Abstract

Multiple-beam Fizeau fringes crossing bent single-mode optical fibers immersed in matching liquid reveal the existence of induced birefringence. Changes in the fiber cladding refractive index δn were measured from the fringe shift to an accuracy of ±1 × 10-4. Mathematical expressions were deduced to evaluate Poisson’s ratio and to describe the radial strain distribution profiles of bent optical fibers from the experimental values of the fringe shifts. Experimental results were obtained from microinterferograms. Studying bent fibers by application of Fizeau fringes interferometry provides a nondestructive, accurate, sensitive, and reliable method to measure their parameters and characteristics.

© 2000 Optical Society of America

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1999

F. El-Diasty, “Interferometric determination of induced birefringence due to bending in single-mode optical fibres,” J. Opt. A: Pure Appl. Opt. 1, 197–200 (1999).
[CrossRef]

1998

F. M. Haran, J. K. Rew, P. D. Foote, “A strain-isolated fibre Bragg grating sensor for temperature compensation of fibre Bragg grating strain sensors,” Meas. Sci. Technol. 9, 1163–1166 (1998).
[CrossRef]

B. H. Lee, J. Nishii, “Bending sensitivity of in-series long-period fiber gratings,” Opt. Lett. 23, 1624–1628 (1998).
[CrossRef]

1997

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

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

G. Meltz, W. Morey, W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett. 14, 823–825 (1997).
[CrossRef]

1996

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

V. Bhatia, A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21, 692–694 (1996).
[CrossRef] [PubMed]

1995

1993

R. Kashyap, R. Wyatt, R. J. Campbell, “Wideband gain flattened erbium fibre amplifier using a photosensitive fibre blazed grating,” Electron. Lett. 29, 154–156 (1993).
[CrossRef]

N. Barakat, H. A. El-Hennawi, H. E. Sobeah, “Multiple-beam interferomatric studies on optical fibers,” Pure Appl. Opt. 2, 419–428 (1993).
[CrossRef]

1991

D. R. Roberts, E. Cuellar, J. E. Ritter, T. H. Service, “Design requirements for optical fibres in small radii bends,” J. Mater. Sci. 26, 3197–3201 (1991).
[CrossRef]

1990

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written grating,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

1988

N. Barakat, H. A. El-Hennawi, F. El-Diasty, “Multiple-beam interference fringes applied to GRAIN optical fiber,” Appl. Opt. 27, 5090–5094 (1988).
[CrossRef] [PubMed]

A. Bertholds, R. Dandliker, “Determination of the individual strain-optic coefficients in single-mode optical fibers,” J. Lightwave Technol. 6, 17–20 (1988).
[CrossRef]

1987

M. J. Matthewson, C. R. Kurkjian, “Static fatigue of optical fibers in bending,” J. Am. Ceram. Soc. 70, 662–668 (1987).
[CrossRef]

H. Gerbel, J. Herskowitz, “Effect of strain in periodically deformed single-mode optical fibers,” Appl. Opt. 26, 2155–2158 (1987).
[CrossRef]

H. A. El-Hennawi, M. Medhat, F. El-Diasty, “On the determination of the index profile parameters of a graded index fiber,” Egypt J. Phys. 18, 179–189 (1987).

H. A. El-Hennawi, F. El-Diasty, O. Meshrif, “Interferometric determination of the refractive index of optical fiber cladding and an examination of its homogeneity,” J. Appl. Phys. 62, 4931–4933 (1987).
[CrossRef]

1986

M. J. Matthewson, C. R. Kurkjian, S. T. Gulati, “Strength measurement of optical fibers by bending,” J. Am. Ceram. Soc. 69, 815–821 (1986).
[CrossRef]

1985

X. Fang, Z. Lin, “Birefringence in curved single-mode optical fibers due to waveguide geometry effect-perturbation analysis,” J. Lightwave Technol. LT-3, 789–794 (1985).
[CrossRef]

N. Barakat, A. A. Hamza, A. S. Goneid, “Multiple-beam interference fringes applied to GRIN optical waveguides to determine fiber characteristics,” Appl. Opt. 24, 4383–4386 (1985).
[CrossRef] [PubMed]

