Abstract

We present a theoretical study of bistability in an optical fiber ring resonator connected to a 3 × 3 fiber coupler. The bistability is caused by the Kerr effect when the ring resonator is working in the nonlinear regime. The dependence of the bistability on various parameters of the fiber and the coupler is investigated.

© 1993 Optical Society of America

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References

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  1. P. A. Davies, G. Abd-El-Hamid, “Four-port fiber-optical ring resonator,” Electron. Lett. 24, 662–663 (1988).
    [CrossRef]
  2. Y. H. Ja, “Analysis of four-port optical fiber ring and loop resonators using a 3 × 3 fiber coupler and degenerate two-wave mixing,” IEEE J. Quantum Electron. 28, 2749–2757 (1992).
    [CrossRef]
  3. F. J. Fraile-Pelaez, J. Capmany, M. A. Murel, “Transmission bistability in a double-coupler fiber ring resonator,” Opt. Lett. 16, 907–909 (1991).
    [CrossRef] [PubMed]

1992 (1)

Y. H. Ja, “Analysis of four-port optical fiber ring and loop resonators using a 3 × 3 fiber coupler and degenerate two-wave mixing,” IEEE J. Quantum Electron. 28, 2749–2757 (1992).
[CrossRef]

1991 (1)

1988 (1)

P. A. Davies, G. Abd-El-Hamid, “Four-port fiber-optical ring resonator,” Electron. Lett. 24, 662–663 (1988).
[CrossRef]

Abd-El-Hamid, G.

P. A. Davies, G. Abd-El-Hamid, “Four-port fiber-optical ring resonator,” Electron. Lett. 24, 662–663 (1988).
[CrossRef]

Capmany, J.

Davies, P. A.

P. A. Davies, G. Abd-El-Hamid, “Four-port fiber-optical ring resonator,” Electron. Lett. 24, 662–663 (1988).
[CrossRef]

Fraile-Pelaez, F. J.

Ja, Y. H.

Y. H. Ja, “Analysis of four-port optical fiber ring and loop resonators using a 3 × 3 fiber coupler and degenerate two-wave mixing,” IEEE J. Quantum Electron. 28, 2749–2757 (1992).
[CrossRef]

Murel, M. A.

Electron. Lett. (1)

P. A. Davies, G. Abd-El-Hamid, “Four-port fiber-optical ring resonator,” Electron. Lett. 24, 662–663 (1988).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. H. Ja, “Analysis of four-port optical fiber ring and loop resonators using a 3 × 3 fiber coupler and degenerate two-wave mixing,” IEEE J. Quantum Electron. 28, 2749–2757 (1992).
[CrossRef]

Opt. Lett. (1)

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Figures (2)

Fig. 1
Fig. 1

A fiber ring resonator connected to a 3 × 3 fiber coupler with a length d along its longitudinal axis z.

Fig. 2
Fig. 2

Normalized output intensities I1d and I3d as functions of the normalized input intensity P with (a) the coupling length of the 3 × 3 coupler, kd; (b) the linear phase change of the fiber ring, θ0; (c) the transmission coefficient of the 3 × 3 coupler, a; and (d) the transmission coefficient of the fiber, t, as a parameter.

Equations (6)

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θ + β L + R L I 2 d = θ 0 + R L I 2 d ,
I 2 d I 1 = a 2 C I d ,
I 1 d I 1 = a 2 I d ( G 2 F - G T + F ) ,
I 3 d I 1 = a 2 C I d [ 1 + G 2 - 2 G cos ( θ + k d ) ] .
θ - θ 0 - a 2 C P 1 + G 2 F - G [ 2 cos ( θ + k d ) + cos ( θ - 2 k d ) ] = 0 ,
P = R L I 1

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