Abstract

We show that the coupled-oscillator model accurately describes the dynamics of laser arrays. Excellent qualitative and quantitative agreement is obtained between this model and the results of experiments on Nd:YAG laser arrays. Recent claims of instantaneous phase locking are shown to be in error.

© 1993 Optical Society of America

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References

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  1. J. Xu, S. Li, K. K. Lee, Y. C. Chen, Opt. Lett. 18, 513 (1993).
    [Crossref] [PubMed]
  2. S. S. Wang, H. G. Winful, Appl. Phys. Lett. 52, 1774 (1988).
    [Crossref]
  3. H. G. Winful, S. S. Wang, Appl. Phys. Lett. 53, 1894 (1988).
    [Crossref]
  4. J. G. Tsacoyeanes, J. Appl. Phys. 64, 32 (1988).
    [Crossref]
  5. H. G. Winful, L. Rahman, Phys. Rev. Lett. 65, 1575 (1990).
    [Crossref] [PubMed]
  6. G. A. Wilson, R. K. DeFreez, H. G. Winful, Opt. Commun. 82, 293 (1991).
    [Crossref]
  7. G. A. Wilson, R. K. DeFreez, H. G. Winful, IEEE J. Quantum Electron. 27, 1696 (1991).
    [Crossref]
  8. L. Rahman, H. G. Winful, Opt. Lett. 18, 128 (1993).
    [Crossref] [PubMed]
  9. K. Kobayashi, H. Yonezu, F. Saito, Y. Nannichi, Appl. Phys. Lett. 19, 323 (1971).
    [Crossref]
  10. R. Adler, Proc. IRE 34, 351 (1946); reprinted in Proc. IEEE 61, 1380 (1973).
    [Crossref]
  11. S. S. Wang, H. G. Winful, J. Appl. Phys. 73, 462 (1993).
    [Crossref]
  12. H. Adachihara, O. Hess, R. Indik, J. V. Moloney, J. Opt. Soc. Am. B 10, 496 (1993).
    [Crossref]
  13. P. Ru, P. K. Jakobsen, J. V. Moloney, R. Indik, J. Opt. Soc. Am. B 10, 507 (1993).
    [Crossref]

1993 (5)

1991 (2)

G. A. Wilson, R. K. DeFreez, H. G. Winful, Opt. Commun. 82, 293 (1991).
[Crossref]

G. A. Wilson, R. K. DeFreez, H. G. Winful, IEEE J. Quantum Electron. 27, 1696 (1991).
[Crossref]

1990 (1)

H. G. Winful, L. Rahman, Phys. Rev. Lett. 65, 1575 (1990).
[Crossref] [PubMed]

1988 (3)

S. S. Wang, H. G. Winful, Appl. Phys. Lett. 52, 1774 (1988).
[Crossref]

H. G. Winful, S. S. Wang, Appl. Phys. Lett. 53, 1894 (1988).
[Crossref]

J. G. Tsacoyeanes, J. Appl. Phys. 64, 32 (1988).
[Crossref]

1971 (1)

K. Kobayashi, H. Yonezu, F. Saito, Y. Nannichi, Appl. Phys. Lett. 19, 323 (1971).
[Crossref]

1946 (1)

R. Adler, Proc. IRE 34, 351 (1946); reprinted in Proc. IEEE 61, 1380 (1973).
[Crossref]

Adachihara, H.

Adler, R.

R. Adler, Proc. IRE 34, 351 (1946); reprinted in Proc. IEEE 61, 1380 (1973).
[Crossref]

Chen, Y. C.

DeFreez, R. K.

G. A. Wilson, R. K. DeFreez, H. G. Winful, Opt. Commun. 82, 293 (1991).
[Crossref]

G. A. Wilson, R. K. DeFreez, H. G. Winful, IEEE J. Quantum Electron. 27, 1696 (1991).
[Crossref]

Hess, O.

Indik, R.

Jakobsen, P. K.

Kobayashi, K.

K. Kobayashi, H. Yonezu, F. Saito, Y. Nannichi, Appl. Phys. Lett. 19, 323 (1971).
[Crossref]

Lee, K. K.

Li, S.

Moloney, J. V.

Nannichi, Y.

K. Kobayashi, H. Yonezu, F. Saito, Y. Nannichi, Appl. Phys. Lett. 19, 323 (1971).
[Crossref]

Rahman, L.

L. Rahman, H. G. Winful, Opt. Lett. 18, 128 (1993).
[Crossref] [PubMed]

H. G. Winful, L. Rahman, Phys. Rev. Lett. 65, 1575 (1990).
[Crossref] [PubMed]

Ru, P.

Saito, F.

K. Kobayashi, H. Yonezu, F. Saito, Y. Nannichi, Appl. Phys. Lett. 19, 323 (1971).
[Crossref]

Tsacoyeanes, J. G.