1984

H. F. Taylor, “Bending effects in optical fibers,” J. Lightwave Technol. LT-2, 617–622 (1984).
[CrossRef]

1983

S. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

1981

J. Sakai, T. Kimura, “Birefringence and polarization characteristics of single-mode optical fibers under elastic deformations,” IEEE J. Quantum Electron. QE-17, 1041–1051 (1981).
[CrossRef]

1980

1979

1978

1976

1975

W. A. Gambling, D. N. Payne, H. Matsumura, “Mode conversion coefficients in optical fibers,” Appl. Opt. 14, 1538–1542 (1975).
[CrossRef] [PubMed]

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

W. B. Gardner, “Microbending loss in optical fibers,” Bell Syst. Tech. J. 54, 457–465 (1975).
[CrossRef]

1974

D. B. Keck, “Observation of externally controlled mode coupling in optical waveguides,” Proc. IEEE 62, 649–650 (1974).
[CrossRef]

1959

W. Primak, D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[CrossRef]

Barakat, N.

Bertholds, A.

A. Bertholds, R. Dandliker, “Determination of the individual strain-optic coefficients in single-mode optical fibers,” J. Lightwave Technol. 6, 17–20 (1988).
[CrossRef]

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

V. Bhatia, A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21, 692–694 (1996).
[CrossRef] [PubMed]

Bilodeau, F.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written grating,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

Brown, D. A.

Campbell, R. J.

R. Kashyap, R. Wyatt, R. J. Campbell, “Wideband gain flattened erbium fibre amplifier using a photosensitive fibre blazed grating,” Electron. Lett. 29, 154–156 (1993).
[CrossRef]

Chang, C. T.

Cuellar, E.

D. R. Roberts, E. Cuellar, J. E. Ritter, T. H. Service, “Design requirements for optical fibres in small radii bends,” J. Mater. Sci. 26, 3197–3201 (1991).
[CrossRef]

Dandliker, R.

A. Bertholds, R. Dandliker, “Determination of the individual strain-optic coefficients in single-mode optical fibers,” J. Lightwave Technol. 6, 17–20 (1988).
[CrossRef]

Dde, E.

E. Dde, Fiber Optic Sensors: An Introduction for Scientists and Engineers, 1st ed. (Wiley, New York, 1991).

Eichoff, W.

El-Diasty, F.

F. El-Diasty, “Interferometric determination of induced birefringence due to bending in single-mode optical fibres,” J. Opt. A: Pure Appl. Opt. 1, 197–200 (1999).
[CrossRef]

N. Barakat, H. A. El-Hennawi, F. El-Diasty, “Multiple-beam interference fringes applied to GRAIN optical fiber,” Appl. Opt. 27, 5090–5094 (1988).
[CrossRef] [PubMed]

H. A. El-Hennawi, M. Medhat, F. El-Diasty, “On the determination of the index profile parameters of a graded index fiber,” Egypt J. Phys. 18, 179–189 (1987).

H. A. El-Hennawi, F. El-Diasty, O. Meshrif, “Interferometric determination of the refractive index of optical fiber cladding and an examination of its homogeneity,” J. Appl. Phys. 62, 4931–4933 (1987).
[CrossRef]

El-Hennawi, H. A.

N. Barakat, H. A. El-Hennawi, H. E. Sobeah, “Multiple-beam interferomatric studies on optical fibers,” Pure Appl. Opt. 2, 419–428 (1993).
[CrossRef]

N. Barakat, H. A. El-Hennawi, F. El-Diasty, “Multiple-beam interference fringes applied to GRAIN optical fiber,” Appl. Opt. 27, 5090–5094 (1988).
[CrossRef] [PubMed]

H. A. El-Hennawi, M. Medhat, F. El-Diasty, “On the determination of the index profile parameters of a graded index fiber,” Egypt J. Phys. 18, 179–189 (1987).

H. A. El-Hennawi, F. El-Diasty, O. Meshrif, “Interferometric determination of the refractive index of optical fiber cladding and an examination of its homogeneity,” J. Appl. Phys. 62, 4931–4933 (1987).
[CrossRef]

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Fang, X.

