-coupling oscillations of each longitudinal mode in the two-mode case. The numerical constants used in the calculation are as listed in the text, except for the loss of mode 2 that has the value 0.016.

Fig. 5
Fig. 5

The gain and loss of mode 1 as a function of time for a two-mode laser with an intracavity-doubling crystal. The time sectors (a) through (d) are described in the text. The amplitude of mode 1 versus time is shown as a timing reference.

Fig. 6
Fig. 6

Calculated mode-coupling oscillations for a two-mode laser as a function of the nonlinear coupling constant. The nonlinear coupling coefficient has the following values: (a) 1E-7, (b) 3E-7, (c) 1E-6, (d) 3E-6, (e) 1E-5, and (f) 3E-5. In these curves the saturation and cross-saturation parameters have the numerical values 0.06 and 0.016 W−1, respectively.

Fig. 7
Fig. 7

The calculated amplitude noise of a three-mode laser with an intracavity-doubling crystal. This figure should be compared with the observed noise from the intracavity-doubled laser-diode-pumped Nd:YAG system (see Fig. 2).

Equations (10)

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τ c d I 1 d t = ( G 1 α 1 I 1 ) I 1 ,
τ f d G 1 d t = ( β I 1 + 1 ) G 1 + G 1 0 ,
τ c d I 1 d t = ( G 1 α 1 I 1 2 I 2 ) I 1 ,
τ f d G 1 d t = ( β I 1 + β 12 I 2 + 1 ) G 1 + G 1 0 ,
τ c d I 2 d t = ( G 2 α 2 I 2 2 I 1 ) I 2 ,
τ f d G 2 d t = ( β I 2 + β 21 I 1 + 1 ) G 2 + G 2 0 ,
Δ G 1 G 1 0 t / τ f .
T mc I ss τ f / G 1 0 ,
τ c d I i d t = ( G i α i I i 2 j i N I j ) I i ,
τ f d G i d t = ( β I i + j i N β i j I j + 1 ) G i + G i 0 ,

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