Abstract

A bistable optical system with distributed nonlinear elements is proposed. Novel functions are derived from the collective nature of the optical elements. Collective phenomena including spatial period-doubling bifurcations, hierarchical multistabilities, and various types of cooperative all-optical flip-flop operations are predicted to take place in the proposed optical device.

© 1987 Optical Society of America

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References

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  1. B. S. Wherrett, IEEE J. Quantum Electron. QE-20, 646 (1984).
    [CrossRef]
  2. K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980).
    [CrossRef]
  3. K. Otsuka, K. Ikeda, submitted to Phys. Rev. Lett.
  4. S. S. Tarng, K. Tai, J. L. Jewell, H. M. Gibbs, Appl. Phys. Lett. 40, 205 (1982).
    [CrossRef]
  5. H. Ito, Y. Ogawa, H. Inaba, IEEE J. Quantum Electron. QE-17, 325 (1981).
    [CrossRef]
  6. J.-M. Liu, Y.-C. Chen, IEEE J. Quantum Electron. QE-21, 298 (1985).
  7. K. Okumura, Y. Ogawa, H. Inaba, IEEE J. Quantum Electron. QE-21, 377 (1985).
    [CrossRef]

1985 (2)

J.-M. Liu, Y.-C. Chen, IEEE J. Quantum Electron. QE-21, 298 (1985).

K. Okumura, Y. Ogawa, H. Inaba, IEEE J. Quantum Electron. QE-21, 377 (1985).
[CrossRef]

1984 (1)

B. S. Wherrett, IEEE J. Quantum Electron. QE-20, 646 (1984).
[CrossRef]

1982 (1)

S. S. Tarng, K. Tai, J. L. Jewell, H. M. Gibbs, Appl. Phys. Lett. 40, 205 (1982).
[CrossRef]

1981 (1)

H. Ito, Y. Ogawa, H. Inaba, IEEE J. Quantum Electron. QE-17, 325 (1981).
[CrossRef]

1980 (1)

K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980).
[CrossRef]

Akimoto, O.

K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980).
[CrossRef]

Chen, Y.-C.

J.-M. Liu, Y.-C. Chen, IEEE J. Quantum Electron. QE-21, 298 (1985).

Daido, H.

K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980).
[CrossRef]

Gibbs, H. M.

S. S. Tarng, K. Tai, J. L. Jewell, H. M. Gibbs, Appl. Phys. Lett. 40, 205 (1982).
[CrossRef]

Ikeda, K.

K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980).
[CrossRef]

K. Otsuka, K. Ikeda, submitted to Phys. Rev. Lett.

Inaba, H.

K. Okumura, Y. Ogawa, H. Inaba, IEEE J. Quantum Electron. QE-21, 377 (1985).
[CrossRef]

H. Ito, Y. Ogawa, H. Inaba, IEEE J. Quantum Electron. QE-17, 325 (1981).
[CrossRef]

Ito, H.

H. Ito, Y. Ogawa, H. Inaba, IEEE J. Quantum Electron. QE-17, 325 (1981).
[CrossRef]

Jewell, J. L.

S. S. Tarng, K. Tai, J. L. Jewell, H. M. Gibbs, Appl. Phys. Lett. 40, 205 (1982).
[CrossRef]

Liu, J.-M.

J.-M. Liu, Y.-C. Chen, IEEE J. Quantum Electron. QE-21, 298 (1985).

Ogawa, Y.

K. Okumura, Y. Ogawa, H. Inaba, IEEE J. Quantum Electron. QE-21, 377 (1985).
[CrossRef]

H. Ito, Y. Ogawa, H. Inaba, IEEE J. Quantum Electron. QE-17, 325 (1981).
[CrossRef]

Okumura, K.

K. Okumura, Y. Ogawa, H. Inaba, IEEE J. Quantum Electron. QE-21, 377 (1985).
[CrossRef]

Otsuka, K.

K. Otsuka, K. Ikeda, submitted to Phys. Rev. Lett.

Tai, K.

S. S. Tarng, K. Tai, J. L. Jewell, H. M. Gibbs, Appl. Phys. Lett. 40, 205 (1982).
[CrossRef]

Tarng, S. S.

