Abstract

We present a method for calculating the dynamic input–output characteristics of a nonlinear fiber ring resonator caused by a change in input intensity. It is based on an original method developed by Bischofberger and Shen [Phys. Rev. A 19, 1169 (1979)] to study a transient nonlinear Fabry–Perot resonator. We treat a double-coupler fiber ring resonator, in which two types of optical bistability (transmission bistability and reflection bistability) are available and present the illustrative numerical results for a few cavity parameters. This analysis will be useful for a future experimental verification of optical bistability in fiber ring resonators and for the design of fiber bistable devices.

© 1995 Optical Society of America

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References

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  1. K. Ogusu, S. Yamamoto, IEEE J. Lightwave Technol. 11, 1774 (1993).
    [Crossref]
  2. B. Crosignani, B. Daino, P. Di Porto, S. Wabnitz, Opt. Commun. 59, 309 (1986).
    [Crossref]
  3. F. J. Fraile-Pelaez, J. Capmany, M. A. Muriel, Opt. Lett. 16, 907 (1991).
    [Crossref] [PubMed]
  4. Y. H. Ja, Appl. Opt. 32, 5310 (1993).
    [Crossref] [PubMed]
  5. Y. H. Ja, IEEE J. Quantum Electron. 30, 329 (1994).
    [Crossref]
  6. J. Capmany, F. J. Fraile-Pelaez, M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
    [Crossref]
  7. T. Fukushima, T. Sakamoto, Opt. Lett. 20, 1119 (1995).
    [Crossref] [PubMed]
  8. J. H. Marburger, F. S. Felber, Phys. Rev. A 17, 335 (1978).
    [Crossref]
  9. T. Bischofberger, Y. R. Shen, Phys. Rev. A 19, 1169 (1979).
    [Crossref]
  10. M. Asobe, T. Kanamori, K. Kubodera, IEEE J. Quantum Electron. 29, 2325 (1993).
    [Crossref]

1995 (1)

1994 (2)

Y. H. Ja, IEEE J. Quantum Electron. 30, 329 (1994).
[Crossref]

J. Capmany, F. J. Fraile-Pelaez, M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
[Crossref]

1993 (3)

K. Ogusu, S. Yamamoto, IEEE J. Lightwave Technol. 11, 1774 (1993).
[Crossref]

Y. H. Ja, Appl. Opt. 32, 5310 (1993).
[Crossref] [PubMed]

M. Asobe, T. Kanamori, K. Kubodera, IEEE J. Quantum Electron. 29, 2325 (1993).
[Crossref]

1991 (1)

1986 (1)

B. Crosignani, B. Daino, P. Di Porto, S. Wabnitz, Opt. Commun. 59, 309 (1986).
[Crossref]

1979 (1)

T. Bischofberger, Y. R. Shen, Phys. Rev. A 19, 1169 (1979).
[Crossref]

1978 (1)

J. H. Marburger, F. S. Felber, Phys. Rev. A 17, 335 (1978).
[Crossref]

Asobe, M.

M. Asobe, T. Kanamori, K. Kubodera, IEEE J. Quantum Electron. 29, 2325 (1993).
[Crossref]

Bischofberger, T.

T. Bischofberger, Y. R. Shen, Phys. Rev. A 19, 1169 (1979).
[Crossref]

Capmany, J.

J. Capmany, F. J. Fraile-Pelaez, M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
[Crossref]

F. J. Fraile-Pelaez, J. Capmany, M. A. Muriel, Opt. Lett. 16, 907 (1991).
[Crossref] [PubMed]

Crosignani, B.

B. Crosignani, B. Daino, P. Di Porto, S. Wabnitz, Opt. Commun. 59, 309 (1986).
[Crossref]

Daino, B.

B. Crosignani, B. Daino, P. Di Porto, S. Wabnitz, Opt. Commun. 59, 309 (1986).
[Crossref]

Di Porto, P.

B. Crosignani, B. Daino, P. Di Porto, S. Wabnitz, Opt. Commun. 59, 309 (1986).
[Crossref]

Felber, F. S.

J. H. Marburger, F. S. Felber, Phys. Rev. A 17, 335 (1978).
[Crossref]

Fraile-Pelaez, F. J.

J. Capmany, F. J. Fraile-Pelaez, M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
[Crossref]

F. J. Fraile-Pelaez, J. Capmany, M. A. Muriel, Opt. Lett. 16, 907 (1991).
[Crossref] [PubMed]

Fukushima, T.

Ja, Y. H.

Y. H. Ja, IEEE J. Quantum Electron. 30, 329 (1994).
[Crossref]

Y. H. Ja, Appl. Opt. 32, 5310 (1993).
[Crossref] [PubMed]

Kanamori, T.

