Abstract

We describe the principle of operation of an all-optical flip-flop based on dispersive bistability in a distributed feedback semiconductor optical amplifier. Cross-phase modulation controls the photonic bandgap and Bragg resonances of the amplifier, thereby shifting the hysteresis and switching thresholds to higher or lower powers. We give the details of a simple theoretical model that is used to simulate the set and reset operations. We also experimentally investigate the dependence on set-signal power and the response to back-to-back set signals, and we apply the theoretical model to understand these experimental results.

© 2001 Optical Society of America

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  1. H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
    [CrossRef]
  2. M. J. Adams and R. J. Wyatt, “Optical bistability in distributed feedback semiconductor laser amplifiers,” IEE Proc. 134, 35–40 (1987).
  3. D. N. Maywar and G. P. Agrawal, “Effect of chirped gratings on reflective optical bistability in DFB semiconductor laser amplifiers,” IEEE J. Quantum Electron. 34, 2364–2370 (1998).
    [CrossRef]
  4. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd. ed. (Van Nostrand Reinhold, New York, 1993).
  5. G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25, 2297–2306 (1989).
    [CrossRef]
  6. H. Kawaguchi, “Progress in optical functional devices using two-section laser diodes/amplifiers,” IEE Proc. 140, 3–15 (1993).
  7. R. J. Manning, A. D. Ellis, A. J. Poustie, and K. J. Blow, “Semiconductor laser amplifiers for ultrafast all-optical signal processing,” J. Opt. Soc. Am. B 14, 3204–3216 (1997).
    [CrossRef]
  8. N. Ogasawara and R. Ito, “Static and dynamic properties of nonlinear semiconductor lasers amplifiers,” Jpn. J. Appl. Phys. 25, 739–742 (1986).
    [CrossRef]
  9. K. Inoue, “All-optical flip-flop operation in an optical bistable device using two lights of different frequencies,” Opt. Lett. 12, 918–920 (1987).
    [CrossRef] [PubMed]
  10. D. N. Maywar, G. P. Agrawal, and Y. Nakano, “Robust optical control of an optical-amplifier-based flip-flop,” Opt. Express 6, 75–80 (2000).
    [CrossRef] [PubMed]
  11. H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
    [CrossRef]
  12. K. Otsuka and H. Iwamura, “Analysis of a multistable semiconductor light amplifier,” IEEE J. Quantum Electron. 19, 1184–1186 (1983).
    [CrossRef]
  13. P. Meystre, “On the use of the mean-field theory in optical bistability,” Opt. Commun. 26, 277–280 (1978).
    [CrossRef]
  14. W. F. Sharfin and M. Dagenais, “Dynamics of optically switched bistable diode laser amplifiers,” IEEE J. Quantum Electron. 23, 303–308 (1987).
    [CrossRef]
  15. T. Durhuus, C. Joergensen, B. Mikkelsen, R. J. S. Pedersen, and K. E. Stubkjaer, “All optical wavelength conversion by SOA’s in a Mach-Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
    [CrossRef]
  16. M. J. Adams, D. A. O. Davies, M. C. Tatham, and M. A. Fisher, “Nonlinearities in semiconductor laser amplifiers,” Opt. Quantum Electron. 27, 1–13 (1995).
    [CrossRef]
  17. R. J. Manning, and D. A. O. Davies, and J. K. Lucek, “Recovery rates in semiconductor laser amplifiers: optical and electrical bias dependencies,” Electron. Lett. 30, 1233–1234 (1994).
    [CrossRef]
  18. D. N. Maywar, Govind P. Agrawal, and Y. Nakano, “Robust all-optical control of a semiconductor optical amplifier flip-flop,” presented at Optical Amplifiers and Their Applications, Quebec, Canada, July 9–12, 2000.

