Abstract

Fizeau micro-interferometry is applied to evaluate some parameters of a curved single-mode optical fiber. The field shift of the fundamental mode and the associated transition loss in a perturbed index-profile fiber due to bending are determined. The preceding fiber parameters are determined as a function of the shift of multiple-beam Fizeau fringes. For a curvature range between 0.13 and 0.053 mm-1, a range of field shift between 0.44 and 0.21 μm is determined. A fraction of the transition loss ranging between 0.0056 and 0.028 is calculated within the same curvature range. Because our method has high index resolution and spatial resolution, it shows good agreement with theory. The results and the agreement with theory indicate that the use of multiple-beam Fizeau fringes is a promising technique that is capable of determining with high accuracy some guidance parameters of the optical fibers.

© 2004 Optical Society of America

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References

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  1. B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9, 57–79 (2003).
    [CrossRef]
  2. N. Shibata, M. Ohashi, K. Kitayama, S. Seikai, “Evaluation of bending-induced birefringence based on stimulated four-photon mixing,” Opt. Lett. 10, 154–156 (1985).
    [CrossRef] [PubMed]
  3. S. K. Khijwania, B. D. Gupta, “Maximum achievable sensitivity of fiber optic evanescent field absorption sensor based on the U-shaped probe,” Opt. Commun. 175, 135–137 (2000).
    [CrossRef]
  4. Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Bend sensing by measuring the resonance splitting of long-period fiber gratings,” Opt. Commun. 193, 69–72 (2001).
    [CrossRef]
  5. V. Bahata, A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21, 692–694 (1996).
    [CrossRef]
  6. Y. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8, 355–375 (1997).
    [CrossRef]
  7. T. Allsop, T. Earthrowl, R. Reeves, D. J. Webb, I. Bennion, “The interrogation and multiplexing of long grating curvature sensors using a Bragg grating based, derivative spectroscopy technique,” Meas. Sci. Technol. 15, 44–48 (2004).
    [CrossRef]
  8. F. El-Diasty, “Multiple-beam interferometric determination of Poisson’s ratio and strain profiles along the cross section of bent single-mode optical fibers,” Appl. Opt. 39, 3197–3201 (2000).
    [CrossRef]
  9. H. Tai, R. Rogowski, “Optical anisotropy induced by torsion and bending in an optical fiber,” Opt. Fiber Technol. 8, 162–169 (2002).
    [CrossRef]
  10. Q. Lin, G. P. Agrawal, “Pulse broadening induced by dispersion fluctuations in optical fibers,” Opt. Commun. 206, 313–317 (2002).
    [CrossRef]
  11. J. H. Hannay, “Mode coupling in an elastically deformed optical fibre,” Electron. Lett. 12, 173–174 (1976).
    [CrossRef]
  12. J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227, 317–335 (2003).
    [CrossRef]
  13. W. A. Gambling, H. Matsumura, C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14, 130–132 (1978).
    [CrossRef]
  14. W. A. Gambling, D. N. Payne, H. Matsumura, “Radiation from curved single-mode fibres,” Electron. Lett. 12, 567–569 (1976).
    [CrossRef]
  15. D. Marcuse, “Field deformation and loss caused by curvature of optical fibres,” J. Opt. Soc. Am. 66, 311–320 (1976).
    [CrossRef]
  16. A. W. Snyder, I. White, D. J. Mitchell, “Radiation from bent optical waveguides,” Electron. Lett. 11, 332–333 (1975).
    [CrossRef]
  17. À. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  18. N. Barakat, A. A. Hamza, Interferometry of Fibrous Materials (Hilger, Bristol, UK, 1990).
  19. F. El-Diasty, “Evaluation of some GRIN fiber parameters and associated fraction mode loss due to mechanically induced optical anisotropy,” Appl. Opt. 42, 5263–5273 (2003).
    [CrossRef] [PubMed]
  20. Y. S. Liu, “Direct measurement of the refractive indices for a small numerical aperture claded fiber: a simple method,” Appl. Opt. 13, 1255–1256 (1974).
    [CrossRef] [PubMed]
  21. Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, X. K. Zeng, “Bend-insensitive long-period fiber grating sensors,” Opt. Lasers Eng. 41, 233–239 (2004).
    [CrossRef]

