Abstract

In this paper, the transient response of a double coupler fiber ring resonator containing an erbium-doped fiber amplifier (EDFA) in half part of the fiber ring resonator and a quantum dot-doped fiber (QDF) saturable absorber in the other half, is investigated. It is demonstrated that, depending on the device parameters and the input power of the signal and pump, various types of dynamic behaviors (such as bistability, monostability, and regenerative pulsation) can be observed in this intrinsic, optical bistable device. The proposed device can be exploited by optical communication networks to realize all-optical functionalities.

© 2013 Optical Society of America

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  1. B. A. Daniel and G. P. Agrawal, “Phase-switched all-optical flip-flops using two-input bistable resonators,” IEEE Photon. Technol. Lett. 24, 479–481 (2012).
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    [CrossRef]
  3. A. R. Bahrampour, S. M. A. Mirzaee, F. Farman, and S. S. Zakeri, “All-optical flip-flop composed of a single nonlinear passive microring coupled to two straight waveguides,” Opt. Commun. 282, 427–433 (2009).
    [CrossRef]
  4. A. R. Bahrampour, S. S. Zakeri, S. M. A. Mirzaee, Z. Ghaderi, and F. Farman, “All-optical set-reset flip-flop based on frequency bistability in semiconductor microring lasers,” Opt. Commun. 282, 2451–2456 (2009).
    [CrossRef]
  5. B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical digital logic gates using bistable semiconductor ring lasers,” Opt. Commun. 30, 190–194 (2009).
  6. S. L. McCall, “Instability and regenerative pulsation phenomena in Fabry–Perot nonlinear optic media devices,” Appl. Phys. Lett. 32, 284–286 (1978).
    [CrossRef]
  7. R. Wang, P. Yeh, H. Chang, X. Yi, and J. Zhao, “All-optical pulse generators for pulse coupled neurons,” Proc. SPIE 3715, 46 (1999).
    [CrossRef]
  8. R. Bonifacio and L. A. Lugiato, “Instabilities for a coherently driven absorber in a ring cavity,” Lett. Nuovo Cimento 21, 510–516, 1978.
    [CrossRef]
  9. R. Bonifacio, M. Gronchi, and L. A. Lugiato, “Self-pulsing in bistable absorption,” Opt. Commun. 30, 129–133 (1979).
    [CrossRef]
  10. K. Ikeda and O. Akimoto, “Instability leading to periodic and chaotic self-pulsations in a bistable optical cavity,” Phys. Rev. Lett. 48, 617–620 (1982).
    [CrossRef]
  11. J. W. Song, S. Y. Shin, and Y. S. Kwon, “Optical bistability, regenerative oscillation, and monostable pulse generation in a liquid crystal bistable optical device,” Appl. Opt. 23, 1521–1524 (1984).
    [CrossRef]
  12. N. Mitra and S. Mukhopadhyay, “A method of developing all-optical mono-stable multivibrator system exploiting the Kerr non-linearity of medium,” Optik 122, 92–94 (2011).
    [CrossRef]
  13. K. Ikeda, H. Daido, and O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 7009–7112 (1980).
  14. H. M. Gibbs, F. A. Hopf, D. L. Kaplan, and R. L. Shoemaker, “Observation of chaos in optical bistability,” Phys. Rev. Lett. 46, 474–477 (1981).
    [CrossRef]
  15. T. Takizawa, Y. Liu, and J. Ohtsubo, “Chaos in a feedback Fabry–Perot interferometer,” IEEE J. Quantum Electron. 30, 334–338 (1994).
    [CrossRef]
  16. N. B. An, N. T. Dan, and H. X. Nguyen, “Excitonic bistabilities, instabilities and chaos in laser-pumped semiconductors,” Phys. Scr. 49, 380–384 (1994).
    [CrossRef]
  17. H. M. Gibbs, J. L. Jewell, J. V. Moloney, K. Tai, S. S. Tarng, D. A. Weinberger, A. C. Gossard, S. L. McCall, A. Passner, and W. Weigmann, “Optical bistability, regenerative pulsations, and transverse effects in room-temperature GaAs–AlGaAs superlattice etalons,” J. Phys. 44, 195–204 (1983).
    [CrossRef]
  18. W. J. Firth, A. J. Scroggie, G. S. McDonald, and L. A. Lugiato, “Hexagonal patterns in optical bistability,” Phys. Rev. A 46, R3609–R3612 (1992).
    [CrossRef]
  19. A. E. Barberoshie, I. I. Gontsya, Y. N. Nika, and A. K. Rotaru, “Noise-induced optical multistability,” J. Exp. Theor. Phys. 77, 211–217 (1993).
  20. K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
    [CrossRef]
  21. Z. Zang and Y. Zhang, “Analysis of optical switching in a Yb3+-doped fiber Bragg grating by using self-phase modulation and cross-phase modulation,” Appl. Opt. 51, 3424–3430 (2012).
    [CrossRef]
  22. P. A. Costanzo-Caso, Y. Jin, S. Granieri, and A. Siahmakoun, “Optical bistability in a nonlinear SOA-based fiber ring resonator,” J. Nonlinear Opt. Phys. Mat. 20, 281–292 (2011).
    [CrossRef]
  23. P. P. Yupapin, P. Saeung, and W. Suwancharoen, “Coupler-loss and coupling-coefficient dependence of bistability and instability in a fiber ring resonator: nonlinear behaviors,” J. Nonlinear Opt. Phys. Mat. 16, 111–118 (2007).
    [CrossRef]
  24. J. E. Heebner and R. W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett. 24, 847–849 (1999).
    [CrossRef]
  25. C. Li, N. Dou, and P. P. Yupapin, “Milliwatt and nanosecond all-optical switching in a double-coupler ring resonator containing an EDFA,” J. Opt. A 8, 728 (2006).
    [CrossRef]
  26. N. Dou and C. Li, “Optical bistability in fiber ring resonator containing an EDFA,” Opt. Commun. 281, 2238–2242 (2008).
    [CrossRef]
  27. S. Tofighi, S. S. Farshemi, B. Sajjad, F. Shahshahani, and A. R. Bahrampour, “Optical bistability in fiber ring resonator containing an erbium-doped fiber amplifier and quantum dot doped fiber saturable absorber,” Appl. Opt. 51, 7016–7024 (2012).
    [CrossRef]
  28. R. W. Boyd, Nonlinear Optics (Academic, 2008).
  29. C. Cheng and H. Zhang, “Characteristics of bandwidth, gain and noise of a PbSe quantum dot-doped fiber amplifier,” Opt. Commun. 277, 372–378 (2007).
    [CrossRef]
  30. K. Kang, K. Daneshvar, and R. Tsu, “Size dependence saturation and absorption of PbS quantum dots,” Microelectron. J. 35, 629–633 (2004).
    [CrossRef]
  31. J. F. Philipps, T. Topfer, H. Ebendorff-Heidepriem, D. Ehrt, R. Sauerbrey, and N. F. Borrelli, “Diode-pumped erbium-ytterbium-glass laser passively Q-switched with a PbS semiconductor quantum-dot doped glass,” Appl. Phys. B 72, 175–178 (2001).
    [CrossRef]
  32. J. E. Raynolds and M. LoCascioa, “Semiconductor nanocrystal based saturable absorbers for optical switching applications,” MRS Proc. 737, E4.5 (2002).
    [CrossRef]
  33. A. R. Bahrampour and M. Mahjoei, “Theoretical analysis of spectral hole-burning in all-optical gain-stabilized multi-channel fiber amplifiers,” Sci. Iranica 9, 125–132 (2002).
  34. A. R. Bahrampour, M. Mahjoei, and A. Rasouli, “A theoretical analysis of the effects of erbium ion pair on the dynamics of an optical gain stabilized fiber amplifier,” Opt. Commun. 265, 283–300 (2006).
    [CrossRef]
  35. A. Polman, “Erbium as a probe of everything?” Physica B 300, 78–90 (2001).
  36. G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic, 2008).
    [CrossRef]
  37. A. W. Naji, B. A. Hamida, X. S. Cheng, M. A. Mahdi, S. Harun, S. Khan, W. F. Al-Khateeb, A. A. Zaidan, B. B. Zaidan, and H. Ahmad, “Review of erbium-doped fiber amplifier,” Int. J. Phys. Sci. 6, 4674–4689 (2011).
  38. K. Y. Ko, M. S. Demokan, and H. Y. Tam, “Transient analysis of erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 6, 1436–1438 (1994).
    [CrossRef]
  39. S. Baskoutas and A. F. Terzis, “Size-dependent bandgap of colloidal quantum dots,” J. Appl. Phys. 99, 013708 (2006).
    [CrossRef]
  40. A. R. Bahrampour, H. Rooholamini, L. Rahimi, and A. A. Askari, “An inhomogeneous theoretical model for analysis of PbSe quantum-dot-doped fiber amplifier,” Opt. Commun. 282, 4449–4454 (2009).
    [CrossRef]
  41. C. Cheng, “A multiquantum-dot-doped fiber amplifier with characteristics of broadband, flat gain, and low noise,” J. Lightwave Technol. 26, 1404–1410 (2008).
    [CrossRef]
  42. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  43. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology (Academic, 1999).
  44. B. Pedersen, A. Bjarklev, O. Lumholt, and J. H. Povlsen, “Detailed design analysis of erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 3, 548–550 (1991).
    [CrossRef]
  45. E. X. DeJesus and C. Kaufman, “Routh–Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations,” Phys. Rev. A 35, 5288–5290 (1987).
    [CrossRef]

