Abstract

Optical implementation of a backpropagating neuron by means of a nonlinear Fabry-Perot etalon requires thresholding a forward signal beam while the transmittance of a backpropagating beam is multiplied by the differential of the forward signal. This is achievable by inputting a bichromatic field to a three-level system in an optical cavity. The response characteristics of this device have the added possibility of adaptability of the threshold by the backward probe input intensity.

© 1989 Optical Society of America

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References

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  1. D. Psaltis, N. Farhat, “Optical Information Processing Based on an Associative-Memory Model of Neural Nets with Thresholding and Feedback,” Opt. Lett. 10, 98 (1985).
    [CrossRef] [PubMed]
  2. K. Wagner, D. Psaltis, “Multilayer Optical Learning Networks,” Appl. Opt. 26, 5061 (1987).
    [CrossRef] [PubMed]
  3. R. L. Panock, R. J. Temkin, “Interaction of Two Laser Fields with a Three-Level Molecular System,” IEEE J. Quantum Electron. QE-13, 425 (1977).
    [CrossRef]
  4. R. G. Brewer, E. L. Hahn, “Coherent Two-Photon Processes: Transient and Steady-State Cases,” Phys. Rev. A 11, 1641 (1975).
    [CrossRef]
  5. G. P. Agrawal, H. J. Carmichael, “Optical Bistability Through Nonlinear Dispersion and Absorption,” Phys. Rev. A 19, 2074 (1979).
    [CrossRef]
  6. D. Kagan, H. Friedmann, “Optical Logic Elements from Four-Level Systems Interacting with Two Fields,” Proc. Soc. Photo-Opt. Instrum. Eng. 700, 71 (1986).
  7. D. Kagan, H. Friedmann, “Adaptive Optical Logic and Switching Devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 354 (1987).
  8. D. Kagan, H. Friedmann, “Tunable Optical Bistability of Bichromatic Fields Interacting with Four-Level Systems,” IEEE J. Quantum Electron.QE-25, (June1989), to be published.
  9. N. M. Lawandi, W. S. Rabinovich, “Absorptive Bistability in a Three-Level System Interacting with Two Fields,” IEEE J. Quantum Electron. QE-20, 458 (1984).
    [CrossRef]

1987 (2)

K. Wagner, D. Psaltis, “Multilayer Optical Learning Networks,” Appl. Opt. 26, 5061 (1987).
[CrossRef] [PubMed]

D. Kagan, H. Friedmann, “Adaptive Optical Logic and Switching Devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 354 (1987).

1986 (1)

D. Kagan, H. Friedmann, “Optical Logic Elements from Four-Level Systems Interacting with Two Fields,” Proc. Soc. Photo-Opt. Instrum. Eng. 700, 71 (1986).

1985 (1)

1984 (1)

N. M. Lawandi, W. S. Rabinovich, “Absorptive Bistability in a Three-Level System Interacting with Two Fields,” IEEE J. Quantum Electron. QE-20, 458 (1984).
[CrossRef]

1979 (1)

G. P. Agrawal, H. J. Carmichael, “Optical Bistability Through Nonlinear Dispersion and Absorption,” Phys. Rev. A 19, 2074 (1979).
[CrossRef]

1977 (1)

R. L. Panock, R. J. Temkin, “Interaction of Two Laser Fields with a Three-Level Molecular System,” IEEE J. Quantum Electron. QE-13, 425 (1977).
[CrossRef]

1975 (1)

R. G. Brewer, E. L. Hahn, “Coherent Two-Photon Processes: Transient and Steady-State Cases,” Phys. Rev. A 11, 1641 (1975).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, H. J. Carmichael, “Optical Bistability Through Nonlinear Dispersion and Absorption,” Phys. Rev. A 19, 2074 (1979).
[CrossRef]

Brewer, R. G.

R. G. Brewer, E. L. Hahn, “Coherent Two-Photon Processes: Transient and Steady-State Cases,” Phys. Rev. A 11, 1641 (1975).
[CrossRef]

Carmichael, H. J.