2004 (2)

T. Allsop, T. Earthrowl, R. Reeves, D. J. Webb, I. Bennion, “The interrogation and multiplexing of long grating curvature sensors using a Bragg grating based, derivative spectroscopy technique,” Meas. Sci. Technol. 15, 44–48 (2004).
[CrossRef]

Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, X. K. Zeng, “Bend-insensitive long-period fiber grating sensors,” Opt. Lasers Eng. 41, 233–239 (2004).
[CrossRef]

2003 (3)

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

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227, 317–335 (2003).
[CrossRef]

F. El-Diasty, “Evaluation of some GRIN fiber parameters and associated fraction mode loss due to mechanically induced optical anisotropy,” Appl. Opt. 42, 5263–5273 (2003).
[CrossRef] [PubMed]

2002 (2)

H. Tai, R. Rogowski, “Optical anisotropy induced by torsion and bending in an optical fiber,” Opt. Fiber Technol. 8, 162–169 (2002).
[CrossRef]

Q. Lin, G. P. Agrawal, “Pulse broadening induced by dispersion fluctuations in optical fibers,” Opt. Commun. 206, 313–317 (2002).
[CrossRef]

2001 (1)

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Bend sensing by measuring the resonance splitting of long-period fiber gratings,” Opt. Commun. 193, 69–72 (2001).
[CrossRef]

2000 (2)

F. El-Diasty, “Multiple-beam interferometric determination of Poisson’s ratio and strain profiles along the cross section of bent single-mode optical fibers,” Appl. Opt. 39, 3197–3201 (2000).
[CrossRef]

S. K. Khijwania, B. D. Gupta, “Maximum achievable sensitivity of fiber optic evanescent field absorption sensor based on the U-shaped probe,” Opt. Commun. 175, 135–137 (2000).
[CrossRef]

1997 (1)

Y. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8, 355–375 (1997).
[CrossRef]

1996 (1)

1985 (1)

1978 (1)

W. A. Gambling, H. Matsumura, C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14, 130–132 (1978).
[CrossRef]

1976 (3)

W. A. Gambling, D. N. Payne, H. Matsumura, “Radiation from curved single-mode fibres,” Electron. Lett. 12, 567–569 (1976).
[CrossRef]

D. Marcuse, “Field deformation and loss caused by curvature of optical fibres,” J. Opt. Soc. Am. 66, 311–320 (1976).
[CrossRef]

J. H. Hannay, “Mode coupling in an elastically deformed optical fibre,” Electron. Lett. 12, 173–174 (1976).
[CrossRef]

1975 (1)

A. W. Snyder, I. White, D. J. Mitchell, “Radiation from bent optical waveguides,” Electron. Lett. 11, 332–333 (1975).
[CrossRef]

1974 (1)

Agrawal, G. P.

Q. Lin, G. P. Agrawal, “Pulse broadening induced by dispersion fluctuations in optical fibers,” Opt. Commun. 206, 313–317 (2002).
[CrossRef]

Allsop, T.

T. Allsop, T. Earthrowl, R. Reeves, D. J. Webb, I. Bennion, “The interrogation and multiplexing of long grating curvature sensors using a Bragg grating based, derivative spectroscopy technique,” Meas. Sci. Technol. 15, 44–48 (2004).
[CrossRef]

Baggett, J. C.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227, 317–335 (2003).
[CrossRef]

Bahata, V.

Barakat, N.

N. Barakat, A. A. Hamza, Interferometry of Fibrous Materials (Hilger, Bristol, UK, 1990).

Bennion, I.