2012

2011

P. A. Costanzo-Caso, Y. Jin, S. Granieri, and A. Siahmakoun, “Optical bistability in a nonlinear SOA-based fiber ring resonator,” J. Nonlinear Opt. Phys. Mat. 20, 281–292 (2011).
[CrossRef]

A. W. Naji, B. A. Hamida, X. S. Cheng, M. A. Mahdi, S. Harun, S. Khan, W. F. Al-Khateeb, A. A. Zaidan, B. B. Zaidan, and H. Ahmad, “Review of erbium-doped fiber amplifier,” Int. J. Phys. Sci. 6, 4674–4689 (2011).

N. Mitra and S. Mukhopadhyay, “A method of developing all-optical mono-stable multivibrator system exploiting the Kerr non-linearity of medium,” Optik 122, 92–94 (2011).
[CrossRef]

2009

A. R. Bahrampour, S. M. A. Mirzaee, F. Farman, and S. S. Zakeri, “All-optical flip-flop composed of a single nonlinear passive microring coupled to two straight waveguides,” Opt. Commun. 282, 427–433 (2009).
[CrossRef]

A. R. Bahrampour, S. S. Zakeri, S. M. A. Mirzaee, Z. Ghaderi, and F. Farman, “All-optical set-reset flip-flop based on frequency bistability in semiconductor microring lasers,” Opt. Commun. 282, 2451–2456 (2009).
[CrossRef]

B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical digital logic gates using bistable semiconductor ring lasers,” Opt. Commun. 30, 190–194 (2009).

A. R. Bahrampour, H. Rooholamini, L. Rahimi, and A. A. Askari, “An inhomogeneous theoretical model for analysis of PbSe quantum-dot-doped fiber amplifier,” Opt. Commun. 282, 4449–4454 (2009).
[CrossRef]

2008

C. Cheng, “A multiquantum-dot-doped fiber amplifier with characteristics of broadband, flat gain, and low noise,” J. Lightwave Technol. 26, 1404–1410 (2008).
[CrossRef]

N. Dou and C. Li, “Optical bistability in fiber ring resonator containing an EDFA,” Opt. Commun. 281, 2238–2242 (2008).
[CrossRef]

2007

P. P. Yupapin, P. Saeung, and W. Suwancharoen, “Coupler-loss and coupling-coefficient dependence of bistability and instability in a fiber ring resonator: nonlinear behaviors,” J. Nonlinear Opt. Phys. Mat. 16, 111–118 (2007).
[CrossRef]

C. Cheng and H. Zhang, “Characteristics of bandwidth, gain and noise of a PbSe quantum dot-doped fiber amplifier,” Opt. Commun. 277, 372–378 (2007).
[CrossRef]

2006

A. R. Bahrampour, M. Mahjoei, and A. Rasouli, “A theoretical analysis of the effects of erbium ion pair on the dynamics of an optical gain stabilized fiber amplifier,” Opt. Commun. 265, 283–300 (2006).
[CrossRef]

C. Li, N. Dou, and P. P. Yupapin, “Milliwatt and nanosecond all-optical switching in a double-coupler ring resonator containing an EDFA,” J. Opt. A 8, 728 (2006).
[CrossRef]

S. Baskoutas and A. F. Terzis, “Size-dependent bandgap of colloidal quantum dots,” J. Appl. Phys. 99, 013708 (2006).
[CrossRef]

2004

K. Kang, K. Daneshvar, and R. Tsu, “Size dependence saturation and absorption of PbS quantum dots,” Microelectron. J. 35, 629–633 (2004).
[CrossRef]

2002

J. E. Raynolds and M. LoCascioa, “Semiconductor nanocrystal based saturable absorbers for optical switching applications,” MRS Proc. 737, E4.5 (2002).
[CrossRef]

A. R. Bahrampour and M. Mahjoei, “Theoretical analysis of spectral hole-burning in all-optical gain-stabilized multi-channel fiber amplifiers,” Sci. Iranica 9, 125–132 (2002).

2001

A. Polman, “Erbium as a probe of everything?” Physica B 300, 78–90 (2001).

J. F. Philipps, T. Topfer, H. Ebendorff-Heidepriem, D. Ehrt, R. Sauerbrey, and N. F. Borrelli, “Diode-pumped erbium-ytterbium-glass laser passively Q-switched with a PbS semiconductor quantum-dot doped glass,” Appl. Phys. B 72, 175–178 (2001).
[CrossRef]

1999

J. E. Heebner and R. W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett. 24, 847–849 (1999).
[CrossRef]

R. Wang, P. Yeh, H. Chang, X. Yi, and J. Zhao, “All-optical pulse generators for pulse coupled neurons,” Proc. SPIE 3715, 46 (1999).
[CrossRef]

1994

T. Takizawa, Y. Liu, and J. Ohtsubo, “Chaos in a feedback Fabry–Perot interferometer,” IEEE J. Quantum Electron. 30, 334–338 (1994).
[CrossRef]

N. B. An, N. T. Dan, and H. X. Nguyen, “Excitonic bistabilities, instabilities and chaos in laser-pumped semiconductors,” Phys. Scr. 49, 380–384 (1994).
[CrossRef]

K. Y. Ko, M. S. Demokan, and H. Y. Tam, “Transient analysis of erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 6, 1436–1438 (1994).
[CrossRef]

1993

A. E. Barberoshie, I. I. Gontsya, Y. N. Nika, and A. K. Rotaru, “Noise-induced optical multistability,” J. Exp. Theor. Phys. 77, 211–217 (1993).