X. Fang, Z. Lin, “Birefringence in curved single-mode optical fibers due to waveguide geometry effect-perturbation analysis,” J. Lightwave Technol. LT-3, 789–794 (1985).
[CrossRef]

Foote, P. D.

F. M. Haran, J. K. Rew, P. D. Foote, “A strain-isolated fibre Bragg grating sensor for temperature compensation of fibre Bragg grating strain sensors,” Meas. Sci. Technol. 9, 1163–1166 (1998).
[CrossRef]

Gambling, W. A.

Gardner, W. B.

W. B. Gardner, “Microbending loss in optical fibers,” Bell Syst. Tech. J. 54, 457–465 (1975).
[CrossRef]

Gerbel, H.

Giallorenzi, T. G.

Glenn, W. H.

Goneid, A. S.

Gulati, S. T.

M. J. Matthewson, C. R. Kurkjian, S. T. Gulati, “Strength measurement of optical fibers by bending,” J. Am. Ceram. Soc. 69, 815–821 (1986).
[CrossRef]

Hamza, A. A.

Haran, F. M.

F. M. Haran, J. K. Rew, P. D. Foote, “A strain-isolated fibre Bragg grating sensor for temperature compensation of fibre Bragg grating strain sensors,” Meas. Sci. Technol. 9, 1163–1166 (1998).
[CrossRef]

Herskowitz, J.

Hill, K. O.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written grating,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

Johnson, D. C.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written grating,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

Johnson, M.

Judkins, J. B.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Jurgensen, K.

Kashyap, R.

R. Kashyap, R. Wyatt, R. J. Campbell, “Wideband gain flattened erbium fibre amplifier using a photosensitive fibre blazed grating,” Electron. Lett. 29, 154–156 (1993).
[CrossRef]

Kawakami, S.

Keck, D. B.

D. B. Keck, “Observation of externally controlled mode coupling in optical waveguides,” Proc. IEEE 62, 649–650 (1974).
[CrossRef]

Kimura, T.

J. Sakai, T. Kimura, “Birefringence and polarization characteristics of single-mode optical fibers under elastic deformations,” IEEE J. Quantum Electron. QE-17, 1041–1051 (1981).
[CrossRef]

Kurkjian, C. R.

M. J. Matthewson, C. R. Kurkjian, “Static fatigue of optical fibers in bending,” J. Am. Ceram. Soc. 70, 662–668 (1987).
[CrossRef]

M. J. Matthewson, C. R. Kurkjian, S. T. Gulati, “Strength measurement of optical fibers by bending,” J. Am. Ceram. Soc. 69, 815–821 (1986).
[CrossRef]

Lee, B. H.

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Lin, Z.

X. Fang, Z. Lin, “Birefringence in curved single-mode optical fibers due to waveguide geometry effect-perturbation analysis,” J. Lightwave Technol. LT-3, 789–794 (1985).
[CrossRef]

Malo, B.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written grating,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

Marcuse, D.

Matsumura, H.

Matthewson, M. J.

M. J. Matthewson, C. R. Kurkjian, “Static fatigue of optical fibers in bending,” J. Am. Ceram. Soc. 70, 662–668 (1987).
[CrossRef]

M. J. Matthewson, C. R. Kurkjian, S. T. Gulati, “Strength measurement of optical fibers by bending,” J. Am. Ceram. Soc. 69, 815–821 (1986).
[CrossRef]

Medhat, M.

H. A. El-Hennawi, M. Medhat, F. El-Diasty, “On the determination of the index profile parameters of a graded index fiber,” Egypt J. Phys. 18, 179–189 (1987).

Meltz, G.

Meshrif, O.

H. A. El-Hennawi, F. El-Diasty, O. Meshrif, “Interferometric determination of the refractive index of optical fiber cladding and an examination of its homogeneity,” J. Appl. Phys. 62, 4931–4933 (1987).
[CrossRef]

Mitchell, D. J.

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

Morey, W.

Morse, T. F.

Nagano, K.

Nishida, S.

Nishii, J.

Nye, J. F.

J. F. Nye, Physical Properties of Crystals, 2nd ed. (Clarendon, Oxford, UK, 1964), p. 243.

Okoshi, T.