T. Allsop, T. Earthrowl, R. Reeves, D. J. Webb, I. Bennion, “The interrogation and multiplexing of long grating curvature sensors using a Bragg grating based, derivative spectroscopy technique,” Meas. Sci. Technol. 15, 44–48 (2004).
[CrossRef]

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Bend sensing by measuring the resonance splitting of long-period fiber gratings,” Opt. Commun. 193, 69–72 (2001).
[CrossRef]

Earthrowl, T.

T. Allsop, T. Earthrowl, R. Reeves, D. J. Webb, I. Bennion, “The interrogation and multiplexing of long grating curvature sensors using a Bragg grating based, derivative spectroscopy technique,” Meas. Sci. Technol. 15, 44–48 (2004).
[CrossRef]

El-Diasty, F.

Finazzi, V.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227, 317–335 (2003).
[CrossRef]

Furusawa, K.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227, 317–335 (2003).
[CrossRef]

Gambling, W. A.

W. A. Gambling, H. Matsumura, C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14, 130–132 (1978).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, “Radiation from curved single-mode fibres,” Electron. Lett. 12, 567–569 (1976).
[CrossRef]

Gupta, B. D.

S. K. Khijwania, B. D. Gupta, “Maximum achievable sensitivity of fiber optic evanescent field absorption sensor based on the U-shaped probe,” Opt. Commun. 175, 135–137 (2000).
[CrossRef]

Hamza, A. A.

N. Barakat, A. A. Hamza, Interferometry of Fibrous Materials (Hilger, Bristol, UK, 1990).

Hannay, J. H.

J. H. Hannay, “Mode coupling in an elastically deformed optical fibre,” Electron. Lett. 12, 173–174 (1976).
[CrossRef]

Khijwania, S. K.

S. K. Khijwania, B. D. Gupta, “Maximum achievable sensitivity of fiber optic evanescent field absorption sensor based on the U-shaped probe,” Opt. Commun. 175, 135–137 (2000).
[CrossRef]

Kitayama, K.

Lee, B.

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

Lin, Q.

Q. Lin, G. P. Agrawal, “Pulse broadening induced by dispersion fluctuations in optical fibers,” Opt. Commun. 206, 313–317 (2002).
[CrossRef]

Liu, Y.

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Bend sensing by measuring the resonance splitting of long-period fiber gratings,” Opt. Commun. 193, 69–72 (2001).
[CrossRef]

Liu, Y. S.

Love, J. D.

À. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Marcuse, D.

Matsumura, H.

W. A. Gambling, H. Matsumura, C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14, 130–132 (1978).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, “Radiation from curved single-mode fibres,” Electron. Lett. 12, 567–569 (1976).
[CrossRef]

Mitchell, D. J.

A. W. Snyder, I. White, D. J. Mitchell, “Radiation from bent optical waveguides,” Electron. Lett. 11, 332–333 (1975).
[CrossRef]

Monro, T. M.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227, 317–335 (2003).
[CrossRef]

Ohashi, M.

Payne, D. N.

W. A. Gambling, D. N. Payne, H. Matsumura, “Radiation from curved single-mode fibres,” Electron. Lett. 12, 567–569 (1976).
[CrossRef]

Ragdale, C. M.

W. A. Gambling, H. Matsumura, C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14, 130–132 (1978).
[CrossRef]

Ran, Z. L.

Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, X. K. Zeng, “Bend-insensitive long-period fiber grating sensors,” Opt. Lasers Eng. 41, 233–239 (2004).
[CrossRef]

Rao, Y.

Y. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8, 355–375 (1997).
[CrossRef]

Rao, Y. J.

Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, X. K. Zeng, “Bend-insensitive long-period fiber grating sensors,” Opt. Lasers Eng. 41, 233–239 (2004).
[CrossRef]

Reeves, R.