1992

W. J. Firth, A. J. Scroggie, G. S. McDonald, and L. A. Lugiato, “Hexagonal patterns in optical bistability,” Phys. Rev. A 46, R3609–R3612 (1992).
[CrossRef]

1991

B. Pedersen, A. Bjarklev, O. Lumholt, and J. H. Povlsen, “Detailed design analysis of erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 3, 548–550 (1991).
[CrossRef]

1987

E. X. DeJesus and C. Kaufman, “Routh–Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations,” Phys. Rev. A 35, 5288–5290 (1987).
[CrossRef]

1984

1983

H. M. Gibbs, J. L. Jewell, J. V. Moloney, K. Tai, S. S. Tarng, D. A. Weinberger, A. C. Gossard, S. L. McCall, A. Passner, and W. Weigmann, “Optical bistability, regenerative pulsations, and transverse effects in room-temperature GaAs–AlGaAs superlattice etalons,” J. Phys. 44, 195–204 (1983).
[CrossRef]

1982

K. Ikeda and O. Akimoto, “Instability leading to periodic and chaotic self-pulsations in a bistable optical cavity,” Phys. Rev. Lett. 48, 617–620 (1982).
[CrossRef]

1981

H. M. Gibbs, F. A. Hopf, D. L. Kaplan, and R. L. Shoemaker, “Observation of chaos in optical bistability,” Phys. Rev. Lett. 46, 474–477 (1981).
[CrossRef]

1980

K. Ikeda, H. Daido, and O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 7009–7112 (1980).

1979

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
[CrossRef]

R. Bonifacio, M. Gronchi, and L. A. Lugiato, “Self-pulsing in bistable absorption,” Opt. Commun. 30, 129–133 (1979).
[CrossRef]

1978

R. Bonifacio and L. A. Lugiato, “Instabilities for a coherently driven absorber in a ring cavity,” Lett. Nuovo Cimento 21, 510–516, 1978.
[CrossRef]

S. L. McCall, “Instability and regenerative pulsation phenomena in Fabry–Perot nonlinear optic media devices,” Appl. Phys. Lett. 32, 284–286 (1978).
[CrossRef]

Agrawal, G. P.

B. A. Daniel and G. P. Agrawal, “Phase-switched all-optical flip-flops using two-input bistable resonators,” IEEE Photon. Technol. Lett. 24, 479–481 (2012).
[CrossRef]

G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic, 2008).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

Ahmad, H.

A. W. Naji, B. A. Hamida, X. S. Cheng, M. A. Mahdi, S. Harun, S. Khan, W. F. Al-Khateeb, A. A. Zaidan, B. B. Zaidan, and H. Ahmad, “Review of erbium-doped fiber amplifier,” Int. J. Phys. Sci. 6, 4674–4689 (2011).

Akimoto, O.

K. Ikeda and O. Akimoto, “Instability leading to periodic and chaotic self-pulsations in a bistable optical cavity,” Phys. Rev. Lett. 48, 617–620 (1982).
[CrossRef]

K. Ikeda, H. Daido, and O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 7009–7112 (1980).

Al-Khateeb, W. F.

A. W. Naji, B. A. Hamida, X. S. Cheng, M. A. Mahdi, S. Harun, S. Khan, W. F. Al-Khateeb, A. A. Zaidan, B. B. Zaidan, and H. Ahmad, “Review of erbium-doped fiber amplifier,” Int. J. Phys. Sci. 6, 4674–4689 (2011).

An, N. B.

N. B. An, N. T. Dan, and H. X. Nguyen, “Excitonic bistabilities, instabilities and chaos in laser-pumped semiconductors,” Phys. Scr. 49, 380–384 (1994).
[CrossRef]

Askari, A. A.

A. R. Bahrampour, H. Rooholamini, L. Rahimi, and A. A. Askari, “An inhomogeneous theoretical model for analysis of PbSe quantum-dot-doped fiber amplifier,” Opt. Commun. 282, 4449–4454 (2009).
[CrossRef]

Bahrampour, A. R.

S. Tofighi, S. S. Farshemi, B. Sajjad, F. Shahshahani, and A. R. Bahrampour, “Optical bistability in fiber ring resonator containing an erbium-doped fiber amplifier and quantum dot doped fiber saturable absorber,” Appl. Opt. 51, 7016–7024 (2012).
[CrossRef]

A. R. Bahrampour, H. Rooholamini, L. Rahimi, and A. A. Askari, “An inhomogeneous theoretical model for analysis of PbSe quantum-dot-doped fiber amplifier,” Opt. Commun. 282, 4449–4454 (2009).
[CrossRef]

A. R. Bahrampour, S. M. A. Mirzaee, F. Farman, and S. S. Zakeri, “All-optical flip-flop composed of a single nonlinear passive microring coupled to two straight waveguides,” Opt. Commun. 282, 427–433 (2009).
[CrossRef]

A. R. Bahrampour, S. S. Zakeri, S. M. A. Mirzaee, Z. Ghaderi, and F. Farman, “All-optical set-reset flip-flop based on frequency bistability in semiconductor microring lasers,” Opt. Commun. 282, 2451–2456 (2009).
[CrossRef]

A. R. Bahrampour, M. Mahjoei, and A. Rasouli, “A theoretical analysis of the effects of erbium ion pair on the dynamics of an optical gain stabilized fiber amplifier,” Opt. Commun. 265, 283–300 (2006).
[CrossRef]

A. R. Bahrampour and M. Mahjoei, “Theoretical analysis of spectral hole-burning in all-optical gain-stabilized multi-channel fiber amplifiers,” Sci. Iranica 9, 125–132 (2002).

Barberoshie, A. E.

A. E. Barberoshie, I. I. Gontsya, Y. N. Nika, and A. K. Rotaru, “Noise-induced optical multistability,” J. Exp. Theor. Phys. 77, 211–217 (1993).

Baskoutas, S.

S. Baskoutas and A. F. Terzis, “Size-dependent bandgap of colloidal quantum dots,” J. Appl. Phys. 99, 013708 (2006).
[CrossRef]

Becker, P. C.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology (Academic, 1999).

Bjarklev, A.

B. Pedersen, A. Bjarklev, O. Lumholt, and J. H. Povlsen, “Detailed design analysis of erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 3, 548–550 (1991).
[CrossRef]

Bonifacio, R.

R. Bonifacio, M. Gronchi, and L. A. Lugiato, “Self-pulsing in bistable absorption,” Opt. Commun. 30, 129–133 (1979).
[CrossRef]

R. Bonifacio and L. A. Lugiato, “Instabilities for a coherently driven absorber in a ring cavity,” Lett. Nuovo Cimento 21, 510–516, 1978.
[CrossRef]

Borrelli, N. F.

J. F. Philipps, T. Topfer, H. Ebendorff-Heidepriem, D. Ehrt, R. Sauerbrey, and N. F. Borrelli, “Diode-pumped erbium-ytterbium-glass laser passively Q-switched with a PbS semiconductor quantum-dot doped glass,” Appl. Phys. B 72, 175–178 (2001).
[CrossRef]

Boyd, R. W.

Chang, H.

R. Wang, P. Yeh, H. Chang, X. Yi, and J. Zhao, “All-optical pulse generators for pulse coupled neurons,” Proc. SPIE 3715, 46 (1999).
[CrossRef]

Cheng, C.

C. Cheng, “A multiquantum-dot-doped fiber amplifier with characteristics of broadband, flat gain, and low noise,” J. Lightwave Technol. 26, 1404–1410 (2008).
[CrossRef]

C. Cheng and H. Zhang, “Characteristics of bandwidth, gain and noise of a PbSe quantum dot-doped fiber amplifier,” Opt. Commun. 277, 372–378 (2007).
[CrossRef]

Cheng, X. S.

