Abstract

The transmission bistability of a two-coupler nonlinear ring resonator is demonstrated and described by using a geometrical method that provides a qualitative understanding of the operation characteristics of the device. Results showing the influence of the coupling constants and the linear phase are presented.

© 1991 Optical Society of America

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References

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  1. J. Capmany, M. A. Muriel, IEEE J. Lightwave Technol. 8, 1904 (1990).
    [CrossRef]
  2. B. Crosignani, B. Daino, P. DiPorto, S. Wabnitz, Opt. Commun. 59, 309 (1986).
    [CrossRef]
  3. L. F. Stokes, M. Chodorow, H. J. Shaw, Opt. Lett. 7, 288 (1982).
    [CrossRef] [PubMed]
  4. P. Urquhart, J. Opt. Soc. Am. A 5, 803 (1988).
    [CrossRef]
  5. J. A. Martín-Pereda, M. A. Muriel, in Optical Bistability 2 (Plenum, New York, 1984), p. 143.
    [CrossRef]
  6. M. A. Muriel, J. A. Martín-Pereda, in Optical Bistability III (Springer-Verlag, Berlin, 1986), p. 335.
    [CrossRef]
  7. B. Crosignani, P. DiPorto, J. Opt. Soc. Am. 72, 1553 (1982).
    [CrossRef]

1990 (1)

J. Capmany, M. A. Muriel, IEEE J. Lightwave Technol. 8, 1904 (1990).
[CrossRef]

1988 (1)

1986 (1)

B. Crosignani, B. Daino, P. DiPorto, S. Wabnitz, Opt. Commun. 59, 309 (1986).
[CrossRef]

1982 (2)

Capmany, J.

J. Capmany, M. A. Muriel, IEEE J. Lightwave Technol. 8, 1904 (1990).
[CrossRef]

Chodorow, M.

Crosignani, B.

B. Crosignani, B. Daino, P. DiPorto, S. Wabnitz, Opt. Commun. 59, 309 (1986).
[CrossRef]

B. Crosignani, P. DiPorto, J. Opt. Soc. Am. 72, 1553 (1982).
[CrossRef]

Daino, B.

B. Crosignani, B. Daino, P. DiPorto, S. Wabnitz, Opt. Commun. 59, 309 (1986).
[CrossRef]

DiPorto, P.

B. Crosignani, B. Daino, P. DiPorto, S. Wabnitz, Opt. Commun. 59, 309 (1986).
[CrossRef]

B. Crosignani, P. DiPorto, J. Opt. Soc. Am. 72, 1553 (1982).
[CrossRef]

Martín-Pereda, J. A.

M. A. Muriel, J. A. Martín-Pereda, in Optical Bistability III (Springer-Verlag, Berlin, 1986), p. 335.
[CrossRef]

J. A. Martín-Pereda, M. A. Muriel, in Optical Bistability 2 (Plenum, New York, 1984), p. 143.
[CrossRef]

Muriel, M. A.

J. Capmany, M. A. Muriel, IEEE J. Lightwave Technol. 8, 1904 (1990).
[CrossRef]

J. A. Martín-Pereda, M. A. Muriel, in Optical Bistability 2 (Plenum, New York, 1984), p. 143.
[CrossRef]

M. A. Muriel, J. A. Martín-Pereda, in Optical Bistability III (Springer-Verlag, Berlin, 1986), p. 335.
[CrossRef]

Shaw, H. J.

Stokes, L. F.

Urquhart, P.

Wabnitz, S.

B. Crosignani, B. Daino, P. DiPorto, S. Wabnitz, Opt. Commun. 59, 309 (1986).
[CrossRef]

IEEE J. Lightwave Technol. (1)

J. Capmany, M. A. Muriel, IEEE J. Lightwave Technol. 8, 1904 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (1)

B. Crosignani, B. Daino, P. DiPorto, S. Wabnitz, Opt. Commun. 59, 309 (1986).
[CrossRef]

Opt. Lett. (1)

Other (2)

J. A. Martín-Pereda, M. A. Muriel, in Optical Bistability 2 (Plenum, New York, 1984), p. 143.
[CrossRef]

M. A. Muriel, J. A. Martín-Pereda, in Optical Bistability III (Springer-Verlag, Berlin, 1986), p. 335.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Double-coupler fiber ring resonator.

Fig. 2
Fig. 2

(a) Linear (Fabry–Perot) (y) and nonlinear (h) transmissivities versus the normalized phase ϕ/π with βL/π = 1.27 and k1 = k2 = 0.1. The latter is plotted for several normalized input powers P. (b) Linear (Fabry–Perot) (y) and nonlinear (h) transmissivities versus the normalized phase ϕ/π with βL/π = 1.75 and k1 = k2 = 0.1. The latter is plotted for several normalized input powers P.

Fig. 3
Fig. 3

Output normalized power versus input normalized power for various cases: βL/π = 1.27 and k1 = k2 = 0.1 (solid curves), βL/π = 1.75 and k1 = k2 = 0.1 (vertical dashed line), and βL/π = 1.27 and k1 = k2 = 0.5 (dashed-dotted curve).

Fig. 4
Fig. 4

Linear (Fabry–Perot) (y) and nonlinear (h) transmissivities versus the normalizied phase ϕ/π. The former is plotted for k1 = k2 = 0.1 (sharp resonances) and k1 = k2 = 0.5 (broad resonances). The latter is plotted for βL/π = 1.27 (dashed curves) and βL/π = 1.75 (solid curves) with k1 = k2 = 0.1 and k1 = k2 = 0.5 for both cases.

Fig. 5
Fig. 5

Switching powers as a function of the normalized linear phase for several coupling constants k1 = k2k.

Fig. 6
Fig. 6

Switching powers versus the coupling constant k1 = k2k for two values of the linear phase.

Equations (3)

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| E 2 + E 1 + | 2 y ( Φ ) = T 1 T 2 exp ( - 2 α L a ) ( 1 - χ 1 χ 2 ) 2 + 4 χ 1 χ 2 sin 2 ( Φ / 2 ) ,
ϕ = β L + R L a E a 2 + R L b E b 2 ,
h ( Φ ) = ( Φ - β L ) k 2 R E 1 + 2 [ L a exp ( 2 α L a ) 1 - γ 2 + L b ( 1 - k 2 ) ] .

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