Abstract

A new kind of fiber-optic sensor, to our knowledge, is proposed: a chaotic sensor. The sensor is based on a fiber-ring resonator that is optically driven by a train of pulses whose period equals the round-trip delay of the resonator. This sensor exploits the extremely high dependence of chaotic systems on initial conditions to sense several physical parameters (elongation, attenuation, index of refraction). The measured information is encoded in different geometrical characteristics of the chaotic attractor. The proposed sensing scheme has been modeled and simulated. The simulations reveal high potential for this structure as a multiparameter sensor.

© 2006 Optical Society of America

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References

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  1. E. N. Lorenz, "Deterministic nonperiodic flow," J. Atmos. Sci. 20130-141 (1963).
    [CrossRef]
  2. K. Suzuki, Y. Imai, and F. Okumura, "Proposal for temperature and pressure sensing based on periodic chaos synchronization in optical fiber ring resonator systems," in Proceedings of Optical Fibre Sensors Conference Series 16, K.Hotate, ed. (Institute of Electronics, Information and Communication Engineers, 2003), pp. 204-207.
  3. K. Ikeda, H. Daido, and O. Akimoto, "Optical turbulence: chaotic behavior of transmitted light from a ring cavity," Phys. Rev. Lett. 45, 709-712 (1980).
    [CrossRef]
  4. J. Gleick, Chaos—Making a New Science (Seix Barral, 1998).

1980 (1)

K. Ikeda, H. Daido, and O. Akimoto, "Optical turbulence: chaotic behavior of transmitted light from a ring cavity," Phys. Rev. Lett. 45, 709-712 (1980).
[CrossRef]

1963 (1)

E. N. Lorenz, "Deterministic nonperiodic flow," J. Atmos. Sci. 20130-141 (1963).
[CrossRef]

Akimoto, O.

K. Ikeda, H. Daido, and O. Akimoto, "Optical turbulence: chaotic behavior of transmitted light from a ring cavity," Phys. Rev. Lett. 45, 709-712 (1980).
[CrossRef]

Daido, H.

K. Ikeda, H. Daido, and O. Akimoto, "Optical turbulence: chaotic behavior of transmitted light from a ring cavity," Phys. Rev. Lett. 45, 709-712 (1980).
[CrossRef]

Gleick, J.

J. Gleick, Chaos—Making a New Science (Seix Barral, 1998).

Ikeda, K.

K. Ikeda, H. Daido, and O. Akimoto, "Optical turbulence: chaotic behavior of transmitted light from a ring cavity," Phys. Rev. Lett. 45, 709-712 (1980).
[CrossRef]

Imai, Y.

K. Suzuki, Y. Imai, and F. Okumura, "Proposal for temperature and pressure sensing based on periodic chaos synchronization in optical fiber ring resonator systems," in Proceedings of Optical Fibre Sensors Conference Series 16, K.Hotate, ed. (Institute of Electronics, Information and Communication Engineers, 2003), pp. 204-207.

Lorenz, E. N.

E. N. Lorenz, "Deterministic nonperiodic flow," J. Atmos. Sci. 20130-141 (1963).
[CrossRef]

Okumura, F.

K. Suzuki, Y. Imai, and F. Okumura, "Proposal for temperature and pressure sensing based on periodic chaos synchronization in optical fiber ring resonator systems," in Proceedings of Optical Fibre Sensors Conference Series 16, K.Hotate, ed. (Institute of Electronics, Information and Communication Engineers, 2003), pp. 204-207.

Suzuki, K.

K. Suzuki, Y. Imai, and F. Okumura, "Proposal for temperature and pressure sensing based on periodic chaos synchronization in optical fiber ring resonator systems," in Proceedings of Optical Fibre Sensors Conference Series 16, K.Hotate, ed. (Institute of Electronics, Information and Communication Engineers, 2003), pp. 204-207.

