Abstract

A step index multimode optical fiber with a perturbation on a micrometer scale, inducing a periodic deformation of the fiber section along its propagation axis, is theoretically investigated. The studied microperturbation is mechanically achieved using two microstructured jaws squeezing the straight fiber. As opposed to optical fiber microbend sensors, the optical axis of the proposed transducer is not bended; only the optical fiber section is deformed. Further, the strain applied on the fiber produces a periodical elliptical modification of the core and a modulation of the index of refraction. As a consequence of the micrometer scale perturbation period, the resulting mode coupling occurs directly between guided and radiated modes. To simulate the transmission induced by these kinds of perturbations, simplified models considering only total mode couplings are often used. In order to investigate the range of validity of this approximation, results are compared to the electromagnetic mode couplings rigorously computed for the first time, to our knowledge, with a large multimode fiber (more than 6000 linear polarized modes) using the Marcuse model. In addition, in order to have a more complete modeling of the proposed transducer, the anisotropic elasto-optic effects in the stressed multimode fiber are considered. In this way, the transmission of the microperturbed optical fiber transmission and, therefore, the behavior of the transducer are physically explained and its applications as a future stretching sensor are discussed.

© 2012 Optical Society of America

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References

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    [CrossRef]
  2. P. Ferdinand, S. Magne, V. Dewynter-Marty, C. Martinez, S. Rougeault, and M. Bugaud, “Applications of Bragg grating sensors in Europe,” in Optical Fiber Sensors, OSA Technical Digest Series (Optical Society of America, 1997), paper OTuB1.
  3. A. Bichler, B. Serio, S. Lecler, and S. Fischer, “Design and performance of a mechanical strain optical sensor using a multimode fiber locally stressed by a periodical micrometric perturbation,” Proc. SPIE 7726, 77262B (2010).
    [CrossRef]
  4. D. Marcuse, Principles of Optical Fiber Measurements(Academic, 1981).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. C. I. Merzbacher, A. D. Kersey, and E. J. Friebele, “Fiber optic sensors in concrete structures: a review,” Smart Mater. Struc. 5–2, 196–208 (1996).
    [CrossRef]
  14. S. Timoshenko and J. N. Goodier, Theory of Elasticity, (McGraw-Hill, 1951).
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    [CrossRef]
  16. Y. Lukang and B. S. Rawat, “Mode-coupling analysis of depolarization effects in a multimode optical fiber,” J. Lightwave Technol. 10, 556–562 (1992).
    [CrossRef]

2010

A. Bichler, B. Serio, S. Lecler, and S. Fischer, “Design and performance of a mechanical strain optical sensor using a multimode fiber locally stressed by a periodical micrometric perturbation,” Proc. SPIE 7726, 77262B (2010).
[CrossRef]

2009

2008

J. S. Witkowski and A. Grobelny, “Ray tracing method in a 3D analysis of fiber-optic elements,” Opt. Appl. 38, 281–294(2008).

2007

M. Remouche, R. Mokdad, and M. Lahrashe, “Intrinsic optical fiber temperature sensor operating by modulation of the local numerical aperture,” Opt. Eng. 46, 24401 (2007).
[CrossRef]

2003

1996

C. I. Merzbacher, A. D. Kersey, and E. J. Friebele, “Fiber optic sensors in concrete structures: a review,” Smart Mater. Struc. 5–2, 196–208 (1996).
[CrossRef]

H. E. Engan, “Analysis of polarization-mode coupling by acoustic torsional waves in optical fibers,” J. Opt. Soc. Am. A 13, 112–118 (1996).
[CrossRef]

1992

Y. Lukang and B. S. Rawat, “Mode-coupling analysis of depolarization effects in a multimode optical fiber,” J. Lightwave Technol. 10, 556–562 (1992).
[CrossRef]

1981

1980

J. D. Love and C. Winckler, “Generalized Fresnel power transmission coefficients for curved graded-index media,” IEEE Trans. Microwave Theory Tech. 28, 689–695 (1980).
[CrossRef]

1975

A. W. Snyder and J. D. Love, “Reflection at a curved dielectric interface—Electromagnetic tunneling,” IEEE Trans. Microwave Theory Tech. 23, 134–141 (1975).
[CrossRef]

Bichler, A.

A. Bichler, B. Serio, S. Lecler, and S. Fischer, “Design and performance of a mechanical strain optical sensor using a multimode fiber locally stressed by a periodical micrometric perturbation,” Proc. SPIE 7726, 77262B (2010).
[CrossRef]

Bugaud, M.