G. P. Agrawal, H. J. Carmichael, “Optical Bistability Through Nonlinear Dispersion and Absorption,” Phys. Rev. A 19, 2074 (1979).
[CrossRef]

Farhat, N.

Friedmann, H.

D. Kagan, H. Friedmann, “Adaptive Optical Logic and Switching Devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 354 (1987).

D. Kagan, H. Friedmann, “Optical Logic Elements from Four-Level Systems Interacting with Two Fields,” Proc. Soc. Photo-Opt. Instrum. Eng. 700, 71 (1986).

D. Kagan, H. Friedmann, “Tunable Optical Bistability of Bichromatic Fields Interacting with Four-Level Systems,” IEEE J. Quantum Electron.QE-25, (June1989), to be published.

Hahn, E. L.

R. G. Brewer, E. L. Hahn, “Coherent Two-Photon Processes: Transient and Steady-State Cases,” Phys. Rev. A 11, 1641 (1975).
[CrossRef]

Kagan, D.

D. Kagan, H. Friedmann, “Adaptive Optical Logic and Switching Devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 354 (1987).

D. Kagan, H. Friedmann, “Optical Logic Elements from Four-Level Systems Interacting with Two Fields,” Proc. Soc. Photo-Opt. Instrum. Eng. 700, 71 (1986).

D. Kagan, H. Friedmann, “Tunable Optical Bistability of Bichromatic Fields Interacting with Four-Level Systems,” IEEE J. Quantum Electron.QE-25, (June1989), to be published.

Lawandi, N. M.

N. M. Lawandi, W. S. Rabinovich, “Absorptive Bistability in a Three-Level System Interacting with Two Fields,” IEEE J. Quantum Electron. QE-20, 458 (1984).
[CrossRef]

Panock, R. L.

R. L. Panock, R. J. Temkin, “Interaction of Two Laser Fields with a Three-Level Molecular System,” IEEE J. Quantum Electron. QE-13, 425 (1977).
[CrossRef]

Psaltis, D.

Rabinovich, W. S.

N. M. Lawandi, W. S. Rabinovich, “Absorptive Bistability in a Three-Level System Interacting with Two Fields,” IEEE J. Quantum Electron. QE-20, 458 (1984).
[CrossRef]

Temkin, R. J.

R. L. Panock, R. J. Temkin, “Interaction of Two Laser Fields with a Three-Level Molecular System,” IEEE J. Quantum Electron. QE-13, 425 (1977).
[CrossRef]

Wagner, K.

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

R. L. Panock, R. J. Temkin, “Interaction of Two Laser Fields with a Three-Level Molecular System,” IEEE J. Quantum Electron. QE-13, 425 (1977).
[CrossRef]

N. M. Lawandi, W. S. Rabinovich, “Absorptive Bistability in a Three-Level System Interacting with Two Fields,” IEEE J. Quantum Electron. QE-20, 458 (1984).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

R. G. Brewer, E. L. Hahn, “Coherent Two-Photon Processes: Transient and Steady-State Cases,” Phys. Rev. A 11, 1641 (1975).
[CrossRef]

G. P. Agrawal, H. J. Carmichael, “Optical Bistability Through Nonlinear Dispersion and Absorption,” Phys. Rev. A 19, 2074 (1979).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

D. Kagan, H. Friedmann, “Optical Logic Elements from Four-Level Systems Interacting with Two Fields,” Proc. Soc. Photo-Opt. Instrum. Eng. 700, 71 (1986).

D. Kagan, H. Friedmann, “Adaptive Optical Logic and Switching Devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 354 (1987).

Other (1)

D. Kagan, H. Friedmann, “Tunable Optical Bistability of Bichromatic Fields Interacting with Four-Level Systems,” IEEE J. Quantum Electron.QE-25, (June1989), to be published.

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Figures (6)

Fig. 1
Fig. 1

Three level system interacting with a bichromatic field. One field ω1 tuned to the 1–3 resonance, the other ω2 to the 3–2 resonance.