2000

1998

D. N. Maywar and G. P. Agrawal, “Effect of chirped gratings on reflective optical bistability in DFB semiconductor laser amplifiers,” IEEE J. Quantum Electron. 34, 2364–2370 (1998).
[CrossRef]

1997

1995

M. J. Adams, D. A. O. Davies, M. C. Tatham, and M. A. Fisher, “Nonlinearities in semiconductor laser amplifiers,” Opt. Quantum Electron. 27, 1–13 (1995).
[CrossRef]

1994

R. J. Manning, and D. A. O. Davies, and J. K. Lucek, “Recovery rates in semiconductor laser amplifiers: optical and electrical bias dependencies,” Electron. Lett. 30, 1233–1234 (1994).
[CrossRef]

T. Durhuus, C. Joergensen, B. Mikkelsen, R. J. S. Pedersen, and K. E. Stubkjaer, “All optical wavelength conversion by SOA’s in a Mach-Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
[CrossRef]

1993

H. Kawaguchi, “Progress in optical functional devices using two-section laser diodes/amplifiers,” IEE Proc. 140, 3–15 (1993).

1989

G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25, 2297–2306 (1989).
[CrossRef]

1987

M. J. Adams and R. J. Wyatt, “Optical bistability in distributed feedback semiconductor laser amplifiers,” IEE Proc. 134, 35–40 (1987).

W. F. Sharfin and M. Dagenais, “Dynamics of optically switched bistable diode laser amplifiers,” IEEE J. Quantum Electron. 23, 303–308 (1987).
[CrossRef]

K. Inoue, “All-optical flip-flop operation in an optical bistable device using two lights of different frequencies,” Opt. Lett. 12, 918–920 (1987).
[CrossRef] [PubMed]

1986

N. Ogasawara and R. Ito, “Static and dynamic properties of nonlinear semiconductor lasers amplifiers,” Jpn. J. Appl. Phys. 25, 739–742 (1986).
[CrossRef]

1983

K. Otsuka and H. Iwamura, “Analysis of a multistable semiconductor light amplifier,” IEEE J. Quantum Electron. 19, 1184–1186 (1983).
[CrossRef]

1979

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

1978

P. Meystre, “On the use of the mean-field theory in optical bistability,” Opt. Commun. 26, 277–280 (1978).
[CrossRef]

1972

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[CrossRef]

Adams, M. J.

M. J. Adams, D. A. O. Davies, M. C. Tatham, and M. A. Fisher, “Nonlinearities in semiconductor laser amplifiers,” Opt. Quantum Electron. 27, 1–13 (1995).
[CrossRef]

M. J. Adams and R. J. Wyatt, “Optical bistability in distributed feedback semiconductor laser amplifiers,” IEE Proc. 134, 35–40 (1987).

Agrawal, G. P.

D. N. Maywar, G. P. Agrawal, and Y. Nakano, “Robust optical control of an optical-amplifier-based flip-flop,” Opt. Express 6, 75–80 (2000).
[CrossRef] [PubMed]

D. N. Maywar and G. P. Agrawal, “Effect of chirped gratings on reflective optical bistability in DFB semiconductor laser amplifiers,” IEEE J. Quantum Electron. 34, 2364–2370 (1998).
[CrossRef]

G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25, 2297–2306 (1989).
[CrossRef]

Blow, K. J.

Dagenais, M.

W. F. Sharfin and M. Dagenais, “Dynamics of optically switched bistable diode laser amplifiers,” IEEE J. Quantum Electron. 23, 303–308 (1987).
[CrossRef]

Davies, D. A. O.

M. J. Adams, D. A. O. Davies, M. C. Tatham, and M. A. Fisher, “Nonlinearities in semiconductor laser amplifiers,” Opt. Quantum Electron. 27, 1–13 (1995).
[CrossRef]

R. J. Manning, and D. A. O. Davies, and J. K. Lucek, “Recovery rates in semiconductor laser amplifiers: optical and electrical bias dependencies,” Electron. Lett. 30, 1233–1234 (1994).
[CrossRef]

Durhuus, T.

T. Durhuus, C. Joergensen, B. Mikkelsen, R. J. S. Pedersen, and K. E. Stubkjaer, “All optical wavelength conversion by SOA’s in a Mach-Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
[CrossRef]

Ellis, A. D.

Fisher, M. A.

