Abstract

The transmission spectrum of an all-fiber cavity is theoretically analyzed, in order to evaluate the perturbation induced in the eigenfrequency measurement by the Kerr effect. Existence of a threshold separating the bistable operation region from the monostable is shown. In the weakly nonlinear operation, the asymmetry of the line is evaluated and the resulting error in the frequency measurement is analytically derived.

© 1990 Optical Society of America

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References

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  1. P. Grollman, J. Herth, M. Kemmler, K. Kempf, G. Neumann, S. Oster, W. Schroder, “Passive Fiber Resonator Gyro,” in Proceedings Symposium on Gyro Techology (Stuttgart, Germany, September 22–23, 1986) pp. 8.0–8.19.
  2. M. Ohtsu, S. Araki, “Using a 1.5 μm DFB InGaAsP Laser in a Passive Ring Cavity-Type Fiber Gyroscope,” Appl. Opt. 26, 464–470 (1987).
    [CrossRef] [PubMed]
  3. D. Nelson, Electric, Optic and Acoustic Interactions in Dielectrics (Wiley, New York, 1979).
  4. D. Marcuse, “Loss Analysis of Single-Mode Fiber Splices,” Bell Syst. Tech. J. 56, 703–717 (1977).
  5. L. F. Stokes, M. Chodorow, H. J. Shaw, “All-Single-Mode Fiber Resonator,” Opt. Lett. 7, 288–290 (1982).
    [CrossRef] [PubMed]
  6. G. A. Sanders, M. G. Prentiss, S. Ezekiel, “Passive Ring Resonator Method for Sensitive Inertial Rotation Measurement in Geophysics and Relativity,” Opt. Lett. 16, 569–571 (1981).
    [CrossRef]
  7. B. Prade, J. Y. Vinet, “Guided Optics in Rotating Dielectric Media,” II Nuovo Cimento 101B, 323–334 (1988).

1988 (1)

B. Prade, J. Y. Vinet, “Guided Optics in Rotating Dielectric Media,” II Nuovo Cimento 101B, 323–334 (1988).

1987 (1)

1982 (1)

1981 (1)

1977 (1)

D. Marcuse, “Loss Analysis of Single-Mode Fiber Splices,” Bell Syst. Tech. J. 56, 703–717 (1977).

Araki, S.

Chodorow, M.

Ezekiel, S.

Grollman, P.

P. Grollman, J. Herth, M. Kemmler, K. Kempf, G. Neumann, S. Oster, W. Schroder, “Passive Fiber Resonator Gyro,” in Proceedings Symposium on Gyro Techology (Stuttgart, Germany, September 22–23, 1986) pp. 8.0–8.19.

Herth, J.

P. Grollman, J. Herth, M. Kemmler, K. Kempf, G. Neumann, S. Oster, W. Schroder, “Passive Fiber Resonator Gyro,” in Proceedings Symposium on Gyro Techology (Stuttgart, Germany, September 22–23, 1986) pp. 8.0–8.19.

Kemmler, M.

P. Grollman, J. Herth, M. Kemmler, K. Kempf, G. Neumann, S. Oster, W. Schroder, “Passive Fiber Resonator Gyro,” in Proceedings Symposium on Gyro Techology (Stuttgart, Germany, September 22–23, 1986) pp. 8.0–8.19.

Kempf, K.

P. Grollman, J. Herth, M. Kemmler, K. Kempf, G. Neumann, S. Oster, W. Schroder, “Passive Fiber Resonator Gyro,” in Proceedings Symposium on Gyro Techology (Stuttgart, Germany, September 22–23, 1986) pp. 8.0–8.19.

Marcuse, D.

D. Marcuse, “Loss Analysis of Single-Mode Fiber Splices,” Bell Syst. Tech. J. 56, 703–717 (1977).

Nelson, D.

D. Nelson, Electric, Optic and Acoustic Interactions in Dielectrics (Wiley, New York, 1979).

Neumann, G.

P. Grollman, J. Herth, M. Kemmler, K. Kempf, G. Neumann, S. Oster, W. Schroder, “Passive Fiber Resonator Gyro,” in Proceedings Symposium on Gyro Techology (Stuttgart, Germany, September 22–23, 1986) pp. 8.0–8.19.

Ohtsu, M.

Oster, S.

P. Grollman, J. Herth, M. Kemmler, K. Kempf, G. Neumann, S. Oster, W. Schroder, “Passive Fiber Resonator Gyro,” in Proceedings Symposium on Gyro Techology (Stuttgart, Germany, September 22–23, 1986) pp. 8.0–8.19.

Prade, B.

B. Prade, J. Y. Vinet, “Guided Optics in Rotating Dielectric Media,” II Nuovo Cimento 101B, 323–334 (1988).

Prentiss, M. G.

Sanders, G. A.

Schroder, W.

P. Grollman, J. Herth, M. Kemmler, K. Kempf, G. Neumann, S. Oster, W. Schroder, “Passive Fiber Resonator Gyro,” in Proceedings Symposium on Gyro Techology (Stuttgart, Germany, September 22–23, 1986) pp. 8.0–8.19.