T. Allsop, T. Earthrowl, R. Reeves, D. J. Webb, I. Bennion, “The interrogation and multiplexing of long grating curvature sensors using a Bragg grating based, derivative spectroscopy technique,” Meas. Sci. Technol. 15, 44–48 (2004).
[CrossRef]

Richardson, D. J.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227, 317–335 (2003).
[CrossRef]

Rogowski, R.

H. Tai, R. Rogowski, “Optical anisotropy induced by torsion and bending in an optical fiber,” Opt. Fiber Technol. 8, 162–169 (2002).
[CrossRef]

Seikai, S.

Shibata, N.

Snyder, A. W.

A. W. Snyder, I. White, D. J. Mitchell, “Radiation from bent optical waveguides,” Electron. Lett. 11, 332–333 (1975).
[CrossRef]

Snyder, À. W.

À. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Tai, H.

H. Tai, R. Rogowski, “Optical anisotropy induced by torsion and bending in an optical fiber,” Opt. Fiber Technol. 8, 162–169 (2002).
[CrossRef]

Vengsarkar, A. M.

Wang, Y. P.

Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, X. K. Zeng, “Bend-insensitive long-period fiber grating sensors,” Opt. Lasers Eng. 41, 233–239 (2004).
[CrossRef]

Webb, D. J.

T. Allsop, T. Earthrowl, R. Reeves, D. J. Webb, I. Bennion, “The interrogation and multiplexing of long grating curvature sensors using a Bragg grating based, derivative spectroscopy technique,” Meas. Sci. Technol. 15, 44–48 (2004).
[CrossRef]

White, I.

A. W. Snyder, I. White, D. J. Mitchell, “Radiation from bent optical waveguides,” Electron. Lett. 11, 332–333 (1975).
[CrossRef]

Williams, J. A. R.

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Bend sensing by measuring the resonance splitting of long-period fiber gratings,” Opt. Commun. 193, 69–72 (2001).
[CrossRef]

Zeng, X. K.

Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, X. K. Zeng, “Bend-insensitive long-period fiber grating sensors,” Opt. Lasers Eng. 41, 233–239 (2004).
[CrossRef]

Zhang, L.

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Bend sensing by measuring the resonance splitting of long-period fiber gratings,” Opt. Commun. 193, 69–72 (2001).
[CrossRef]

Zhu, T.

Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, X. K. Zeng, “Bend-insensitive long-period fiber grating sensors,” Opt. Lasers Eng. 41, 233–239 (2004).
[CrossRef]

Appl. Opt. (3)

Electron. Lett. (4)

A. W. Snyder, I. White, D. J. Mitchell, “Radiation from bent optical waveguides,” Electron. Lett. 11, 332–333 (1975).
[CrossRef]

J. H. Hannay, “Mode coupling in an elastically deformed optical fibre,” Electron. Lett. 12, 173–174 (1976).
[CrossRef]

W. A. Gambling, H. Matsumura, C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14, 130–132 (1978).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, “Radiation from curved single-mode fibres,” Electron. Lett. 12, 567–569 (1976).
[CrossRef]

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (2)

Y. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8, 355–375 (1997).
[CrossRef]

T. Allsop, T. Earthrowl, R. Reeves, D. J. Webb, I. Bennion, “The interrogation and multiplexing of long grating curvature sensors using a Bragg grating based, derivative spectroscopy technique,” Meas. Sci. Technol. 15, 44–48 (2004).
[CrossRef]

Opt. Commun. (4)

S. K. Khijwania, B. D. Gupta, “Maximum achievable sensitivity of fiber optic evanescent field absorption sensor based on the U-shaped probe,” Opt. Commun. 175, 135–137 (2000).
[CrossRef]

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Bend sensing by measuring the resonance splitting of long-period fiber gratings,” Opt. Commun. 193, 69–72 (2001).
[CrossRef]

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227, 317–335 (2003).
[CrossRef]