M. J. Adams, D. A. O. Davies, M. C. Tatham, and M. A. Fisher, “Nonlinearities in semiconductor laser amplifiers,” Opt. Quantum Electron. 27, 1–13 (1995).
[CrossRef]

Garmire, E.

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

Inoue, K.

Ito, R.

N. Ogasawara and R. Ito, “Static and dynamic properties of nonlinear semiconductor lasers amplifiers,” Jpn. J. Appl. Phys. 25, 739–742 (1986).
[CrossRef]

Iwamura, H.

K. Otsuka and H. Iwamura, “Analysis of a multistable semiconductor light amplifier,” IEEE J. Quantum Electron. 19, 1184–1186 (1983).
[CrossRef]

Joergensen, C.

T. Durhuus, C. Joergensen, B. Mikkelsen, R. J. S. Pedersen, and K. E. Stubkjaer, “All optical wavelength conversion by SOA’s in a Mach-Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
[CrossRef]

Kawaguchi, H.

H. Kawaguchi, “Progress in optical functional devices using two-section laser diodes/amplifiers,” IEE Proc. 140, 3–15 (1993).

Kogelnik, H.

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[CrossRef]

Lucek, J. K.

R. J. Manning, and D. A. O. Davies, and J. K. Lucek, “Recovery rates in semiconductor laser amplifiers: optical and electrical bias dependencies,” Electron. Lett. 30, 1233–1234 (1994).
[CrossRef]

Manning, R. J.

R. J. Manning, A. D. Ellis, A. J. Poustie, and K. J. Blow, “Semiconductor laser amplifiers for ultrafast all-optical signal processing,” J. Opt. Soc. Am. B 14, 3204–3216 (1997).
[CrossRef]

R. J. Manning, and D. A. O. Davies, and J. K. Lucek, “Recovery rates in semiconductor laser amplifiers: optical and electrical bias dependencies,” Electron. Lett. 30, 1233–1234 (1994).
[CrossRef]

Marburger, J. H.

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

Maywar, D. N.

D. N. Maywar, G. P. Agrawal, and Y. Nakano, “Robust optical control of an optical-amplifier-based flip-flop,” Opt. Express 6, 75–80 (2000).
[CrossRef] [PubMed]

D. N. Maywar and G. P. Agrawal, “Effect of chirped gratings on reflective optical bistability in DFB semiconductor laser amplifiers,” IEEE J. Quantum Electron. 34, 2364–2370 (1998).
[CrossRef]

Meystre, P.

P. Meystre, “On the use of the mean-field theory in optical bistability,” Opt. Commun. 26, 277–280 (1978).
[CrossRef]

Mikkelsen, B.

T. Durhuus, C. Joergensen, B. Mikkelsen, R. J. S. Pedersen, and K. E. Stubkjaer, “All optical wavelength conversion by SOA’s in a Mach-Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
[CrossRef]

Nakano, Y.

Ogasawara, N.

N. Ogasawara and R. Ito, “Static and dynamic properties of nonlinear semiconductor lasers amplifiers,” Jpn. J. Appl. Phys. 25, 739–742 (1986).
[CrossRef]

Olsson, N. A.

G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25, 2297–2306 (1989).
[CrossRef]

Otsuka, K.

K. Otsuka and H. Iwamura, “Analysis of a multistable semiconductor light amplifier,” IEEE J. Quantum Electron. 19, 1184–1186 (1983).
[CrossRef]

Pedersen, R. J. S.

T. Durhuus, C. Joergensen, B. Mikkelsen, R. J. S. Pedersen, and K. E. Stubkjaer, “All optical wavelength conversion by SOA’s in a Mach-Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
[CrossRef]

Poustie, A. J.

Shank, C. V.

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[CrossRef]

Sharfin, W. F.

W. F. Sharfin and M. Dagenais, “Dynamics of optically switched bistable diode laser amplifiers,” IEEE J. Quantum Electron. 23, 303–308 (1987).
[CrossRef]

Stubkjaer, K. E.

T. Durhuus, C. Joergensen, B. Mikkelsen, R. J. S. Pedersen, and K. E. Stubkjaer, “All optical wavelength conversion by SOA’s in a Mach-Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
[CrossRef]

Tatham, M. C.