A. W. Naji, B. A. Hamida, X. S. Cheng, M. A. Mahdi, S. Harun, S. Khan, W. F. Al-Khateeb, A. A. Zaidan, B. B. Zaidan, and H. Ahmad, “Review of erbium-doped fiber amplifier,” Int. J. Phys. Sci. 6, 4674–4689 (2011).

Costanzo-Caso, P. A.

P. A. Costanzo-Caso, Y. Jin, S. Granieri, and A. Siahmakoun, “Optical bistability in a nonlinear SOA-based fiber ring resonator,” J. Nonlinear Opt. Phys. Mat. 20, 281–292 (2011).
[CrossRef]

Daido, H.

K. Ikeda, H. Daido, and O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 7009–7112 (1980).

Dan, N. T.

N. B. An, N. T. Dan, and H. X. Nguyen, “Excitonic bistabilities, instabilities and chaos in laser-pumped semiconductors,” Phys. Scr. 49, 380–384 (1994).
[CrossRef]

Daneshvar, K.

K. Kang, K. Daneshvar, and R. Tsu, “Size dependence saturation and absorption of PbS quantum dots,” Microelectron. J. 35, 629–633 (2004).
[CrossRef]

Daniel, B. A.

B. A. Daniel and G. P. Agrawal, “Phase-switched all-optical flip-flops using two-input bistable resonators,” IEEE Photon. Technol. Lett. 24, 479–481 (2012).
[CrossRef]

DeJesus, E. X.

E. X. DeJesus and C. Kaufman, “Routh–Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations,” Phys. Rev. A 35, 5288–5290 (1987).
[CrossRef]

Demokan, M. S.

K. Y. Ko, M. S. Demokan, and H. Y. Tam, “Transient analysis of erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 6, 1436–1438 (1994).
[CrossRef]

Dou, N.

N. Dou and C. Li, “Optical bistability in fiber ring resonator containing an EDFA,” Opt. Commun. 281, 2238–2242 (2008).
[CrossRef]

C. Li, N. Dou, and P. P. Yupapin, “Milliwatt and nanosecond all-optical switching in a double-coupler ring resonator containing an EDFA,” J. Opt. A 8, 728 (2006).
[CrossRef]

Ebendorff-Heidepriem, H.

J. F. Philipps, T. Topfer, H. Ebendorff-Heidepriem, D. Ehrt, R. Sauerbrey, and N. F. Borrelli, “Diode-pumped erbium-ytterbium-glass laser passively Q-switched with a PbS semiconductor quantum-dot doped glass,” Appl. Phys. B 72, 175–178 (2001).
[CrossRef]

Ehrt, D.

J. F. Philipps, T. Topfer, H. Ebendorff-Heidepriem, D. Ehrt, R. Sauerbrey, and N. F. Borrelli, “Diode-pumped erbium-ytterbium-glass laser passively Q-switched with a PbS semiconductor quantum-dot doped glass,” Appl. Phys. B 72, 175–178 (2001).
[CrossRef]

Farman, F.

A. R. Bahrampour, S. M. A. Mirzaee, F. Farman, and S. S. Zakeri, “All-optical flip-flop composed of a single nonlinear passive microring coupled to two straight waveguides,” Opt. Commun. 282, 427–433 (2009).
[CrossRef]

A. R. Bahrampour, S. S. Zakeri, S. M. A. Mirzaee, Z. Ghaderi, and F. Farman, “All-optical set-reset flip-flop based on frequency bistability in semiconductor microring lasers,” Opt. Commun. 282, 2451–2456 (2009).
[CrossRef]

Farshemi, S. S.

Firth, W. J.

W. J. Firth, A. J. Scroggie, G. S. McDonald, and L. A. Lugiato, “Hexagonal patterns in optical bistability,” Phys. Rev. A 46, R3609–R3612 (1992).
[CrossRef]

Ghaderi, Z.

A. R. Bahrampour, S. S. Zakeri, S. M. A. Mirzaee, Z. Ghaderi, and F. Farman, “All-optical set-reset flip-flop based on frequency bistability in semiconductor microring lasers,” Opt. Commun. 282, 2451–2456 (2009).
[CrossRef]

Gibbs, H. M.

H. M. Gibbs, J. L. Jewell, J. V. Moloney, K. Tai, S. S. Tarng, D. A. Weinberger, A. C. Gossard, S. L. McCall, A. Passner, and W. Weigmann, “Optical bistability, regenerative pulsations, and transverse effects in room-temperature GaAs–AlGaAs superlattice etalons,” J. Phys. 44, 195–204 (1983).
[CrossRef]

H. M. Gibbs, F. A. Hopf, D. L. Kaplan, and R. L. Shoemaker, “Observation of chaos in optical bistability,” Phys. Rev. Lett. 46, 474–477 (1981).
[CrossRef]

Gontsya, I. I.

A. E. Barberoshie, I. I. Gontsya, Y. N. Nika, and A. K. Rotaru, “Noise-induced optical multistability,” J. Exp. Theor. Phys. 77, 211–217 (1993).

Gossard, A. C.

H. M. Gibbs, J. L. Jewell, J. V. Moloney, K. Tai, S. S. Tarng, D. A. Weinberger, A. C. Gossard, S. L. McCall, A. Passner, and W. Weigmann, “Optical bistability, regenerative pulsations, and transverse effects in room-temperature GaAs–AlGaAs superlattice etalons,” J. Phys. 44, 195–204 (1983).
[CrossRef]

Granieri, S.

P. A. Costanzo-Caso, Y. Jin, S. Granieri, and A. Siahmakoun, “Optical bistability in a nonlinear SOA-based fiber ring resonator,” J. Nonlinear Opt. Phys. Mat. 20, 281–292 (2011).
[CrossRef]

Gronchi, M.

R. Bonifacio, M. Gronchi, and L. A. Lugiato, “Self-pulsing in bistable absorption,” Opt. Commun. 30, 129–133 (1979).
[CrossRef]

Hamida, B. A.

A. W. Naji, B. A. Hamida, X. S. Cheng, M. A. Mahdi, S. Harun, S. Khan, W. F. Al-Khateeb, A. A. Zaidan, B. B. Zaidan, and H. Ahmad, “Review of erbium-doped fiber amplifier,” Int. J. Phys. Sci. 6, 4674–4689 (2011).

Harun, S.

A. W. Naji, B. A. Hamida, X. S. Cheng, M. A. Mahdi, S. Harun, S. Khan, W. F. Al-Khateeb, A. A. Zaidan, B. B. Zaidan, and H. Ahmad, “Review of erbium-doped fiber amplifier,” Int. J. Phys. Sci. 6, 4674–4689 (2011).

Heebner, J. E.

Hopf, F. A.

H. M. Gibbs, F. A. Hopf, D. L. Kaplan, and R. L. Shoemaker, “Observation of chaos in optical bistability,” Phys. Rev. Lett. 46, 474–477 (1981).
[CrossRef]

Ikeda, K.

K. Ikeda and O. Akimoto, “Instability leading to periodic and chaotic self-pulsations in a bistable optical cavity,” Phys. Rev. Lett. 48, 617–620 (1982).
[CrossRef]

K. Ikeda, H. Daido, and O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 7009–7112 (1980).

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
[CrossRef]

Jewell, J. L.

H. M. Gibbs, J. L. Jewell, J. V. Moloney, K. Tai, S. S. Tarng, D. A. Weinberger, A. C. Gossard, S. L. McCall, A. Passner, and W. Weigmann, “Optical bistability, regenerative pulsations, and transverse effects in room-temperature GaAs–AlGaAs superlattice etalons,” J. Phys. 44, 195–204 (1983).
[CrossRef]

Jin, Y.