J. Atmos. Sci. (1)

E. N. Lorenz, "Deterministic nonperiodic flow," J. Atmos. Sci. 20130-141 (1963).
[CrossRef]

Phys. Rev. Lett. (1)

K. Ikeda, H. Daido, and O. Akimoto, "Optical turbulence: chaotic behavior of transmitted light from a ring cavity," Phys. Rev. Lett. 45, 709-712 (1980).
[CrossRef]

Other (2)

J. Gleick, Chaos—Making a New Science (Seix Barral, 1998).

K. Suzuki, Y. Imai, and F. Okumura, "Proposal for temperature and pressure sensing based on periodic chaos synchronization in optical fiber ring resonator systems," in Proceedings of Optical Fibre Sensors Conference Series 16, K.Hotate, ed. (Institute of Electronics, Information and Communication Engineers, 2003), pp. 204-207.

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Figures (9)

Fig. 1
Fig. 1

Chaotic fiber-ring resonator driven by a pulsed input signal whose period ( τ ) equals the round-trip delay of the fiber ring.

Fig. 2
Fig. 2

Bifurcation diagram of the proposed chaotic sensor. This diagram shows the different possible working states of the system as a function of the input power: (a) stable state, (b) periodic state (two values), (c) periodic state (four values), (d) chaotic state, (e) periodic state (two values).

Fig. 3
Fig. 3

Chaotic attractor of the proposed fiber-ring chaotic sensor. The fit provided by the mathematical model presented in the paper is also shown. The inset shows a close-up of the central part of the attractor.

Fig. 4
Fig. 4

Evolution of the radius of the spiral with each half-turn (dotted curve) together with the fit provided by the Belehdarek fit (solid curve).

Fig. 5
Fig. 5

Dependence of the radius evolution rate on the L λ ratio (dotted curve) and its fit revealing a potential relationship (solid curve).

Fig. 6
Fig. 6

Behavior of the initial angle of the attractor ( ϕ i ) with length (left graph) and refractive index change ( Δ n 1 ) (right graph). The left graph also shows how the dependence of ϕ i on the fiber length varies with the index of refraction n 1 . The right graph shows the evolution of ϕ i for two indices of refraction (1.448, dotted curve, and 1.4486, crossed curve).

Fig. 7
Fig. 7

Fiber length as recovered by the proposed sensor when the SNR of the input train of pulses is varied. The inset shows the attractor for a SNR of 15 dB . The noise blurs the spiral.

Fig. 8
Fig. 8

Evolution of the maximum radius of the chaotic attractor with the attenuation factor of the fiber.

Fig. 9
Fig. 9

Index of refraction recovered using the information provided by ϕ i (dotted curve) and ϕ o (curve with triangles), as compared with the actual values (solid curve).

Equations (12)

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n ( z ) = n 1 ( z ) + n 2 E ̃ ( z ) 2 + .
E t ( t ) = j 1 ρ κ E in ( t ) + 1 ρ 1 κ E t ( t τ ) exp ( α L 2 ) exp ( j 2 π λ { n 1 L + n 2 E t ( t τ ) 2 [ 1 exp ( α L ) α ] } ) .
E out ( t ) = 1 ρ 1 κ E in ( t ) + j κ 1 κ [ E t ( t ) j 1 ρ κ E in ( t ) ] .
r s = r ϕ ϕ o π , with r = a ( L λ ) β ,
A t = 1 κ 1 ρ E in + F ρ F κ a ( L λ ) β ϕ ϕ o π exp ( j ϕ ) , ϕ i ϕ ϕ f ,
β = 0.12236 α 0.49527 ,
F ρ = 0.21113 ρ 2 0.5928 ρ + 1.1961 ,
F κ = 0.2304 κ 2 + 1.0188 κ + 0.36663 ,
a = p 1 n 1 + p 2 ,
p 1 = 2.8646 × 10 3 ( α + 3.6555 × 10 4 ) ,
p 2 = 4.9471 × 10 3 ( α + 5.3399 × 10 4 ) .
ϕ v = ( a a ϕ v n 1 + b a ϕ v ) L + ( a b ϕ v n 1 + b b ϕ v ) , with v = i , f , or o .

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