Shaw, H. J.

Stokes, L. F.

Vinet, J. Y.

B. Prade, J. Y. Vinet, “Guided Optics in Rotating Dielectric Media,” II Nuovo Cimento 101B, 323–334 (1988).

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

D. Marcuse, “Loss Analysis of Single-Mode Fiber Splices,” Bell Syst. Tech. J. 56, 703–717 (1977).

II Nuovo Cimento (1)

B. Prade, J. Y. Vinet, “Guided Optics in Rotating Dielectric Media,” II Nuovo Cimento 101B, 323–334 (1988).

Opt. Lett. (2)

Other (2)

P. Grollman, J. Herth, M. Kemmler, K. Kempf, G. Neumann, S. Oster, W. Schroder, “Passive Fiber Resonator Gyro,” in Proceedings Symposium on Gyro Techology (Stuttgart, Germany, September 22–23, 1986) pp. 8.0–8.19.

D. Nelson, Electric, Optic and Acoustic Interactions in Dielectrics (Wiley, New York, 1979).

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Figures (3)

Fig. 1
Fig. 1

Sketch of the all-fiber cavity closed by means of a directional coupler.

Fig. 2
Fig. 2

Resonance curve of a nonlinear cavity, monostable region: S = 100; A = 0; 2 × 10−5; 5 × 10−5.

Fig. 3
Fig. 3

Resonance curve of a nonlinear cavity, bistable region: S = 100; A = 0; 1 × 10−4; 2 × 10−4; 5 × 10−4; 10−3.

Equations (35)

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n = n ( 0 ) + γ E 2 ,
n eff = - i k ( E * curl H - H * curl E ) d S + i k ( H H * + n 2 E E * ) d S ( E × H * + E * × H ) e z d S ,
n eff = n eff ( 0 ) + n eff ( 1 ) ;             E = E ( 0 ) + E ( 1 ) ;             H = H ( 0 ) + H ( 1 ) ,
n eff ( 1 ) = 2 n ( 0 ) γ E ( 0 ) 2 · E ( 0 ) 2 d S ( E ( 0 ) × H ( 0 ) * + E ( 0 ) * × H ( 0 ) ) e z d S .
n eff ( 1 ) = c 0 n eff ( 0 ) 2 P γ n eff ( 0 ) E ( 0 ) 4 d S .
E = A exp ( - r 2 / w 2 ) ,
P = 1 2 c 0 n eff ( 0 ) A 2 0 2 π 0 exp ( - 2 r 2 / w 2 ) r d r d θ ,
w = a ( 0.65 + 1.619 V - 3 / 2 + 2.879 V - 6 ) .
n eff ( 1 ) = γ n eff ( 0 ) P π w 2 .
T = 1 - 1 1 + 4 S 2 sin 2 Ψ ,
I = S I 0 1 + 4 S 2 sin 2 Ψ ,
Ψ = k n eff L / 2 + π / 4 ,
τ = n eff ( 0 ) L S / c
A = ω ( 0 ) c n eff ( 0 ) L 2 n ( 2 ) n eff ( 0 ) I 0 ,
n ( 2 ) = γ / π w 2 .
{ x = ( ω - ω ( 0 ) ) τ y = I / I 0 .
Ψ = x 2 S + A y + B x y with B = 1 2 S n 2 n eff ( 0 ) I 0 .
y = S 1 + 4 S 2 sin 2 ( x / 2 S + A y + B x y ) .
x = 2 S 1 + B y { ± sin - 1 ( 1 2 S S y - 1 ) - A y } .
y = S 1 + 4 S 2 sin 2 Ψ
Ψ = x 2 S + A y
Ψ = Ψ ( 0 ) + .
Ψ = Ψ ( 0 ) + ,
/ = - 8 A S 3 sin Ψ ( 0 ) cos Ψ ( 0 ) [ 1 + 4 S 2 sin 2 Ψ ( 0 ) ] - 2 .
θ ( 1 + θ 2 ) 2 < 1 4 A S 2
T = θ 2 1 + θ 2
T = x 2 1 + x 2 + η x ( 1 + x 2 ) 3 .
T = ω m 2 π 0 2 π / ω m T ( t ) sin ω m t d t .
T = x 0 T 1 + η T 2
T 1 = 1 π 0 2 π Δ sin 2 α ( 1 + Δ 2 sin 2 α ) 2 d α = Δ ( 1 + Δ 2 ) - 3 / 2
T 2 = 1 π 0 2 π Δ sin 2 α ( 1 + Δ 2 sin 2 α ) 3 d α = 3 8 Δ ( 1 + Δ 2 ) - 5 / 2 ,
T = Δ ( 1 + Δ 2 ) 3 / 2 [ x 0 + 3 8 η 1 1 + Δ 2 ]
δ x = - η / 8.
δ ω S = ω 0 C W - ω 0 C C W = 2 L n eff ( 0 ) λ Ω ,
δ ω N = δ x τ = 1 8 δ η τ ,

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