P. Ferdinand, S. Magne, V. Dewynter-Marty, C. Martinez, S. Rougeault, and M. Bugaud, “Applications of Bragg grating sensors in Europe,” in Optical Fiber Sensors, OSA Technical Digest Series (Optical Society of America, 1997), paper OTuB1.

Dewynter-Marty, V.

P. Ferdinand, S. Magne, V. Dewynter-Marty, C. Martinez, S. Rougeault, and M. Bugaud, “Applications of Bragg grating sensors in Europe,” in Optical Fiber Sensors, OSA Technical Digest Series (Optical Society of America, 1997), paper OTuB1.

Engan, H. E.

Feng, S.

Ferdinand, P.

P. Ferdinand, S. Magne, V. Dewynter-Marty, C. Martinez, S. Rougeault, and M. Bugaud, “Applications of Bragg grating sensors in Europe,” in Optical Fiber Sensors, OSA Technical Digest Series (Optical Society of America, 1997), paper OTuB1.

Fischer, S.

A. Bichler, B. Serio, S. Lecler, and S. Fischer, “Design and performance of a mechanical strain optical sensor using a multimode fiber locally stressed by a periodical micrometric perturbation,” Proc. SPIE 7726, 77262B (2010).
[CrossRef]

Friebele, E. J.

C. I. Merzbacher, A. D. Kersey, and E. J. Friebele, “Fiber optic sensors in concrete structures: a review,” Smart Mater. Struc. 5–2, 196–208 (1996).
[CrossRef]

Goodier, J. N.

S. Timoshenko and J. N. Goodier, Theory of Elasticity, (McGraw-Hill, 1951).

Grobelny, A.

J. S. Witkowski and A. Grobelny, “Ray tracing method in a 3D analysis of fiber-optic elements,” Opt. Appl. 38, 281–294(2008).

Jian, S.

Kersey, A. D.

C. I. Merzbacher, A. D. Kersey, and E. J. Friebele, “Fiber optic sensors in concrete structures: a review,” Smart Mater. Struc. 5–2, 196–208 (1996).
[CrossRef]

Lagakos, N.

Lahrashe, M.

M. Remouche, R. Mokdad, and M. Lahrashe, “Intrinsic optical fiber temperature sensor operating by modulation of the local numerical aperture,” Opt. Eng. 46, 24401 (2007).
[CrossRef]

Lecler, S.

A. Bichler, B. Serio, S. Lecler, and S. Fischer, “Design and performance of a mechanical strain optical sensor using a multimode fiber locally stressed by a periodical micrometric perturbation,” Proc. SPIE 7726, 77262B (2010).
[CrossRef]

Lee, B.

B. Lee, “Review of the present status of fiber sensors,” Opt. Fiber Technol. 9, 57–79 (2003).
[CrossRef]

Lequime, M.

Litovitz, T.

Love, J. D.

J. D. Love and C. Winckler, “Generalized Fresnel power transmission coefficients for curved graded-index media,” IEEE Trans. Microwave Theory Tech. 28, 689–695 (1980).
[CrossRef]

A. W. Snyder and J. D. Love, “Reflection at a curved dielectric interface—Electromagnetic tunneling,” IEEE Trans. Microwave Theory Tech. 23, 134–141 (1975).
[CrossRef]

Lu, S.

Lukang, Y.

Y. Lukang and B. S. Rawat, “Mode-coupling analysis of depolarization effects in a multimode optical fiber,” J. Lightwave Technol. 10, 556–562 (1992).
[CrossRef]

Macedo, P.

Magne, S.

P. Ferdinand, S. Magne, V. Dewynter-Marty, C. Martinez, S. Rougeault, and M. Bugaud, “Applications of Bragg grating sensors in Europe,” in Optical Fiber Sensors, OSA Technical Digest Series (Optical Society of America, 1997), paper OTuB1.

Marcuse, D.

D. Marcuse, Principles of Optical Fiber Measurements(Academic, 1981).

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, 1991).

Martinez, C.

P. Ferdinand, S. Magne, V. Dewynter-Marty, C. Martinez, S. Rougeault, and M. Bugaud, “Applications of Bragg grating sensors in Europe,” in Optical Fiber Sensors, OSA Technical Digest Series (Optical Society of America, 1997), paper OTuB1.

Meister, R.

Merzbacher, C. I.