P. A. Costanzo-Caso, Y. Jin, S. Granieri, and A. Siahmakoun, “Optical bistability in a nonlinear SOA-based fiber ring resonator,” J. Nonlinear Opt. Phys. Mat. 20, 281–292 (2011).
[CrossRef]

Kang, K.

K. Kang, K. Daneshvar, and R. Tsu, “Size dependence saturation and absorption of PbS quantum dots,” Microelectron. J. 35, 629–633 (2004).
[CrossRef]

Kaplan, D. L.

H. M. Gibbs, F. A. Hopf, D. L. Kaplan, and R. L. Shoemaker, “Observation of chaos in optical bistability,” Phys. Rev. Lett. 46, 474–477 (1981).
[CrossRef]

Kaufman, C.

E. X. DeJesus and C. Kaufman, “Routh–Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations,” Phys. Rev. A 35, 5288–5290 (1987).
[CrossRef]

Khan, S.

A. W. Naji, B. A. Hamida, X. S. Cheng, M. A. Mahdi, S. Harun, S. Khan, W. F. Al-Khateeb, A. A. Zaidan, B. B. Zaidan, and H. Ahmad, “Review of erbium-doped fiber amplifier,” Int. J. Phys. Sci. 6, 4674–4689 (2011).

Ko, K. Y.

K. Y. Ko, M. S. Demokan, and H. Y. Tam, “Transient analysis of erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 6, 1436–1438 (1994).
[CrossRef]

Kwon, Y. S.

Lam, V. D.

Le, K. Q.

Li, B.

B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical digital logic gates using bistable semiconductor ring lasers,” Opt. Commun. 30, 190–194 (2009).

Li, C.

N. Dou and C. Li, “Optical bistability in fiber ring resonator containing an EDFA,” Opt. Commun. 281, 2238–2242 (2008).
[CrossRef]

C. Li, N. Dou, and P. P. Yupapin, “Milliwatt and nanosecond all-optical switching in a double-coupler ring resonator containing an EDFA,” J. Opt. A 8, 728 (2006).
[CrossRef]

Liu, Y.

T. Takizawa, Y. Liu, and J. Ohtsubo, “Chaos in a feedback Fabry–Perot interferometer,” IEEE J. Quantum Electron. 30, 334–338 (1994).
[CrossRef]

LoCascioa, M.

J. E. Raynolds and M. LoCascioa, “Semiconductor nanocrystal based saturable absorbers for optical switching applications,” MRS Proc. 737, E4.5 (2002).
[CrossRef]

Lugiato, L. A.

W. J. Firth, A. J. Scroggie, G. S. McDonald, and L. A. Lugiato, “Hexagonal patterns in optical bistability,” Phys. Rev. A 46, R3609–R3612 (1992).
[CrossRef]

R. Bonifacio, M. Gronchi, and L. A. Lugiato, “Self-pulsing in bistable absorption,” Opt. Commun. 30, 129–133 (1979).
[CrossRef]

R. Bonifacio and L. A. Lugiato, “Instabilities for a coherently driven absorber in a ring cavity,” Lett. Nuovo Cimento 21, 510–516, 1978.
[CrossRef]

Lumholt, O.

B. Pedersen, A. Bjarklev, O. Lumholt, and J. H. Povlsen, “Detailed design analysis of erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 3, 548–550 (1991).
[CrossRef]

Mahdi, M. A.

A. W. Naji, B. A. Hamida, X. S. Cheng, M. A. Mahdi, S. Harun, S. Khan, W. F. Al-Khateeb, A. A. Zaidan, B. B. Zaidan, and H. Ahmad, “Review of erbium-doped fiber amplifier,” Int. J. Phys. Sci. 6, 4674–4689 (2011).

Mahjoei, M.

A. R. Bahrampour, M. Mahjoei, and A. Rasouli, “A theoretical analysis of the effects of erbium ion pair on the dynamics of an optical gain stabilized fiber amplifier,” Opt. Commun. 265, 283–300 (2006).
[CrossRef]

A. R. Bahrampour and M. Mahjoei, “Theoretical analysis of spectral hole-burning in all-optical gain-stabilized multi-channel fiber amplifiers,” Sci. Iranica 9, 125–132 (2002).

McCall, S. L.

H. M. Gibbs, J. L. Jewell, J. V. Moloney, K. Tai, S. S. Tarng, D. A. Weinberger, A. C. Gossard, S. L. McCall, A. Passner, and W. Weigmann, “Optical bistability, regenerative pulsations, and transverse effects in room-temperature GaAs–AlGaAs superlattice etalons,” J. Phys. 44, 195–204 (1983).
[CrossRef]

S. L. McCall, “Instability and regenerative pulsation phenomena in Fabry–Perot nonlinear optic media devices,” Appl. Phys. Lett. 32, 284–286 (1978).
[CrossRef]

McDonald, G. S.

W. J. Firth, A. J. Scroggie, G. S. McDonald, and L. A. Lugiato, “Hexagonal patterns in optical bistability,” Phys. Rev. A 46, R3609–R3612 (1992).
[CrossRef]

Memon, M. I.

B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical digital logic gates using bistable semiconductor ring lasers,” Opt. Commun. 30, 190–194 (2009).

Mezosi, G.

B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical digital logic gates using bistable semiconductor ring lasers,” Opt. Commun. 30, 190–194 (2009).

Mirzaee, S. M. A.

A. R. Bahrampour, S. S. Zakeri, S. M. A. Mirzaee, Z. Ghaderi, and F. Farman, “All-optical set-reset flip-flop based on frequency bistability in semiconductor microring lasers,” Opt. Commun. 282, 2451–2456 (2009).
[CrossRef]

A. R. Bahrampour, S. M. A. Mirzaee, F. Farman, and S. S. Zakeri, “All-optical flip-flop composed of a single nonlinear passive microring coupled to two straight waveguides,” Opt. Commun. 282, 427–433 (2009).
[CrossRef]

Mitra, N.

N. Mitra and S. Mukhopadhyay, “A method of developing all-optical mono-stable multivibrator system exploiting the Kerr non-linearity of medium,” Optik 122, 92–94 (2011).
[CrossRef]

Moloney, J. V.

H. M. Gibbs, J. L. Jewell, J. V. Moloney, K. Tai, S. S. Tarng, D. A. Weinberger, A. C. Gossard, S. L. McCall, A. Passner, and W. Weigmann, “Optical bistability, regenerative pulsations, and transverse effects in room-temperature GaAs–AlGaAs superlattice etalons,” J. Phys. 44, 195–204 (1983).
[CrossRef]

Mukhopadhyay, S.

N. Mitra and S. Mukhopadhyay, “A method of developing all-optical mono-stable multivibrator system exploiting the Kerr non-linearity of medium,” Optik 122, 92–94 (2011).
[CrossRef]

Naji, A. W.

A. W. Naji, B. A. Hamida, X. S. Cheng, M. A. Mahdi, S. Harun, S. Khan, W. F. Al-Khateeb, A. A. Zaidan, B. B. Zaidan, and H. Ahmad, “Review of erbium-doped fiber amplifier,” Int. J. Phys. Sci. 6, 4674–4689 (2011).

Ngo, Q. M.

Nguyen, H. X.

N. B. An, N. T. Dan, and H. X. Nguyen, “Excitonic bistabilities, instabilities and chaos in laser-pumped semiconductors,” Phys. Scr. 49, 380–384 (1994).
[CrossRef]

Nika, Y. N.