M. J. Adams, D. A. O. Davies, M. C. Tatham, and M. A. Fisher, “Nonlinearities in semiconductor laser amplifiers,” Opt. Quantum Electron. 27, 1–13 (1995).
[CrossRef]

Winful, H. G.

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

Wyatt, R. J.

M. J. Adams and R. J. Wyatt, “Optical bistability in distributed feedback semiconductor laser amplifiers,” IEE Proc. 134, 35–40 (1987).

Appl. Phys. Lett.

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

Electron. Lett.

R. J. Manning, and D. A. O. Davies, and J. K. Lucek, “Recovery rates in semiconductor laser amplifiers: optical and electrical bias dependencies,” Electron. Lett. 30, 1233–1234 (1994).
[CrossRef]

IEE Proc.

H. Kawaguchi, “Progress in optical functional devices using two-section laser diodes/amplifiers,” IEE Proc. 140, 3–15 (1993).

M. J. Adams and R. J. Wyatt, “Optical bistability in distributed feedback semiconductor laser amplifiers,” IEE Proc. 134, 35–40 (1987).

IEEE J. Quantum Electron.

D. N. Maywar and G. P. Agrawal, “Effect of chirped gratings on reflective optical bistability in DFB semiconductor laser amplifiers,” IEEE J. Quantum Electron. 34, 2364–2370 (1998).
[CrossRef]

K. Otsuka and H. Iwamura, “Analysis of a multistable semiconductor light amplifier,” IEEE J. Quantum Electron. 19, 1184–1186 (1983).
[CrossRef]

W. F. Sharfin and M. Dagenais, “Dynamics of optically switched bistable diode laser amplifiers,” IEEE J. Quantum Electron. 23, 303–308 (1987).
[CrossRef]

G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25, 2297–2306 (1989).
[CrossRef]

IEEE Photonics Technol. Lett.

T. Durhuus, C. Joergensen, B. Mikkelsen, R. J. S. Pedersen, and K. E. Stubkjaer, “All optical wavelength conversion by SOA’s in a Mach-Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
[CrossRef]

J. Appl. Phys.

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[CrossRef]

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

N. Ogasawara and R. Ito, “Static and dynamic properties of nonlinear semiconductor lasers amplifiers,” Jpn. J. Appl. Phys. 25, 739–742 (1986).
[CrossRef]

Opt. Commun.

P. Meystre, “On the use of the mean-field theory in optical bistability,” Opt. Commun. 26, 277–280 (1978).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

M. J. Adams, D. A. O. Davies, M. C. Tatham, and M. A. Fisher, “Nonlinearities in semiconductor laser amplifiers,” Opt. Quantum Electron. 27, 1–13 (1995).
[CrossRef]

Other

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd. ed. (Van Nostrand Reinhold, New York, 1993).

D. N. Maywar, Govind P. Agrawal, and Y. Nakano, “Robust all-optical control of a semiconductor optical amplifier flip-flop,” presented at Optical Amplifiers and Their Applications, Quebec, Canada, July 9–12, 2000.

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Figures (9)

Fig. 1
Fig. 1

Bistable hysteresis curve. Two stable transmission states, Pon and Poff, occur for a single input power PH.

Fig. 2
Fig. 2

Flip-flop operation based on the holding beam: (a) The holding-beam input power P0 is varied beyond the switching thresholds to (b) set and reset its bistable transmission T.

Fig. 3
Fig. 3

XPM-based set: (a) the transmitted power (indicated by the circle) is initially low for a fixed input power PH. (b) XPM (+Δϕ) caused by a set signal pushes the hysteresis curve to smaller powers, thereby switching the transmission to a higher power. (c) After the set signal passes, the hysteresis curve relaxes to its initial shape, with the transmitted-power state on the higher hysteresis branch.

Fig. 4
Fig. 4

XPM-based reset: (a) high initial transmitted power (indicated by the circle). (b) XPM (-Δϕ) caused by a reset signal pushes the hysteresis curve to larger powers, and the transmitted power drops to a lower hysteresis curve branch. (c) Hysteresis curve relaxes to its initial shape, and transmission remains at the lower power.