M. Asobe, T. Kanamori, K. Kubodera, IEEE J. Quantum Electron. 29, 2325 (1993).
[Crossref]

Kubodera, K.

M. Asobe, T. Kanamori, K. Kubodera, IEEE J. Quantum Electron. 29, 2325 (1993).
[Crossref]

Marburger, J. H.

J. H. Marburger, F. S. Felber, Phys. Rev. A 17, 335 (1978).
[Crossref]

Muriel, M. A.

J. Capmany, F. J. Fraile-Pelaez, M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
[Crossref]

F. J. Fraile-Pelaez, J. Capmany, M. A. Muriel, Opt. Lett. 16, 907 (1991).
[Crossref] [PubMed]

Ogusu, K.

K. Ogusu, S. Yamamoto, IEEE J. Lightwave Technol. 11, 1774 (1993).
[Crossref]

Sakamoto, T.

Shen, Y. R.

T. Bischofberger, Y. R. Shen, Phys. Rev. A 19, 1169 (1979).
[Crossref]

Wabnitz, S.

B. Crosignani, B. Daino, P. Di Porto, S. Wabnitz, Opt. Commun. 59, 309 (1986).
[Crossref]

Yamamoto, S.

K. Ogusu, S. Yamamoto, IEEE J. Lightwave Technol. 11, 1774 (1993).
[Crossref]

Appl. Opt. (1)

IEEE J. Lightwave Technol. (1)

K. Ogusu, S. Yamamoto, IEEE J. Lightwave Technol. 11, 1774 (1993).
[Crossref]

IEEE J. Quantum Electron. (3)

M. Asobe, T. Kanamori, K. Kubodera, IEEE J. Quantum Electron. 29, 2325 (1993).
[Crossref]

Y. H. Ja, IEEE J. Quantum Electron. 30, 329 (1994).
[Crossref]

J. Capmany, F. J. Fraile-Pelaez, M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
[Crossref]

Opt. Commun. (1)

B. Crosignani, B. Daino, P. Di Porto, S. Wabnitz, Opt. Commun. 59, 309 (1986).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (2)

J. H. Marburger, F. S. Felber, Phys. Rev. A 17, 335 (1978).
[Crossref]

T. Bischofberger, Y. R. Shen, Phys. Rev. A 19, 1169 (1979).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Schematic of a double-coupler fiber ring resonator.

Fig. 2
Fig. 2

(a) Temporal power profiles of two output pulses when an input pulse with 20-ns pulse duration and 1-kW peak power is incident in the fiber ring resonator with L = 3 cm and initial detuning Δϕ0 = −0.1π. (b) The corresponding input–output characteristics.

Fig. 3
Fig. 3

Input–output characteristics of the fiber ring resonator with L = 3 cm at the transmission port for four initial detunings Δϕ0. The input pulse is the same as that in Fig. 2(a).

Fig. 4
Fig. 4

Input–output characteristics of the fiber ring resonator with Δϕ0 = −0.1π at the transmission port for three fiber ring lengths L. The input pulse is the same as that in Fig. 2(a).

Equations (12)

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n = n 0 + n 2 I = n 0 + n 2 n 0 2 η 0 E 2 = n 0 + n 2 P S eff ,
E in ( t ) = E i ( t ) exp ( j ω t ) ,
E out t ( t ) = T exp ( j ω t ) m = 0 E i [ t - ( m + 1 / 2 ) t R ] R m × exp { - j ϕ [ t , t - ( m + 1 / 2 ) t R ] } ,
T = - ( 1 - γ ) exp ( - α L / 2 ) κ ,
R = ( 1 - γ ) exp ( - α L ) ( 1 - κ ) .
ϕ [ t , t - ( m + 1 / 2 ) t R ] ( m + 1 / 2 ) ϕ 0 + 1 2 Δ ϕ ( t ) + i = 1 m Δ ϕ ( t - l t R ) ,
Δ ϕ ( t ) = k 0 n 0 n 2 2 η 0 E ( t , z ) 2 d z k 0 n 0 n 2 L 2 η 0 ( 1 - γ ) κ E out t ( t ) 2 ,
E out t ( t ) 2 = ( 1 - γ ) κ E ( t , L / 2 ) 2 .
E out r ( t ) = T 0 exp ( j ω t ) { E i ( t ) + T m = 1 E i ( t - m t R ) R m - 1 × exp [ - j ϕ ( t , t - m t R ) ] } ,
T 0 = [ ( 1 - γ ) ( 1 - κ ) ] 1 / 2 ,
T = - ( 1 - γ ) exp ( - α L ) κ ,
ϕ ( t , t - m t R ) m ϕ 0 + l = 1 m Δ ϕ ( t - l t R ) .

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