T. Okoshi, “Heterodyne-type optical fiber communications,” in Proceedings of the International Conference on Integrated Optics and Optical Fiber Communication (N.p., 1981), pp. 17–29.

Payne, D. N.

Pinnow, D. A.

D. A. Pinnow, “Electrooptic materials,” in Handbook of Lasers, R. J. Presley, ed. (CRC, Cleveland, Ohio, 1971).

Post, D.

W. Primak, D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[CrossRef]

Primak, W.

W. Primak, D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[CrossRef]

Rashleigh, S.

S. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

Rashleigh, S. C.

Reinhart, L. J.

Rew, J. K.

F. M. Haran, J. K. Rew, P. D. Foote, “A strain-isolated fibre Bragg grating sensor for temperature compensation of fibre Bragg grating strain sensors,” Meas. Sci. Technol. 9, 1163–1166 (1998).
[CrossRef]

Ritter, J. E.

D. R. Roberts, E. Cuellar, J. E. Ritter, T. H. Service, “Design requirements for optical fibres in small radii bends,” J. Mater. Sci. 26, 3197–3201 (1991).
[CrossRef]

Roberts, D. R.

D. R. Roberts, E. Cuellar, J. E. Ritter, T. H. Service, “Design requirements for optical fibres in small radii bends,” J. Mater. Sci. 26, 3197–3201 (1991).
[CrossRef]

Sakai, J.

J. Sakai, T. Kimura, “Birefringence and polarization characteristics of single-mode optical fibers under elastic deformations,” IEEE J. Quantum Electron. QE-17, 1041–1051 (1981).
[CrossRef]

J. Sakai, “Simplified bending loss formula for single-mode optical fibers,” Appl. Opt. 18, 951–952 (1979).
[CrossRef] [PubMed]

Service, T. H.

D. R. Roberts, E. Cuellar, J. E. Ritter, T. H. Service, “Design requirements for optical fibres in small radii bends,” J. Mater. Sci. 26, 3197–3201 (1991).
[CrossRef]

Sipe, J. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Skinner, I.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written grating,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

Smith, A. M.

Snyder, A. W.

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

Sobeah, H. E.

N. Barakat, H. A. El-Hennawi, H. E. Sobeah, “Multiple-beam interferomatric studies on optical fibers,” Pure Appl. Opt. 2, 419–428 (1993).
[CrossRef]

Steinberg, R. A.

Taylor, H. F.

H. F. Taylor, “Bending effects in optical fibers,” J. Lightwave Technol. LT-2, 617–622 (1984).
[CrossRef]

Ulrich, R.

Urlich, R.

Vengsarkar, A. M.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic representation of the resulting fringe shift components in the cladding of bent single-mode fibers.

Fig. 2
Fig. 2

Microinterferogram of a family of Fizeau fringes across the cladding of a bent single-mode fiber immersed in matching liquid.

Fig. 3
Fig. 3

Microinterferogram showing the separate fringe shift component perpendicular to the fiber axis.

Fig. 4
Fig. 4

Plot showing the measured strain distribution profiles along the cross section of the cladding of bent fiber at different radii of curvature.

Fig. 5
Fig. 5

Plot showing the maximum measured strain values in the cladding of bent fiber versus the fiber curvature, in the case of compressive stresses and tensile stresses.

Tables (1)

Tables Icon

Table 1 Summary of Measured Poisson’s Ratio ν and Maximum Cladding Index Changes Due to Bending with Their Compensating Radii of Curvature

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

zx=4Δz/λMncl-nLr2-x21/2,
ncl=zxλM/4Δzr2-x2-1/2+nL,
δn=zλM/4Δzr2-x2-1/2.
δn=-n3/2j ρijεj,
δn/n=χx/R,
χ=n2/2ρ121-ν-νρ11,
δn=n3/2ρ121-ν-νρ11x/R.
ν=ρ12ρ11+ρ12-zλRMr2-x2-1/22xn3Δzρ11+ρ12.
εx=εy=-νx/R,
εz=x/R.
εx=zλMr2-x2-1/22n3Δzρ11+ρ12-xρ12RMρ11+ρ12.

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