A. E. Barberoshie, I. I. Gontsya, Y. N. Nika, and A. K. Rotaru, “Noise-induced optical multistability,” J. Exp. Theor. Phys. 77, 211–217 (1993).

Ohtsubo, J.

T. Takizawa, Y. Liu, and J. Ohtsubo, “Chaos in a feedback Fabry–Perot interferometer,” IEEE J. Quantum Electron. 30, 334–338 (1994).
[CrossRef]

Olsson, N. A.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology (Academic, 1999).

Passner, A.

H. M. Gibbs, J. L. Jewell, J. V. Moloney, K. Tai, S. S. Tarng, D. A. Weinberger, A. C. Gossard, S. L. McCall, A. Passner, and W. Weigmann, “Optical bistability, regenerative pulsations, and transverse effects in room-temperature GaAs–AlGaAs superlattice etalons,” J. Phys. 44, 195–204 (1983).
[CrossRef]

Pedersen, B.

B. Pedersen, A. Bjarklev, O. Lumholt, and J. H. Povlsen, “Detailed design analysis of erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 3, 548–550 (1991).
[CrossRef]

Philipps, J. F.

J. F. Philipps, T. Topfer, H. Ebendorff-Heidepriem, D. Ehrt, R. Sauerbrey, and N. F. Borrelli, “Diode-pumped erbium-ytterbium-glass laser passively Q-switched with a PbS semiconductor quantum-dot doped glass,” Appl. Phys. B 72, 175–178 (2001).
[CrossRef]

Polman, A.

A. Polman, “Erbium as a probe of everything?” Physica B 300, 78–90 (2001).

Povlsen, J. H.

B. Pedersen, A. Bjarklev, O. Lumholt, and J. H. Povlsen, “Detailed design analysis of erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 3, 548–550 (1991).
[CrossRef]

Rahimi, L.

A. R. Bahrampour, H. Rooholamini, L. Rahimi, and A. A. Askari, “An inhomogeneous theoretical model for analysis of PbSe quantum-dot-doped fiber amplifier,” Opt. Commun. 282, 4449–4454 (2009).
[CrossRef]

Rasouli, A.

A. R. Bahrampour, M. Mahjoei, and A. Rasouli, “A theoretical analysis of the effects of erbium ion pair on the dynamics of an optical gain stabilized fiber amplifier,” Opt. Commun. 265, 283–300 (2006).
[CrossRef]

Raynolds, J. E.

J. E. Raynolds and M. LoCascioa, “Semiconductor nanocrystal based saturable absorbers for optical switching applications,” MRS Proc. 737, E4.5 (2002).
[CrossRef]

Rooholamini, H.

A. R. Bahrampour, H. Rooholamini, L. Rahimi, and A. A. Askari, “An inhomogeneous theoretical model for analysis of PbSe quantum-dot-doped fiber amplifier,” Opt. Commun. 282, 4449–4454 (2009).
[CrossRef]

Rotaru, A. K.

A. E. Barberoshie, I. I. Gontsya, Y. N. Nika, and A. K. Rotaru, “Noise-induced optical multistability,” J. Exp. Theor. Phys. 77, 211–217 (1993).

Saeung, P.

P. P. Yupapin, P. Saeung, and W. Suwancharoen, “Coupler-loss and coupling-coefficient dependence of bistability and instability in a fiber ring resonator: nonlinear behaviors,” J. Nonlinear Opt. Phys. Mat. 16, 111–118 (2007).
[CrossRef]

Sajjad, B.

Sauerbrey, R.

J. F. Philipps, T. Topfer, H. Ebendorff-Heidepriem, D. Ehrt, R. Sauerbrey, and N. F. Borrelli, “Diode-pumped erbium-ytterbium-glass laser passively Q-switched with a PbS semiconductor quantum-dot doped glass,” Appl. Phys. B 72, 175–178 (2001).
[CrossRef]

Scroggie, A. J.

W. J. Firth, A. J. Scroggie, G. S. McDonald, and L. A. Lugiato, “Hexagonal patterns in optical bistability,” Phys. Rev. A 46, R3609–R3612 (1992).
[CrossRef]

Shahshahani, F.

Shin, S. Y.

Shoemaker, R. L.

H. M. Gibbs, F. A. Hopf, D. L. Kaplan, and R. L. Shoemaker, “Observation of chaos in optical bistability,” Phys. Rev. Lett. 46, 474–477 (1981).
[CrossRef]

Siahmakoun, A.

P. A. Costanzo-Caso, Y. Jin, S. Granieri, and A. Siahmakoun, “Optical bistability in a nonlinear SOA-based fiber ring resonator,” J. Nonlinear Opt. Phys. Mat. 20, 281–292 (2011).
[CrossRef]

Simpson, J. R.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology (Academic, 1999).

Song, J. W.

Sorel, M.

B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical digital logic gates using bistable semiconductor ring lasers,” Opt. Commun. 30, 190–194 (2009).

Suwancharoen, W.

P. P. Yupapin, P. Saeung, and W. Suwancharoen, “Coupler-loss and coupling-coefficient dependence of bistability and instability in a fiber ring resonator: nonlinear behaviors,” J. Nonlinear Opt. Phys. Mat. 16, 111–118 (2007).
[CrossRef]

Tai, K.

H. M. Gibbs, J. L. Jewell, J. V. Moloney, K. Tai, S. S. Tarng, D. A. Weinberger, A. C. Gossard, S. L. McCall, A. Passner, and W. Weigmann, “Optical bistability, regenerative pulsations, and transverse effects in room-temperature GaAs–AlGaAs superlattice etalons,” J. Phys. 44, 195–204 (1983).
[CrossRef]

Takizawa, T.

T. Takizawa, Y. Liu, and J. Ohtsubo, “Chaos in a feedback Fabry–Perot interferometer,” IEEE J. Quantum Electron. 30, 334–338 (1994).
[CrossRef]

Tam, H. Y.

K. Y. Ko, M. S. Demokan, and H. Y. Tam, “Transient analysis of erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 6, 1436–1438 (1994).
[CrossRef]

Tarng, S. S.

H. M. Gibbs, J. L. Jewell, J. V. Moloney, K. Tai, S. S. Tarng, D. A. Weinberger, A. C. Gossard, S. L. McCall, A. Passner, and W. Weigmann, “Optical bistability, regenerative pulsations, and transverse effects in room-temperature GaAs–AlGaAs superlattice etalons,” J. Phys. 44, 195–204 (1983).
[CrossRef]

Terzis, A. F.

S. Baskoutas and A. F. Terzis, “Size-dependent bandgap of colloidal quantum dots,” J. Appl. Phys. 99, 013708 (2006).
[CrossRef]

Tofighi, S.

Topfer, T.

J. F. Philipps, T. Topfer, H. Ebendorff-Heidepriem, D. Ehrt, R. Sauerbrey, and N. F. Borrelli, “Diode-pumped erbium-ytterbium-glass laser passively Q-switched with a PbS semiconductor quantum-dot doped glass,” Appl. Phys. B 72, 175–178 (2001).
[CrossRef]

Tsu, R.

K. Kang, K. Daneshvar, and R. Tsu, “Size dependence saturation and absorption of PbS quantum dots,” Microelectron. J. 35, 629–633 (2004).
[CrossRef]

Wang, R.

R. Wang, P. Yeh, H. Chang, X. Yi, and J. Zhao, “All-optical pulse generators for pulse coupled neurons,” Proc. SPIE 3715, 46 (1999).
[CrossRef]

Wang, Z.