Fig. 2
Fig. 2

On-resonance susceptibility of ω1 as a function of X1 for different values of X2: a, X2 = 0.0; b, X2 = 2.0; c, X2 = 4.0. As X1 increases the susceptibility saturates.

Fig. 3
Fig. 3

On-resonance susceptibility of ω2 as a function of X1 for different values of X2: a, X2 = 0.0; b, X2 = 2.0; c, X2 = 4.0. As X1 increases the susceptibility first reaches a maximum then falls to zero because of detuning caused by splitting of level 3.

Fig. 4
Fig. 4

Three signals: a, X1 vs Y1 the forward output response; b, the backward propagating signal transmission response, scaled approximately (×1.67), X2/Y2 vs Y1; and c, the gain of the forward signal dX1/dY1. The parameter values are C1 = 20, C2 = −35, and Y2 = 0.5.

Fig. 5
Fig. 5

Optical bistability response curves of X1 vs Y1 for varying values of Y2: a, Y2 = 0.01; b, Y2 = 0.5; c, Y2 = 1.0. As Y2 increases the switch-up point is shifted to the left. The parameter values are C1 = 40 and C2 = −22.

Fig. 6
Fig. 6

Optical bistability response curves of X2 vs Y1 for varying values of Y2: a, Y2 = 0.01; b, Y2 = 0.5; c, Y2 = 1.0. As Y2 increases the switch-up point is shifted to the left. The parameter values are C1 = 40 and C2 = −22.

Equations (16)

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E ( t , z ) = E 1 exp ( i ω 1 t ) + E 2 exp ( i ω 2 t ) ,
ρ t = i ћ [ ρ , H ] ,
ρ 12 t = i E ( t ) ћ [ μ 13 ρ 32 μ 32 ρ 13 ] ρ 12 ( γ i ω 21 ) ,
ρ 13 t = i E ( t ) ћ [ μ 13 r 13 + μ 23 ρ 12 ] ρ 13 ( γ i ω 31 ) ,
ρ 32 t = i E ( t ) ћ [ μ 32 r 32 + μ 31 ρ 12 ] ρ 32 ( γ i ω 32 ) ,
r 13 t = i E ( t ) ћ [ 2 ( μ 13 ρ 31 μ 31 ρ 13 ) ( μ 32 ρ 23 μ 23 ρ 32 ) ] ( r 13 r 13 e q ) γ,
r 32 t = i E ( t ) ћ [ ( μ 31 ρ 13 μ 13 ρ 31 ) + 2 ( μ 32 ρ 23 μ 23 ρ 32 ) ] ( r 32 r 32 e q ) γ,
ω i j = ( ε i ε j ) ћ ,
χ ( ω 1 ) = 2 α o a k 1 4 + X 1 2 + 4 X 2 2 ( 1 + X 1 2 + X 2 2 ) ( 4 + X 1 2 + X 2 2 ) ,
χ ( ω 2 ) = 2 α o e k 2 3 X 1 2 ( 1 + X 2 2 + X 1 2 ) ( 4 + X 2 2 + X 1 2 ) .
X 1 = | E 1 | | μ 13 | ћ γ 2 , X 2 = | E 2 | | μ 32 | ћ γ 2 , α o a = N V μ 13 2 γ k 1 2 ε 0 ћ , α o e = N V μ 32 2 γ k 2 2 ε 0 ћ ,
Y 1 = X 1 [ 1 + 2 C 1 F ( 4 + X 1 2 + 4 X 2 2 ) ] ,
Y 2 = X 2 [ 1 + 2 C 2 F ( 3 X 1 2 ) ] ,
F = ( 1 + X 1 2 + X 2 2 ) ( 4 + X 1 2 + X 2 2 ) ,
Y 1 = | E 1 i n | | μ 13 | ћ γ 2 , Y 2 = | E 2 i n | | μ 32 | ћ γ 2 .
C 1 = α o a L R 1 2 ( 1 R 1 ) , C 2 = α o e L R 2 2 ( 1 R 2 ) ,

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