Abstract

We show and identify the role of the backward amplified spontaneous emission (ASE) in inducing bistability and hysteresis in a unidirectional ring erbium-doped fiber (edf) laser. It results from the interplay between the signal and the backward ASE in the gain medium that is ejected from the fiber loop by an isolator. A removal of the isolator eliminates the bistability. Another important factor is the strong wavelength dependence of the absorption and emission coefficients and their ratio.

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References

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  1. H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).
  2. H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bista-bility in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).
  3. H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, Orlando, 1985).
  4. A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its applications,” Appl. Phys. Lett. 15, 376 (1969).
  5. V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29(20), 2387–2389 (2004).
    [PubMed]
  6. A. Baas, J. Ph. Karr, H. Eleuch, and E. Giacobino, “Optical bistability in semiconductor microcavities,” Phys. Rev. A 69, 023809 (2004).
  7. J. Shao, S. Li, Q. Shen, Z. Wu, Z. Cao, and J. Gu, “Experiment and theoretical explanation of optical bistability in a single erbium-doped fiber ring laser,” Opt. Express 15(7), 3673–3679 (2007).
    [PubMed]
  8. J. M. Oh and D. Lee, “Strong optical bistability in a simple L-band tunable erbium-doped fiber ring laser,” IEEE J. Quantum Electron. 40, 374–377 (2004).
  9. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium Doped Fiber Amplifiers: Fundamentals and Technology (Academic, 1999).
  10. E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley, 1994).
  11. R. Weill, A. Bekker, B. Levit, M. Zhurahov, and B. Fischer, “Thermalization of one-dimensional photon gas and thermal lasers in erbium-doped fibers,” Opt. Express 25(16), 18963–18973 (2017).
    [PubMed]
  12. D. E. McCumber, “Theory of phonon terminated optical masers,” Phys. Rev. 134, 299 (1964).
  13. R. M. Martin and R. S. Quimby, “Experimental evidence of the validity of the McCumber theory relating emission and absorption for rare-earth glasses,” J. Opt. Soc. Am. B 23(9), 1770 (2006).
  14. E. H. Kennard, “On the Interaction of Radiation with Matter and on Fluorescent Exciting Power,” Phys. Rev. 28, 672 (1926).
  15. B. I. Stepanov, “A universal relation between the absorption and luminescence spectra of complex molecules,” Dokl. Akad. Nauk SSR 112, 839 (1957).

2017 (1)

2007 (1)

2006 (1)

2004 (3)

V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29(20), 2387–2389 (2004).
[PubMed]

A. Baas, J. Ph. Karr, H. Eleuch, and E. Giacobino, “Optical bistability in semiconductor microcavities,” Phys. Rev. A 69, 023809 (2004).

J. M. Oh and D. Lee, “Strong optical bistability in a simple L-band tunable erbium-doped fiber ring laser,” IEEE J. Quantum Electron. 40, 374–377 (2004).

1979 (1)

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bista-bility in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).

1976 (1)

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).

1969 (1)

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its applications,” Appl. Phys. Lett. 15, 376 (1969).

1964 (1)

D. E. McCumber, “Theory of phonon terminated optical masers,” Phys. Rev. 134, 299 (1964).

1957 (1)

B. I. Stepanov, “A universal relation between the absorption and luminescence spectra of complex molecules,” Dokl. Akad. Nauk SSR 112, 839 (1957).

1926 (1)

E. H. Kennard, “On the Interaction of Radiation with Matter and on Fluorescent Exciting Power,” Phys. Rev. 28, 672 (1926).

Almeida, V. R.

Baas, A.

A. Baas, J. Ph. Karr, H. Eleuch, and E. Giacobino, “Optical bistability in semiconductor microcavities,” Phys. Rev. A 69, 023809 (2004).

Bekker, A.

Cao, Z.

Daneu, V.

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its applications,” Appl. Phys. Lett. 15, 376 (1969).

Eleuch, H.

A. Baas, J. Ph. Karr, H. Eleuch, and E. Giacobino, “Optical bistability in semiconductor microcavities,” Phys. Rev. A 69, 023809 (2004).

Fischer, B.

Giacobino, E.