C. I. Merzbacher, A. D. Kersey, and E. J. Friebele, “Fiber optic sensors in concrete structures: a review,” Smart Mater. Struc. 5–2, 196–208 (1996).
[CrossRef]

Mohr, R.

Mokdad, R.

M. Remouche, R. Mokdad, and M. Lahrashe, “Intrinsic optical fiber temperature sensor operating by modulation of the local numerical aperture,” Opt. Eng. 46, 24401 (2007).
[CrossRef]

Parmentier, R.

Rawat, B. S.

Y. Lukang and B. S. Rawat, “Mode-coupling analysis of depolarization effects in a multimode optical fiber,” J. Lightwave Technol. 10, 556–562 (1992).
[CrossRef]

Remouche, M.

M. Remouche, R. Mokdad, and M. Lahrashe, “Intrinsic optical fiber temperature sensor operating by modulation of the local numerical aperture,” Opt. Eng. 46, 24401 (2007).
[CrossRef]

Rougeault, S.

P. Ferdinand, S. Magne, V. Dewynter-Marty, C. Martinez, S. Rougeault, and M. Bugaud, “Applications of Bragg grating sensors in Europe,” in Optical Fiber Sensors, OSA Technical Digest Series (Optical Society of America, 1997), paper OTuB1.

Serio, B.

A. Bichler, B. Serio, S. Lecler, and S. Fischer, “Design and performance of a mechanical strain optical sensor using a multimode fiber locally stressed by a periodical micrometric perturbation,” Proc. SPIE 7726, 77262B (2010).
[CrossRef]

Snyder, A. W.

A. W. Snyder and J. D. Love, “Reflection at a curved dielectric interface—Electromagnetic tunneling,” IEEE Trans. Microwave Theory Tech. 23, 134–141 (1975).
[CrossRef]

Timoshenko, S.

S. Timoshenko and J. N. Goodier, Theory of Elasticity, (McGraw-Hill, 1951).

Winckler, C.

J. D. Love and C. Winckler, “Generalized Fresnel power transmission coefficients for curved graded-index media,” IEEE Trans. Microwave Theory Tech. 28, 689–695 (1980).
[CrossRef]

Witkowski, J. S.

J. S. Witkowski and A. Grobelny, “Ray tracing method in a 3D analysis of fiber-optic elements,” Opt. Appl. 38, 281–294(2008).

Xu, O.

Appl. Opt.

IEEE Trans. Microwave Theory Tech.

A. W. Snyder and J. D. Love, “Reflection at a curved dielectric interface—Electromagnetic tunneling,” IEEE Trans. Microwave Theory Tech. 23, 134–141 (1975).
[CrossRef]

J. D. Love and C. Winckler, “Generalized Fresnel power transmission coefficients for curved graded-index media,” IEEE Trans. Microwave Theory Tech. 28, 689–695 (1980).
[CrossRef]

J. Lightwave Technol.

Y. Lukang and B. S. Rawat, “Mode-coupling analysis of depolarization effects in a multimode optical fiber,” J. Lightwave Technol. 10, 556–562 (1992).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Appl.

J. S. Witkowski and A. Grobelny, “Ray tracing method in a 3D analysis of fiber-optic elements,” Opt. Appl. 38, 281–294(2008).

Opt. Eng.

M. Remouche, R. Mokdad, and M. Lahrashe, “Intrinsic optical fiber temperature sensor operating by modulation of the local numerical aperture,” Opt. Eng. 46, 24401 (2007).
[CrossRef]

Opt. Fiber Technol.

B. Lee, “Review of the present status of fiber sensors,” Opt. Fiber Technol. 9, 57–79 (2003).
[CrossRef]

Opt. Lett.

Proc. SPIE

A. Bichler, B. Serio, S. Lecler, and S. Fischer, “Design and performance of a mechanical strain optical sensor using a multimode fiber locally stressed by a periodical micrometric perturbation,” Proc. SPIE 7726, 77262B (2010).
[CrossRef]

Smart Mater. Struc.

C. I. Merzbacher, A. D. Kersey, and E. J. Friebele, “Fiber optic sensors in concrete structures: a review,” Smart Mater. Struc. 5–2, 196–208 (1996).
[CrossRef]

Other

S. Timoshenko and J. N. Goodier, Theory of Elasticity, (McGraw-Hill, 1951).

D. Marcuse, Principles of Optical Fiber Measurements(Academic, 1981).

P. Ferdinand, S. Magne, V. Dewynter-Marty, C. Martinez, S. Rougeault, and M. Bugaud, “Applications of Bragg grating sensors in Europe,” in Optical Fiber Sensors, OSA Technical Digest Series (Optical Society of America, 1997), paper OTuB1.