J. G. Tsacoyeanes, J. Appl. Phys. 64, 32 (1988).
[Crossref]

Wang, S. S.

S. S. Wang, H. G. Winful, J. Appl. Phys. 73, 462 (1993).
[Crossref]

H. G. Winful, S. S. Wang, Appl. Phys. Lett. 53, 1894 (1988).
[Crossref]

S. S. Wang, H. G. Winful, Appl. Phys. Lett. 52, 1774 (1988).
[Crossref]

Wilson, G. A.

G. A. Wilson, R. K. DeFreez, H. G. Winful, Opt. Commun. 82, 293 (1991).
[Crossref]

G. A. Wilson, R. K. DeFreez, H. G. Winful, IEEE J. Quantum Electron. 27, 1696 (1991).
[Crossref]

Winful, H. G.

S. S. Wang, H. G. Winful, J. Appl. Phys. 73, 462 (1993).
[Crossref]

L. Rahman, H. G. Winful, Opt. Lett. 18, 128 (1993).
[Crossref] [PubMed]

G. A. Wilson, R. K. DeFreez, H. G. Winful, IEEE J. Quantum Electron. 27, 1696 (1991).
[Crossref]

G. A. Wilson, R. K. DeFreez, H. G. Winful, Opt. Commun. 82, 293 (1991).
[Crossref]

H. G. Winful, L. Rahman, Phys. Rev. Lett. 65, 1575 (1990).
[Crossref] [PubMed]

S. S. Wang, H. G. Winful, Appl. Phys. Lett. 52, 1774 (1988).
[Crossref]

H. G. Winful, S. S. Wang, Appl. Phys. Lett. 53, 1894 (1988).
[Crossref]

Xu, J.

Yonezu, H.

K. Kobayashi, H. Yonezu, F. Saito, Y. Nannichi, Appl. Phys. Lett. 19, 323 (1971).
[Crossref]

Appl. Phys. Lett. (3)

S. S. Wang, H. G. Winful, Appl. Phys. Lett. 52, 1774 (1988).
[Crossref]

H. G. Winful, S. S. Wang, Appl. Phys. Lett. 53, 1894 (1988).
[Crossref]

K. Kobayashi, H. Yonezu, F. Saito, Y. Nannichi, Appl. Phys. Lett. 19, 323 (1971).
[Crossref]

IEEE J. Quantum Electron. (1)

G. A. Wilson, R. K. DeFreez, H. G. Winful, IEEE J. Quantum Electron. 27, 1696 (1991).
[Crossref]

J. Appl. Phys. (2)

J. G. Tsacoyeanes, J. Appl. Phys. 64, 32 (1988).
[Crossref]

S. S. Wang, H. G. Winful, J. Appl. Phys. 73, 462 (1993).
[Crossref]

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

Opt. Commun. (1)

G. A. Wilson, R. K. DeFreez, H. G. Winful, Opt. Commun. 82, 293 (1991).
[Crossref]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

H. G. Winful, L. Rahman, Phys. Rev. Lett. 65, 1575 (1990).
[Crossref] [PubMed]

Proc. IRE (1)

R. Adler, Proc. IRE 34, 351 (1946); reprinted in Proc. IEEE 61, 1380 (1973).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1

(a) Field amplitude, (b) inversion, and (c) phase difference (units of π) in the Nd:YAG lasers before, during, and after the interruption of the pump beams. The pump beams were turned off at t = 6 μs for 250 ns. These results were obtained with the coupled-mode equations [Eqs. (1)].

Fig. 2
Fig. 2

Calculated intensities at (a) the peak and (b) the valley of the far-field profile. This is to be compared with experimental results of Fig. 2 of Ref. 1.

Fig. 3
Fig. 3

Evolution of the fields X1 (solid curve) and X2 (dotted curve) after perturbation of pump laser 2. The pump laser 2 was turned off at t = 6 μs for 250 ns. Note the delay in the response of laser 1.

Equations (9)

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X ˙ 1 = Z 1 X 1 + η r X 2 sin θ η i X 2 cos θ ,
X ˙ 2 = Z 2 X 2 η r X 1 sin θ η i X 1 cos θ ,
θ ˙ = η r ( X 2 X 1 X 1 X 2 ) cos θ + η i ( X 2 X 1 + X 1 X 2 ) sin θ Δ Ω ,
T Z ˙ 1 = p Z 1 ( 1 + 2 Z 1 ) X 1 2 ,
T Z ˙ 2 = p Z 2 ( 1 + 2 Z 2 ) X 2 2 .
p = 1 2 g N th τ p ( P P th 1 ) ,
θ ˙ = 2 η i sin θ Δ Ω .
Δ Ω < 2 η i .
θ ( τ ) = ± 2 tan 1 [ ( tan θ 0 / 2 ) exp ( 2 η i τ ) ] ,

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