Q. Lin, G. P. Agrawal, “Pulse broadening induced by dispersion fluctuations in optical fibers,” Opt. Commun. 206, 313–317 (2002).
[CrossRef]

Opt. Fiber Technol. (2)

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

H. Tai, R. Rogowski, “Optical anisotropy induced by torsion and bending in an optical fiber,” Opt. Fiber Technol. 8, 162–169 (2002).
[CrossRef]

Opt. Lasers Eng. (1)

Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, X. K. Zeng, “Bend-insensitive long-period fiber grating sensors,” Opt. Lasers Eng. 41, 233–239 (2004).
[CrossRef]

Opt. Lett. (2)

Other (2)

À. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

N. Barakat, A. A. Hamza, Interferometry of Fibrous Materials (Hilger, Bristol, UK, 1990).

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of the induced field shift due to bending of fiber.

Fig. 2
Fig. 2

Schematic diagram of the wedge interferometer and the Fizeau fringes at transmission crossing perpendicular to a bent single-mode fiber.

Fig. 3
Fig. 3

Micro-interferogram of a strain-free, straight single-mode fiber immersed in liquid with a refractive index lower than the fiber-cladding index.

Fig. 4
Fig. 4

Micro-interferogram of a strain-free, straight single-mode fiber immersed in matching liquid.

Fig. 5
Fig. 5

(a) Micro-interferogram of the induced-birefringence components in the cladding of a bare bent fiber immersed in a matching liquid at a radius of curvature of 19 mm. (b) Micro-interferogram of the ordinary component of the induced birefringence at a radius of curvature of 8 mm. (c) Micro-interferogram of the extraordinary component of the induced birefringence at a radius of curvature of 8 mm.

Fig. 6
Fig. 6

Micro-interferogram of the extraordinary component of the induced birefringence at a radius of curvature of 14 mm.

Fig. 7
Fig. 7

Micro-interferogram of the extraordinary component of the induced birefringence at a radius of curvature of 15 mm.

Fig. 8
Fig. 8

Plot of a comparison between experiment and theory for the field shift of the fundamental mode.

Fig. 9
Fig. 9

Plot of a comparison of the results with the theoretical prediction of the associated transition loss in a bent single-mode fiber with different radii of curvature.

Fig. 10
Fig. 10

Plot of the relation between the field shift of the fundamental mode and curvature R-1.

Fig. 11
Fig. 11

Plot of the associated transition loss versus R-2.

Tables (1)

Tables Icon

Table 1 Specifications of the Standard Single-Mode Fiber Used in Our Experiment

Equations (19)

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r2d2ψ(r)dr2+r dψ(r)dr+U2r2a2-l2ψ(r)=0,
0<r<a,
r2d2ψ(r)dr2+r dψ(r)dr+W2r2a2+l2ψ(r)=0,
r>a,
U=a(k02nco2-β2)1/2.
W=a(β2-k02ncl2)1/2,
Q=a(k02ncl2-β2)1/2=iW.
V=(U2+W2)1/2=k0a(nco2-ncl2)1/2.
Pco=Cπa21-Jl-1(U)Jl+1(U)Jl2(U),
Pcl=Cπa2Kl-1(W)Kl+1(W)Kl2(W)-1,
Ptot=Pco+Pcl,
Ptot=Cπa2V2U2Kl+1(W)Kl-1(W)Kl2(W).
rd=V2a22ΔRroa4,Ra,
ro=a(V-1)1/2.
z(x)=4λ Δz(ncl-nL)(r2-x2)1/2,
ncl=z(x)λ4Δz (r2-x2)-1/2±nL,
δn=(no3/2)[ρ12(1-ν)-νρ11](x/R),
P=1-PoPi=1-exp-rd22roaR2roa6V48Δ2.
nco=nclf[(1-f2)1/2-(1-f)]+nLf1-(1-f2)1/2[(1-f2)(1-n2f2)]1/2+n2f2,

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