Abstract

The characteristics of a dual-input hybrid acousto-optic device are investigated numerically and experimentally. The device, which operates as a set-reset flip-flop, uses the well-known bistable acousto-optic device with feedback to which two input beams are applied. The resulting flip-flop is analyzed numerically by use of nonlinear dynamical and nonlinear circuit-modeling techniques, and some of its properties are demonstrated experimentally.

© 1997 Optical Society of America

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References

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  1. J. Chrostowski, C. Delisle, and T. Tremblay, “Oscillations in an acoustooptic bistable device,” Can. J. Phys. 61, 188–191 (1983).
    [CrossRef]
  2. G. J. Yue and Z. Z. Ren, “The stability analysis and the modulation effect on a Bragg acoustooptic bistable system,” IEEE J. Quantum Electron. 26, 815–817 (1990).
    [CrossRef]
  3. H. Jerominek, J. Y. D. Pomerleau, R. Tremblay, and C. Delisle, “An integrated acousto-optic bistable device,” Opt. Commun. 51, 6–10 (1984).
    [CrossRef]
  4. J. Chrostowski, “Noisy bifurcations in acousto-optic bistability,” Phys. Rev. A 26, 3023–3025 (1982).
    [CrossRef]
  5. M. R. Chatterjee and J.-J. Huang, “Demonstration of acousto-optic bistability and chaos by direct nonlinear circuit modeling,” Appl. Opt. 31, 2506–2517 (1992).
    [CrossRef] [PubMed]
  6. T.-C. Poon and S. K. Cheung, “Performance of a hybrid bistable device using an acoustooptic modulator,” Appl. Opt. 28, 4787–4791 (1989).
    [CrossRef] [PubMed]
  7. A. Korpel and T.-C. Poon, “Explicit formalism for acousto-optic multiple plane-wave scattering,” J. Opt. Soc. Am. 70, 817–820 (1980).
    [CrossRef]

1992 (1)

1990 (1)

G. J. Yue and Z. Z. Ren, “The stability analysis and the modulation effect on a Bragg acoustooptic bistable system,” IEEE J. Quantum Electron. 26, 815–817 (1990).
[CrossRef]

1989 (1)

1984 (1)

H. Jerominek, J. Y. D. Pomerleau, R. Tremblay, and C. Delisle, “An integrated acousto-optic bistable device,” Opt. Commun. 51, 6–10 (1984).
[CrossRef]

1983 (1)

J. Chrostowski, C. Delisle, and T. Tremblay, “Oscillations in an acoustooptic bistable device,” Can. J. Phys. 61, 188–191 (1983).
[CrossRef]

1982 (1)

J. Chrostowski, “Noisy bifurcations in acousto-optic bistability,” Phys. Rev. A 26, 3023–3025 (1982).
[CrossRef]

1980 (1)

Chatterjee, M. R.

Cheung, S. K.

Chrostowski, J.

J. Chrostowski, C. Delisle, and T. Tremblay, “Oscillations in an acoustooptic bistable device,” Can. J. Phys. 61, 188–191 (1983).
[CrossRef]

J. Chrostowski, “Noisy bifurcations in acousto-optic bistability,” Phys. Rev. A 26, 3023–3025 (1982).
[CrossRef]

Delisle, C.

H. Jerominek, J. Y. D. Pomerleau, R. Tremblay, and C. Delisle, “An integrated acousto-optic bistable device,” Opt. Commun. 51, 6–10 (1984).
[CrossRef]

J. Chrostowski, C. Delisle, and T. Tremblay, “Oscillations in an acoustooptic bistable device,” Can. J. Phys. 61, 188–191 (1983).
[CrossRef]

Huang, J.-J.

Jerominek, H.

H. Jerominek, J. Y. D. Pomerleau, R. Tremblay, and C. Delisle, “An integrated acousto-optic bistable device,” Opt. Commun. 51, 6–10 (1984).
[CrossRef]

Korpel, A.

Pomerleau, J. Y. D.

H. Jerominek, J. Y. D. Pomerleau, R. Tremblay, and C. Delisle, “An integrated acousto-optic bistable device,” Opt. Commun. 51, 6–10 (1984).
[CrossRef]

Poon, T.-C.

Ren, Z. Z.

G. J. Yue and Z. Z. Ren, “The stability analysis and the modulation effect on a Bragg acoustooptic bistable system,” IEEE J. Quantum Electron. 26, 815–817 (1990).
[CrossRef]

Tremblay, R.

H. Jerominek, J. Y. D. Pomerleau, R. Tremblay, and C. Delisle, “An integrated acousto-optic bistable device,” Opt. Commun. 51, 6–10 (1984).
[CrossRef]

Tremblay, T.

J. Chrostowski, C. Delisle, and T. Tremblay, “Oscillations in an acoustooptic bistable device,” Can. J. Phys. 61, 188–191 (1983).
[CrossRef]

Yue, G. J.