B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical digital logic gates using bistable semiconductor ring lasers,” Opt. Commun. 30, 190–194 (2009).

Weigmann, W.

H. M. Gibbs, J. L. Jewell, J. V. Moloney, K. Tai, S. S. Tarng, D. A. Weinberger, A. C. Gossard, S. L. McCall, A. Passner, and W. Weigmann, “Optical bistability, regenerative pulsations, and transverse effects in room-temperature GaAs–AlGaAs superlattice etalons,” J. Phys. 44, 195–204 (1983).
[CrossRef]

Weinberger, D. A.

H. M. Gibbs, J. L. Jewell, J. V. Moloney, K. Tai, S. S. Tarng, D. A. Weinberger, A. C. Gossard, S. L. McCall, A. Passner, and W. Weigmann, “Optical bistability, regenerative pulsations, and transverse effects in room-temperature GaAs–AlGaAs superlattice etalons,” J. Phys. 44, 195–204 (1983).
[CrossRef]

Yeh, P.

R. Wang, P. Yeh, H. Chang, X. Yi, and J. Zhao, “All-optical pulse generators for pulse coupled neurons,” Proc. SPIE 3715, 46 (1999).
[CrossRef]

Yi, X.

R. Wang, P. Yeh, H. Chang, X. Yi, and J. Zhao, “All-optical pulse generators for pulse coupled neurons,” Proc. SPIE 3715, 46 (1999).
[CrossRef]

Yu, S.

B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical digital logic gates using bistable semiconductor ring lasers,” Opt. Commun. 30, 190–194 (2009).

Yupapin, P. P.

P. P. Yupapin, P. Saeung, and W. Suwancharoen, “Coupler-loss and coupling-coefficient dependence of bistability and instability in a fiber ring resonator: nonlinear behaviors,” J. Nonlinear Opt. Phys. Mat. 16, 111–118 (2007).
[CrossRef]

C. Li, N. Dou, and P. P. Yupapin, “Milliwatt and nanosecond all-optical switching in a double-coupler ring resonator containing an EDFA,” J. Opt. A 8, 728 (2006).
[CrossRef]

Zaidan, A. A.

A. W. Naji, B. A. Hamida, X. S. Cheng, M. A. Mahdi, S. Harun, S. Khan, W. F. Al-Khateeb, A. A. Zaidan, B. B. Zaidan, and H. Ahmad, “Review of erbium-doped fiber amplifier,” Int. J. Phys. Sci. 6, 4674–4689 (2011).

Zaidan, B. B.

A. W. Naji, B. A. Hamida, X. S. Cheng, M. A. Mahdi, S. Harun, S. Khan, W. F. Al-Khateeb, A. A. Zaidan, B. B. Zaidan, and H. Ahmad, “Review of erbium-doped fiber amplifier,” Int. J. Phys. Sci. 6, 4674–4689 (2011).

Zakeri, S. S.

A. R. Bahrampour, S. S. Zakeri, S. M. A. Mirzaee, Z. Ghaderi, and F. Farman, “All-optical set-reset flip-flop based on frequency bistability in semiconductor microring lasers,” Opt. Commun. 282, 2451–2456 (2009).
[CrossRef]

A. R. Bahrampour, S. M. A. Mirzaee, F. Farman, and S. S. Zakeri, “All-optical flip-flop composed of a single nonlinear passive microring coupled to two straight waveguides,” Opt. Commun. 282, 427–433 (2009).
[CrossRef]

Zang, Z.

Zhang, H.

C. Cheng and H. Zhang, “Characteristics of bandwidth, gain and noise of a PbSe quantum dot-doped fiber amplifier,” Opt. Commun. 277, 372–378 (2007).
[CrossRef]

Zhang, Y.

Zhao, J.

R. Wang, P. Yeh, H. Chang, X. Yi, and J. Zhao, “All-optical pulse generators for pulse coupled neurons,” Proc. SPIE 3715, 46 (1999).
[CrossRef]

Appl. Opt.

Appl. Phys. B

J. F. Philipps, T. Topfer, H. Ebendorff-Heidepriem, D. Ehrt, R. Sauerbrey, and N. F. Borrelli, “Diode-pumped erbium-ytterbium-glass laser passively Q-switched with a PbS semiconductor quantum-dot doped glass,” Appl. Phys. B 72, 175–178 (2001).
[CrossRef]

Appl. Phys. Lett.

S. L. McCall, “Instability and regenerative pulsation phenomena in Fabry–Perot nonlinear optic media devices,” Appl. Phys. Lett. 32, 284–286 (1978).
[CrossRef]

IEEE J. Quantum Electron.

T. Takizawa, Y. Liu, and J. Ohtsubo, “Chaos in a feedback Fabry–Perot interferometer,” IEEE J. Quantum Electron. 30, 334–338 (1994).
[CrossRef]

IEEE Photon. Technol. Lett.

B. A. Daniel and G. P. Agrawal, “Phase-switched all-optical flip-flops using two-input bistable resonators,” IEEE Photon. Technol. Lett. 24, 479–481 (2012).
[CrossRef]

K. Y. Ko, M. S. Demokan, and H. Y. Tam, “Transient analysis of erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 6, 1436–1438 (1994).
[CrossRef]

B. Pedersen, A. Bjarklev, O. Lumholt, and J. H. Povlsen, “Detailed design analysis of erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 3, 548–550 (1991).
[CrossRef]

Int. J. Phys. Sci.

A. W. Naji, B. A. Hamida, X. S. Cheng, M. A. Mahdi, S. Harun, S. Khan, W. F. Al-Khateeb, A. A. Zaidan, B. B. Zaidan, and H. Ahmad, “Review of erbium-doped fiber amplifier,” Int. J. Phys. Sci. 6, 4674–4689 (2011).

J. Appl. Phys.

S. Baskoutas and A. F. Terzis, “Size-dependent bandgap of colloidal quantum dots,” J. Appl. Phys. 99, 013708 (2006).
[CrossRef]

J. Exp. Theor. Phys.

A. E. Barberoshie, I. I. Gontsya, Y. N. Nika, and A. K. Rotaru, “Noise-induced optical multistability,” J. Exp. Theor. Phys. 77, 211–217 (1993).

J. Lightwave Technol.

J. Nonlinear Opt. Phys. Mat.

P. A. Costanzo-Caso, Y. Jin, S. Granieri, and A. Siahmakoun, “Optical bistability in a nonlinear SOA-based fiber ring resonator,” J. Nonlinear Opt. Phys. Mat. 20, 281–292 (2011).
[CrossRef]

P. P. Yupapin, P. Saeung, and W. Suwancharoen, “Coupler-loss and coupling-coefficient dependence of bistability and instability in a fiber ring resonator: nonlinear behaviors,” J. Nonlinear Opt. Phys. Mat. 16, 111–118 (2007).
[CrossRef]

J. Opt. A

C. Li, N. Dou, and P. P. Yupapin, “Milliwatt and nanosecond all-optical switching in a double-coupler ring resonator containing an EDFA,” J. Opt. A 8, 728 (2006).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys.

H. M. Gibbs, J. L. Jewell, J. V. Moloney, K. Tai, S. S. Tarng, D. A. Weinberger, A. C. Gossard, S. L. McCall, A. Passner, and W. Weigmann, “Optical bistability, regenerative pulsations, and transverse effects in room-temperature GaAs–AlGaAs superlattice etalons,” J. Phys. 44, 195–204 (1983).
[CrossRef]

Lett. Nuovo Cimento

R. Bonifacio and L. A. Lugiato, “Instabilities for a coherently driven absorber in a ring cavity,” Lett. Nuovo Cimento 21, 510–516, 1978.
[CrossRef]

Microelectron. J.

