Abstract

We report a numerical analysis performed to determine the range of parameters necessary for observing stable phase-locked solutions in the case of three next-neighbor coupled lasers. The locking band is determined not only by the coupling strength and by the different array elements’ field amplitude ratios but also by the field phase retardation in the coupling channels.

© 1993 Optical Society of America

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References

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  1. See, e.g., V. V. Likhanskii, A. P. Napartovich, Sov. Phys. Usp. 33, 228 (1990).
    [CrossRef]
  2. R. A. Elliot, R. K. DeFreez, T. L. Paoli, R. D. Burnham, W. Streifer, IEEE J. Quantum Electron. QE-21, 598 (1985); A. V. Bondarenko, A. F. Glova, S. N. Kozlov, F. V. Lebedev, V. V. Likhankii, A. P. Napartovich, V. D. Pismennyi, V. P. Yartsev, Sov. Phys. JETP 68, 461 (1989).
    [CrossRef]
  3. A. Lapucci, G. Cangioli, Appl. Phys. Lett. 62, 7 (1993).
    [CrossRef]
  4. W. W. Chow, Opt. Lett. 10, 442 (1985).
    [CrossRef] [PubMed]
  5. M. B. Spencer, W. E. Lamb, Phys. Rev. A 5, 893 (1972).
    [CrossRef]
  6. H. G. Winful, S. S. Wang, Appl. Phys. Lett. 53, 1894, (1988).

1993

A. Lapucci, G. Cangioli, Appl. Phys. Lett. 62, 7 (1993).
[CrossRef]

1990

See, e.g., V. V. Likhanskii, A. P. Napartovich, Sov. Phys. Usp. 33, 228 (1990).
[CrossRef]

1985

R. A. Elliot, R. K. DeFreez, T. L. Paoli, R. D. Burnham, W. Streifer, IEEE J. Quantum Electron. QE-21, 598 (1985); A. V. Bondarenko, A. F. Glova, S. N. Kozlov, F. V. Lebedev, V. V. Likhankii, A. P. Napartovich, V. D. Pismennyi, V. P. Yartsev, Sov. Phys. JETP 68, 461 (1989).
[CrossRef]

W. W. Chow, Opt. Lett. 10, 442 (1985).
[CrossRef] [PubMed]

1972

M. B. Spencer, W. E. Lamb, Phys. Rev. A 5, 893 (1972).
[CrossRef]

1894

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

Burnham, R. D.

R. A. Elliot, R. K. DeFreez, T. L. Paoli, R. D. Burnham, W. Streifer, IEEE J. Quantum Electron. QE-21, 598 (1985); A. V. Bondarenko, A. F. Glova, S. N. Kozlov, F. V. Lebedev, V. V. Likhankii, A. P. Napartovich, V. D. Pismennyi, V. P. Yartsev, Sov. Phys. JETP 68, 461 (1989).
[CrossRef]

Cangioli, G.

A. Lapucci, G. Cangioli, Appl. Phys. Lett. 62, 7 (1993).
[CrossRef]

Chow, W. W.

DeFreez, R. K.

R. A. Elliot, R. K. DeFreez, T. L. Paoli, R. D. Burnham, W. Streifer, IEEE J. Quantum Electron. QE-21, 598 (1985); A. V. Bondarenko, A. F. Glova, S. N. Kozlov, F. V. Lebedev, V. V. Likhankii, A. P. Napartovich, V. D. Pismennyi, V. P. Yartsev, Sov. Phys. JETP 68, 461 (1989).
[CrossRef]

Elliot, R. A.

R. A. Elliot, R. K. DeFreez, T. L. Paoli, R. D. Burnham, W. Streifer, IEEE J. Quantum Electron. QE-21, 598 (1985); A. V. Bondarenko, A. F. Glova, S. N. Kozlov, F. V. Lebedev, V. V. Likhankii, A. P. Napartovich, V. D. Pismennyi, V. P. Yartsev, Sov. Phys. JETP 68, 461 (1989).
[CrossRef]

Lamb, W. E.

M. B. Spencer, W. E. Lamb, Phys. Rev. A 5, 893 (1972).
[CrossRef]

Lapucci, A.

A. Lapucci, G. Cangioli, Appl. Phys. Lett. 62, 7 (1993).
[CrossRef]

Likhanskii, V. V.

See, e.g., V. V. Likhanskii, A. P. Napartovich, Sov. Phys. Usp. 33, 228 (1990).
[CrossRef]

Napartovich, A. P.