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, 1991).

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Figures (11)

Fig. 1.
Fig. 1.

(a) Schematic view of the fiber squeezed between two jaws. (b) Microscope view of the jaw crenellation. (c) Schematic view of the optical fiber elliptical section modulation.

Fig. 2.
Fig. 2.

Schematic view of the distribution of the propagation constants of radiated and guided modes. Possible couplings due to a perturbation of spatial period Λ.

Fig. 3.
Fig. 3.

Optical fiber transmission computed by the two models as a function of the perturbation period with a constant modulation amplitude A whatever the value of Λ (L=12cm).

Fig. 4.
Fig. 4.

Approximation of the amplitude of the fiber sinusoidal deformation (A) and offset cc induced by the jaws as a function of the perturbation period computed using a 2D FEM Comsol approximation. Fiber crushing Ec=20μm.

Fig. 5.
Fig. 5.

Optical fiber transmission computed by the two models as a function of the perturbation period with a modulation amplitude A depending of the value of Λ. (L=12cm).

Fig. 6.
Fig. 6.

Geometry of the considered Hertzian contact.

Fig. 7.
Fig. 7.

Computed stress components in the squeezed fiber for a crushing Ec of 20 μm.

Fig. 8.
Fig. 8.

Anistropic elasto-optic induced refractive indexes of the fiber core for Ec=20μm.

Fig. 9.
Fig. 9.

2D-FEM larger computed effective indices of (a) guided, (b) radiated modes and the deduced, (c) numerical aperture, and (d) largest perturbation period that allows the coupling of all the guided modes in the anisotropic inhomogeneous perturbed optical fiber.

Fig. 10.
Fig. 10.

Computation of the fiber optical transmission using the Marcuse model, and taking into account the mechanical response of the fiber and elasto-optic effects, as a function of the perturbation period Λ for: (a) several perturbation lengths L, (b) source wavelengths λ, (c) crushings E, and (d) numerical aperture ON. Default values: λ=630nm, Ec=20μm, duty cycle 50%, ON=0.22, L=12cm, rc=100μm, nco=1.456.

Fig. 11.
Fig. 11.

Theoretical microperturbed optical fiber transmission as a function of a longitudinal stretching for three different perturbation periods of the aluminum jaws. 240 μm silica/silica fiber.

Tables (1)

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Table 1. Mechanical Properties of the Used Materials

Equations (17)

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|β1β2|=2πΛ.
αμ=12TE,TM0k0ngo|kμ,ν++|2|F(βμβν2π)|2βνdβν.
kμ,ν++=πcε02λ0j(nco2ngo2)02πcos(mθ)[nco2ngo2Eμ,r*(rccc,θ)·Eν,r(rccc,θ)+Eμ,θ*(rccc,θ)·Eν,θ(rccc,θ)+Eμ,z*(rccc,θ)·Eν,z(rccc,θ)]dθ.
βm=k0nco1NA2nco2mM.
T=1I0μI0μe2αμL.
|F(f)|=AL2|sin(πL(f1/Λ))πL(f1/Λ)|.
ΛCT=λ0ncongo.
1Eeq=1υ1E1+1υ2E2,
a=4PRπEeq.
m12=12[(a2x2+y2)2+4x2y2+(a2x2+y2)]n12=12[(a2x2+y2)2+4x2y2(a2x2+y2)],
m22=12[(a2x2+(2Ry)2)2+4x2(2Ry)2+(a2x2+(2Ry)2)]n22=12[(a2x2+(2Ry)2)2+4x2(2Ry)2(a2x2+(2Ry)2)],
σX=pπ[1R2a2(m1(1+y2+n12m12+n12)+m2(1+(2Ry)2+n22m22+n22)4R)]σY=pπ[1R2a2(m1(1y2+n12m12+n12)+m2(1(2Ry)2+n22m22+n22))],
εX=1υ2E2σXυ2(1+υ2)E2σYεY=1υ2E2σYυ2(1+υ2)E2σX.
Ec=02RεY(x=0,y)dy,
Ec=2P1υ22πE2(1υ21υ22ln(4Ra)).
[Δ(1nSi2)XXΔ(1nSi2)YYΔ(1nSi2)ZZ]=[P11P12P12P12P11P12P12P12P11][εXεYεZ],
nX=nSi1+nSi2(P11εX+P12εY)nY=nSi1+nSi2(P11εY+P12εX).

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