A. Baas, J. Ph. Karr, H. Eleuch, and E. Giacobino, “Optical bistability in semiconductor microcavities,” Phys. Rev. A 69, 023809 (2004).

Gibbs, H. M.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bista-bility in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).

Goldhar, J.

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its applications,” Appl. Phys. Lett. 15, 376 (1969).

Gossard, A. C.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bista-bility in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).

Gu, J.

Karr, J. Ph.

A. Baas, J. Ph. Karr, H. Eleuch, and E. Giacobino, “Optical bistability in semiconductor microcavities,” Phys. Rev. A 69, 023809 (2004).

Kennard, E. H.

E. H. Kennard, “On the Interaction of Radiation with Matter and on Fluorescent Exciting Power,” Phys. Rev. 28, 672 (1926).

Kurnit, N. A.

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its applications,” Appl. Phys. Lett. 15, 376 (1969).

Lee, D.

J. M. Oh and D. Lee, “Strong optical bistability in a simple L-band tunable erbium-doped fiber ring laser,” IEEE J. Quantum Electron. 40, 374–377 (2004).

Levit, B.

Li, S.

Lipson, M.

Martin, R. M.

McCall, S. L.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bista-bility in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).

McCumber, D. E.

D. E. McCumber, “Theory of phonon terminated optical masers,” Phys. Rev. 134, 299 (1964).

Oh, J. M.

J. M. Oh and D. Lee, “Strong optical bistability in a simple L-band tunable erbium-doped fiber ring laser,” IEEE J. Quantum Electron. 40, 374–377 (2004).

Passner, A.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bista-bility in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).

Quimby, R. S.

Shao, J.

Shen, Q.

Stepanov, B. I.

B. I. Stepanov, “A universal relation between the absorption and luminescence spectra of complex molecules,” Dokl. Akad. Nauk SSR 112, 839 (1957).

Szoke, A.

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its applications,” Appl. Phys. Lett. 15, 376 (1969).

Venkatesan, T. N. C.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bista-bility in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).

Weill, R.

Wiegmann, W.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bista-bility in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).

Wu, Z.

Zhurahov, M.

Appl. Phys. Lett. (2)

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its applications,” Appl. Phys. Lett. 15, 376 (1969).

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bista-bility in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979).

Dokl. Akad. Nauk SSR (1)

B. I. Stepanov, “A universal relation between the absorption and luminescence spectra of complex molecules,” Dokl. Akad. Nauk SSR 112, 839 (1957).

IEEE J. Quantum Electron. (1)

J. M. Oh and D. Lee, “Strong optical bistability in a simple L-band tunable erbium-doped fiber ring laser,” IEEE J. Quantum Electron. 40, 374–377 (2004).

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. (2)

D. E. McCumber, “Theory of phonon terminated optical masers,” Phys. Rev. 134, 299 (1964).

E. H. Kennard, “On the Interaction of Radiation with Matter and on Fluorescent Exciting Power,” Phys. Rev. 28, 672 (1926).

Phys. Rev. A (1)

A. Baas, J. Ph. Karr, H. Eleuch, and E. Giacobino, “Optical bistability in semiconductor microcavities,” Phys. Rev. A 69, 023809 (2004).

Phys. Rev. Lett. (1)

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).

Other (3)

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, Orlando, 1985).

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

E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley, 1994).

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Figures (7)

Fig. 1
Fig. 1 Schematics of (a) the basic edf laser system, and (b) the experimental laser system with two edf sections and a second isolator.

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Fig. 2
Fig. 2 Experimental output power as a function of pump power, showing the bistability. The arrows show the pump increase or decrease directions.

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Fig. 3
Fig. 3 Experimental output power as a function of pump power when isolator 2 is removed. The bistability region is nearly absent. The arrows show the pump increase or decrease directions.

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Fig. 4
Fig. 4 (a) Emission (red), and absorption (blue) spectra for erbium. (b) Emission-absorption ratio as a function of wavelength.

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Fig. 5
Fig. 5 Theoretical output power as a function of pump power. The pump power is normalized by the 980/1605 wavelength ratio.

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Fig. 6
Fig. 6 Backwards ASE power as a function of the pump power. The bistability region is exactly the same as that of the output power.

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Fig. 7
Fig. 7 Theoretical results for the output power as a function of pump power when Isolator 2 is removed.

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