See, e.g., V. V. Likhanskii, A. P. Napartovich, Sov. Phys. Usp. 33, 228 (1990).
[CrossRef]

Paoli, T. L.

R. A. Elliot, R. K. DeFreez, T. L. Paoli, R. D. Burnham, W. Streifer, IEEE J. Quantum Electron. QE-21, 598 (1985); A. V. Bondarenko, A. F. Glova, S. N. Kozlov, F. V. Lebedev, V. V. Likhankii, A. P. Napartovich, V. D. Pismennyi, V. P. Yartsev, Sov. Phys. JETP 68, 461 (1989).
[CrossRef]

Spencer, M. B.

M. B. Spencer, W. E. Lamb, Phys. Rev. A 5, 893 (1972).
[CrossRef]

Streifer, W.

R. A. Elliot, R. K. DeFreez, T. L. Paoli, R. D. Burnham, W. Streifer, IEEE J. Quantum Electron. QE-21, 598 (1985); A. V. Bondarenko, A. F. Glova, S. N. Kozlov, F. V. Lebedev, V. V. Likhankii, A. P. Napartovich, V. D. Pismennyi, V. P. Yartsev, Sov. Phys. JETP 68, 461 (1989).
[CrossRef]

Wang, S. S.

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

Winful, H. G.

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

Appl. Phys. Lett.

A. Lapucci, G. Cangioli, Appl. Phys. Lett. 62, 7 (1993).
[CrossRef]

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

IEEE J. Quantum Electron.

R. A. Elliot, R. K. DeFreez, T. L. Paoli, R. D. Burnham, W. Streifer, IEEE J. Quantum Electron. QE-21, 598 (1985); A. V. Bondarenko, A. F. Glova, S. N. Kozlov, F. V. Lebedev, V. V. Likhankii, A. P. Napartovich, V. D. Pismennyi, V. P. Yartsev, Sov. Phys. JETP 68, 461 (1989).
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. B. Spencer, W. E. Lamb, Phys. Rev. A 5, 893 (1972).
[CrossRef]

Sov. Phys. Usp.

See, e.g., V. V. Likhanskii, A. P. Napartovich, Sov. Phys. Usp. 33, 228 (1990).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Contour plot of the larger negative eigenvalue corresponding to stable stationary solutions in the plane (Φ21, Φ23) for the cases (a) A = B = 1, ψ = π; (b) A = 0.6, B = 0.4, ψ = π/2; (c) A = 1, B = 0.5, ψ = π/2; (d) A = 1.5, B = 1.5, ψ = π/2.

Fig. 2
Fig. 2

Marginal stability curves delimiting regions of stable stationary solutions in the plane (Δω21/m, Δω23/m) for three values of A = B calculated at the (a) zero-order and (b) first-order approximations in m (m/Γ = 0.1). Outer curves, A = B = 0.5; middle curves, A = B = 1; inner curves, A = B = 2.0.

Fig. 3
Fig. 3

Contour plots of Δ ω ¯ / m as a function of A and B in the cases (a) ψ = 0, (b) ψ = π/4, (c) ψ = π/2. A and B range from 0.5 to 2.

Equations (9)

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E ˙ i = [ G Δ i Γ i i ( ω 0 ω i ) ] E i + j M i j E j ,
Δ ˙ i = γ ( Δ i Δ 0 i ) 4 G Δ i | E i | 2 ,
M i j = m i j exp ( i ψ i j ) ,
E ˙ i = Γ i E i + G Δ i E i + j m i j E j cos ( ϕ j ϕ i + ψ i j ) ,
ϕ ˙ i = ( ω i ω 0 ) + i m i j E j E i sin ( ϕ j ϕ i + ψ i j ) ,
ϕ ˙ i = ( ω i ω 0 ) + m 12 E 2 E i sin ( ϕ 2 ϕ i + ψ i 2 ) , i = 1 , 3 ,
ϕ ˙ 2 = ( ω 2 ω 0 ) + m 21 E 1 E 2 sin ( ϕ 1 ϕ 2 + ψ 21 ) + m 23 E 3 E 2 sin ( ϕ 3 ϕ 2 + ψ 23 ) .
Φ ˙ 21 = Δ ω 21 m [ 1 A sin ( Φ 21 + ψ ) + A sin ( Φ 21 ψ ) + B sin ( Φ 23 ψ ) ] ,
Φ ˙ 23 = Δ ω 23 m [ 1 B sin ( Φ 23 + ψ ) + B sin ( Φ 23 ψ ) + A sin ( Φ 21 ψ ) ] .

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