Fig. 5
Fig. 5

Flip-flop operation using XPM: (a) set and reset signals control (b) the bistable transmission T by varying the hysteresis curve according to Figs. 3 and 4.

Fig. 6
Fig. 6

Experimental setup. Dashed box indicates the flip-flop circuit. LN, lithium niobate.

Fig. 7
Fig. 7

Set-pulse ledge: (a) ledge feature Px can occur during the application of the set pulse. (b) Severe hysteresis shift is the origin of the ledge. (c) Ledge height Px-Poff decreases with set power.

Fig. 8
Fig. 8

Back-to-back set signals: (a) control signals; an additional set pulse enters the DFB SOA between set and reset signals. (b) In response, the holding-beam transmission remains stable and only experiences a transient dip.

Fig. 9
Fig. 9

Simulated response of the flip-flop to back-to-back set signals: (a) control signals; (b) holding-beam transmitted power, showing a ledge and a notch.

Equations (38)

Equations on this page are rendered with MathJax. Learn more.

E(x, y, z, t)=Re{ˆF(x, y)[A(z, t)exp(iβBz)+B(z, t)exp(-iβBz)]exp(-iωt)},
Az+1v At=iδ-i g2(1-iα)+i αint2A+iκB,
-Bz+1v Bt=iδ-i g2(1-iα)+i αint2B+iκA.
g(x, y, z, t)=aΓ[N(x, y, z, t)-N0],
-D2N+Nt=Jed-Nτ-a(N-N0) Iω,
dNdt=Jed-Nτ-aω(N-N0) ΓσWd(|A|2+|B|2),
τ dgdt=g0-1+PA+PBPsatg.
τ dgdt=g0-1+PA+PBPsatg,
A=A1 exp(iγz)+rB2 exp(-iγz),
B=q-1A1 exp(iγz)+B2 exp(-iγz),
A=h γ cos(γξ)+iΔ sin(γξ)γ cos(γL)-iΔ sin(γL),
B=h iκ sin(γξ)γ cos(γL)-iΔ sin(γL),
PA=P0ζ[cosh(2γiξ)θ1-sinh(2γiξ)θ2+cos(2γrξ)θ3-sin(2γrξ)θ4],
PB=P0ζ|κ|2[cosh(2γiξ)-cos(2γrξ)],
PA=P0ζsinh(2γiL)θ1+[cosh(2γiL)-1]θ22γiL+sin(2γrL)θ3+[1-cos(2γrL)]θ42γrL,
PB=P0ζ|κ|2sinh(2γiL)2γiL-sin(2γrL)2γrL.
T=P0ζ2(γr2+γi2),
R=P0ζ|κ|2[cosh(2γiL)-cos(2γrL)].
ES(x, y, z, t)
=Re{ˆF(x, y)S(z, t)exp(iβSz)exp(-iωSt)},
ER(x, y, z, t)
=Re{ˆF(x, y)R(z, t)exp(iβRz)exp(-iωRt)}.
-D2N+Nt=Jed-Nτ-a(N-N0) Iω-a(N-N0) ISωS+η IRωR.
τ dgdt=g0+η PRPRsat-1+PA+PBPsat+PSPSsat×g,
PSz+1vS PSt=gPS,
PRz+1vR PRt=-ηPR,
dPSdz=gPS,
dPRdz=-ηPR.
PS=PS0 expgz+L2,
PR=PR0 exp-ηz+L2.
PS=PS0 exp(gL)-1gL,
PR=PR0 1-exp(-ηL)ηL.
PS0(t)=Si exp{-[(t-tS)/WS]2M},
PR0(t)=Ri exp{-[(t-tR)/WR]2N},
Δϕ=αDϕ g0L2 PA+PBPsat+g0L2 PSPSsat-ηL2 PRPRsat,
Dϕ=1+PA+PBPsat+PSPSsat.
ΔϕSXPM0.18πPS0,
ΔϕRXPM-0.06πPR0.

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