S. S. Tarng, K. Tai, J. L. Jewell, H. M. Gibbs, Appl. Phys. Lett. 40, 205 (1982).
[CrossRef]

Wherrett, B. S.

B. S. Wherrett, IEEE J. Quantum Electron. QE-20, 646 (1984).
[CrossRef]

Appl. Phys. Lett. (1)

S. S. Tarng, K. Tai, J. L. Jewell, H. M. Gibbs, Appl. Phys. Lett. 40, 205 (1982).
[CrossRef]

IEEE J. Quantum Electron. (4)

H. Ito, Y. Ogawa, H. Inaba, IEEE J. Quantum Electron. QE-17, 325 (1981).
[CrossRef]

J.-M. Liu, Y.-C. Chen, IEEE J. Quantum Electron. QE-21, 298 (1985).

K. Okumura, Y. Ogawa, H. Inaba, IEEE J. Quantum Electron. QE-21, 377 (1985).
[CrossRef]

B. S. Wherrett, IEEE J. Quantum Electron. QE-20, 646 (1984).
[CrossRef]

Phys. Rev. Lett. (1)

K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980).
[CrossRef]

Other (1)

K. Otsuka, K. Ikeda, submitted to Phys. Rev. Lett.

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Figures (4)

Fig. 1
Fig. 1

Conceptual model of a proposed bistable optical system.

Fig. 2
Fig. 2

Stable stationary solution | E ̅ k | 2 as a function of input intensity A2. Dashed curves stand for unstable regions. B = 0.1 and ϕ0 = 0. Stable windows of spatial period p = 3, 5, 6 solutions exist in greater A2 value regions, which are not shown in the figure.

Fig. 3
Fig. 3

(a) All-optical T flip-flop operation, Ab2 = 11, AP2 = 3, Δt/τ (pulse width) = 5, N = 6. Trigger pulses are applied to a k = 1 cell. (b) Assignment to a period-2 spatial solution. Ab2 = 11.3, AP2 = 3.7, Δt/τ = 4, N = 6, and trigger pulses are applied to a k = 2 cell. The upper ( | E ̅ | 2 = 13.6 ) and lower (12.3) states of higher-valued period-2 branches are depicted in the figure. (c) All-optical S–R flip-flop operation. Ab2 = 11, Ap2 = 3.8, Δt/τ = 3, N = 3.

Fig. 4
Fig. 4

(a) Astable multivibrator operation for N = 6. Ab2 = 11, Ap2 (k = 1) = 3. (b) Monostable multivibrator and D flip-flop operation for an open chain. Ab2 = 11, Ap2 = 4, Δt/τ = 2, N = 6.

Equations (7)

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E k + 1 ( t ) = A + B E k ( t t R ) exp i [ ϕ k ( t t R ) + ϕ 0 ] , E N + 1 = E 1 ,
τ ϕ ˙ k ( t ) = ϕ k ( t ) + | E k ( t t R ) | 2 , ϕ N + 1 = ϕ 1 , k = 1 , 2 , 3 , , N .
τ ϕ ˙ k + 1 ( t ) = ϕ k + 1 ( t ) + f [ ϕ k ( t t R ) ] , ϕ N + 1 = ϕ 1 , | E k + 1 ( t ) | 2 = f [ ϕ k ( t t R ) ] = A 2 { 1 + 2 B cos [ ϕ k ( t t R ) + ϕ 0 ] } .
ϕ ̅ k + 1 = f ( ϕ ̅ k ) , ϕ ̅ N + 1 = ϕ ̅ 1 .
( λ + 1 ) N = exp N ( λ t R / τ + α ) sgn σ , σ = k = 1 N f ( ϕ ̅ k ) , α = ( 1 / N ) k = 1 N ln | f ( ϕ ̅ k ) | .
α < 0 for σ > 0 , α < ln | 1 / cos ( π / N ) | for σ < 0 .
δ ϕ k ( t ) = ( t k / k ! ) f ( ϕ ̅ 1 ) f ( ϕ ̅ 2 ) f ( ϕ ̅ k 1 ) exp ( t ) .

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