G. J. Yue and Z. Z. Ren, “The stability analysis and the modulation effect on a Bragg acoustooptic bistable system,” IEEE J. Quantum Electron. 26, 815–817 (1990).
[CrossRef]

Appl. Opt. (2)

Can. J. Phys. (1)

J. Chrostowski, C. Delisle, and T. Tremblay, “Oscillations in an acoustooptic bistable device,” Can. J. Phys. 61, 188–191 (1983).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. J. Yue and Z. Z. Ren, “The stability analysis and the modulation effect on a Bragg acoustooptic bistable system,” IEEE J. Quantum Electron. 26, 815–817 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

H. Jerominek, J. Y. D. Pomerleau, R. Tremblay, and C. Delisle, “An integrated acousto-optic bistable device,” Opt. Commun. 51, 6–10 (1984).
[CrossRef]

Phys. Rev. A (1)

J. Chrostowski, “Noisy bifurcations in acousto-optic bistability,” Phys. Rev. A 26, 3023–3025 (1982).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Dual-input acousto-optic cell, with the two beams incident symmetrically relative to the horizontal axis at ±θ B , the Bragg angle. AOM, acousto-optic modulator.

Fig. 2
Fig. 2

Normalized intensity versus α showing the optical energy exchange between light beams in a dual-input acousto-optic modulator.

Fig. 3
Fig. 3

Zeroth-order acousto-optic flip-flop. AOM is the acousto-optic modulator; α and α0 are the acoustic bias drives; TD is the time delay in the feedback loop; PD is the photdetector; β is the amplifier gain; and Q and are the output states of the flip-flop. TRIG and/RESET are the set and reset input (optical) signals, respectively.

Fig. 4
Fig. 4

First-order acousto-optic flip-flop. The labels are as for Fig. 3.

Fig. 5
Fig. 5

Deterministic map of the zeroth-order optical flip-flop.

Fig. 6
Fig. 6

Trace diagrams for several different cases: (a) β̃ = 0.6π (monostable), (b) β̃ = π (bistable), (c) β̃ = 4.0 (bifurcation), and (d) β̃ = 1.7π (multistable, chaotic).

Fig. 7
Fig. 7

Asymptotic attractors of the zeroth-order bistable device. β̃ is varied from 1.5 to 5.5 to observe the range of behavior from monostability through chaos. Note that a ground state exists throughout the range of β̃.

Fig. 8
Fig. 8

Equivalent circuit diagram of a zeroth-order acousto-optic flip-flop.

Fig. 9
Fig. 9

Spice simulation of the zeroth-order acousto-optic flip-flop, where β̃ = 3.0 and the time delay is TD = 0.01 ms.

Fig. 10
Fig. 10

(a) Spice simulation of the zeroth-order acousto-optic flip-flop, where β̃ = 4.0 and the time delay is TD = 0.01 ms. Note that the Q output is beginning to exhibit the bifurcation phenomenon. (b) Simulation where β̃ = 5.0 and the time delay is TD = 0.01 ms. Note that the Q output has entered the multistate or chaotic regime.

Fig. 11
Fig. 11

Experimental setup for a zeroth-order acousto-optic flip-flop. Laser1 and laser2 are He-Ne lasers; S1 is a toggle-mode shutter (On/Off); S2 is a trigger-mode pulse shutter (fastest speed is ∼1/100 s); STP1 is an optical beam stop; P1 is a cubic beam splitter. A Hewlett-Packard Model HP-606A rf generator (Gen) with AM modulation input (MOD-in) serves as the acoustic driver. Sum, input (bias) adder; A, amplifier gain.

Fig. 12
Fig. 12

(a) Triggering operation of the optical flip-flop, showing Q (upper trace) and Trigger (lower trace). The applied trigger signal is 1/100 s long. The amplifier gain is β = 625. (b) Rising edge of I 1 when the flip-flop is triggered. It takes approximately 640 µs to rise from 10% to 90% of its maximum amplitude.

Tables (1)

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Table 1 Notation Relations between the Symbols Herein and Those of Chrostowskia

Equations (8)

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dE0dξ=-jα2E1, dE1dξ=-jα2E0,
E0z=0=Einc0,
E1z=0=Einc1.
E0=Einc0 cosαξ2-jEinc1 sinαξ2, E1=Einc1 cosαξ2-jEinc0 sinαξ2.
I0=Einc02 cos2αξ2+Einc12 sin2αξ2=Iinc0 cos2αξ2+Iinc1 sin2αξ2, I1=Einc12 cos2αξ2+Einc02 sin2αξ2=Iinc1 cos2αξ2+Iinc0 sin2αξ2.
α=α0+β˜I0t-TD=α0+β˜Einc02 cos2αt-TD2+Einc12 sin2αt-TD2,
Xn+1=1-λ sin2 πXn-0.5,
αn+1=fαn=β˜Einc12 sin2 αn2,

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