K. Kang, K. Daneshvar, and R. Tsu, “Size dependence saturation and absorption of PbS quantum dots,” Microelectron. J. 35, 629–633 (2004).
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Figures (7)

Fig. 1.
Fig. 1.

Schematic configuration of a fiber ring resonator containing an EDFA and QDF. Fiber coupler is denoted by FC.

Fig. 2.
Fig. 2.

(a) Description of state transition in the regenerative pulsation process via the hysteresis loop model. (b) The spatiotemporal variation of power and density in the EDFA and QDF sections of the fiber ring resonator for input power Pb=0.045W and device parameters t1=0.9, t2=0.99, Pp=0.05W, Nt=1025m3, Nt=1.6×1022m3. The fiber ring is divided into 100 parts. i is the number of parts in which the desired quantities are evaluated.

Fig. 3.
Fig. 3.

Real part of the characteristic roots versus the input power for the case where the device parameters are t1=0.9, t2=0.99, Pp=0.05, Nt=1025m3, Nt=1.6×1022m3.

Fig. 4.
Fig. 4.

Real part of the characteristic roots versus the input power for the case in which the device parameters are chosen as t1=0.9, t2=0.99, Pp=0.5W, Nt=1.4×1024m3, Nt=1.2×1022m3.

Fig. 5.
Fig. 5.

Spatiotemporal variation of power and density in the EDFA and QDF sections of the fiber ring resonator in the switch-up process for input power Pb=0.0412+0.001exp((t2×104)2/1012)W and device parameters t1=0.9, t2=0.99, Pp=0.5W, Nt=1.4×1024m3, Nt=1.2×1022m3. The fiber ring is divided into 100 parts. i is the number of parts in which the desired quantities are evaluated.

Fig. 6.
Fig. 6.

Spatiotemporal variation of power and density in the EDFA and QDF sections of the fiber ring resonator in the switch-down process for input power Pb=0.04140.001exp((t2×104)2/1012)W and device parameters t1=0.9, t2=0.99, Pp=0.5W, Nt=1.4×1024m3, Nt=1.2×1022m3. The fiber ring is divided into 100 parts. i is the number of parts in which the desired quantities are evaluated.

Fig. 7.
Fig. 7.

Position of characteristic root λ1 in the complex plane for resonance mode m=0 and off-resonance modes m=(±5,±4,,±1). The device parameters and input power are chosen as t1=0.9, t2=0.99, Pp=0.05, Nt=1.4×1024m3, Nt=1.2×1022m3 (a) Pin=0.035W, (b) Pin=0.0375W, (c) Pin=0.0412W, and (d) Pin=0.0427W. The input power of (b) and (d) lie on the far left and far right sides of the hysteresis loop in which the upper and lower branches become unstable, respectively. Consequently, Re(λ1) of the resonance mode m=0 are located in the right hand side of complex plane for the corresponding power value on the (b) upper branch and (d) lower branch of the hysteresis loop.

Tables (1)

Tables Icon

Table 1. Optical Parameters of Double Coupler Fiber Ring Resonator Containing an EDFA and a QDF Saturable Absorber

Equations (26)

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N(z,t)t=PpΓpSpωpσap(NtN(z,t))Nt+N(z,t)τ+qs(z,t)2ΓsSsωs[(σasσes)Nt(σas+σes)N(z,t)],
qs(z,t)z+ncqs(z,t)t=α2qs(z,t)+(Γs(σes+σas)4N(z,t)+Γs(σesσas)4Nt)qs(z,t).
N2(z,t)t=N2(z,t)τqs(z,t)2ΓsσesSsωsN2(z,t)+qs(z,t)2ΓsσasSsωs(NtN2(z,t)),
qs(z,t)z+ncqs(z,t)t=α2qs(z,t)+[Γsσes2N2(z,t)Γsσas2(NtN2(z,t))]qs(z,t),
qs(0)=t1qs(L)+χ1qin,
qs(L+2)=t2qs(L2),
N¯(z)=Nt(σasσes)q¯s2(z)(σas+σes)PsatEr(z)+τΓpσapPpSpωpτΓpσapPp+Spωp1+q¯s2(z)PsatEr,dq¯s(z)dz=12g01+q¯s2(z)PsatErq¯s(z)α2q¯s(z),N¯2(z)=NtSsωsτΓsσasq¯s2(z)1+q¯s2(z)PsatQD,dq¯s(z)dz=12α01+q¯s2(z)PsatErq¯s(z)α2q¯s(z),
X(z,t)=X¯(z)+δX(z,t),
dδqsdz=(14Γs(σes+σas)[N¯(z)+q¯s(z)A(q¯s(z);λ)]+14Γs(σesσas)Ntnλcα2)δqs(z),
dδqsdz=(12Γs(σes+σas)[N¯2(z)+q¯s(z)B(q¯s(z);λ)]12ΓsσasNtnλcα2)δqs(z),
A(q¯s(z);λ)2Γs[(σasσes)Nt(σas+σes)N¯(z)]Ssωs(λ+1τ)+Γs(σas+σes)q¯s2(z)+ΓpPpσapSsωsSpωpq¯s(z)B(q¯s(z);λ)2Γs[σas(NtN¯2(z))σesN¯2(z)]Ssωs(λ+1τ)+Γs(σas+σes)q¯s2(z)q¯s(z).
δqs(z,t)=δqs(0)eλ(tnzc)exp[(14Γs(σesσas)Ntα2)z+Γs(σes+σas)40z(N¯(z)+q¯s(z)A(q¯s(z);λ))dz],
δqs(z,t)=δqs(L+2)eλ(tnc(zL2))exp[(12ΓsσasNt+α2)(zL2)+Γs(σes+σas)2L2z(N¯2(z)+q¯s(z)B(q¯s(z);λ))dz].
δqs(0,t)=t1δqs(L,t)
δqs(L+2)=t2δqs(L2).
t1t2exp[nsLλ/cαL/2+LΓs(σesσas)Nt/8LΓsσasNt/4+LΓs(σes+σas)(N¯+q¯sA¯)/8+LΓs(σes+σas)(N¯2+q¯sB¯)/4]=1.
2ln(t1t2)/L2nsλ/cα+Γs(σesσas)Nt/4ΓsσasNt/2+Γs(σes+σas)N¯/4+Γs(σes+σas)N¯2/2+12Γs2q¯s2(σes+σas)[(σasσes)Nt(σas+σes)N¯]Ssωs(λ+1τ)+Γs(σas+σes)q¯s2+ΓpPpσapSsωsSpωp+Γs2q¯s2(σes+σas)[σas(NtN¯2)σesN¯2]Ssωs(λ+1τ)+Γs(σas+σes)q¯s2=4mπi/L,
qi+1j=ehφijqij1iM,
qM+1j=t2qM+1j,
qi+1j=ehϕijqijM+1i2M,
q1j+1=t1q2M+1j+χ1qin,
dNij+1dt=AijNij+1+Bij1iM,
dN2ij+1dt=AijNij+1+BijM+1i2M,
Aij=1τ+PpΓpσapSpωp+q¯ij2Γs(σes+σas)Ssωs,Bij=(q¯ij2Γs(σasσes)Ssωs+PpΓpσapSpωp1τ)Nt,Aij=1τ+q¯ij2Γs(σes+σas)SsωsandBij=q¯ij2ΓsσasSsωsNt.
Nij+1=enAijcNij+BijAij(1enAijc)1iM,
N2ij+1=enAijcN2ij+BijAij(1enAijc)M+1i2M.

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