Abstract

Some of the optical parameters of the bent multimode graded-index (GRIN) optical fiber in terms of indices of refraction, where the bending stresses broke the radial symmetry, are evaluated by use of multiple-beam Fizeau fringes. The variation of the index difference between the cladding index and core index in both the compression and tensile fiber regions is measured. The accuracy of measuring the index is ±1 × 10-4. The spatial resolution of the method is 1.39 μm. Evaluation of the acceptance angle, the numerical aperture, and the V number profiles of the bent fiber from the interference pattern at both sides of the bent fiber are presented. The fraction of the mode number lost has been evaluated. The method was used to study the influence of compression on diminishing the index difference that leads to a dissipation of energy and a considerable mode loss. It is obvious from the experimental data that the change of the index difference due to bending strongly affects the fraction of propagating mode number, especially at the small radii of curvature. Ignoring the variation of the index difference we evaluating the number of propagated modes number leads to an insufficient determination of the mode loss. It subsequently leads to an incorrect determination of the mode dispersion and the interface loss in bent GRIN fibers. The study confirms that the deviation of the guide axis from straightness with the radius of curvature of less than 1 cm could lead to a significant fraction mode loss.

© 2003 Optical Society of America

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2003 (1)

P. Hlubina, T. Martynkien, W. Urbanczyk, “Measurements of intermodal dispersion in few-mode optical fibers using a spectral-domain white-light interferometric method,” Meas. Sci. Technol. 14, 784–789 (2003).
[CrossRef]

2002 (4)

F. El-Diasty, “Application of Fizeau fringes with bending technique to determine the shear modulus of the cladding material of single-mode optical fibers through the mechanically induced change of refractive index,” Opt. Commun. 212, 267–274 (2002).
[CrossRef]

M. Medhat, S. Y. Zaiat, A. Radi, M. Omer, “Application of fringes of equal chromatic order for investigating the effect of temperature on optical parameters of a GRIN optical fibre,” J. Opt. A: Pure Appl. Opt. 4, 174–179 (2002).
[CrossRef]

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, M. A. Shams-Eldin, “Determination of GR-IN optical fiber parameters from transverse interferograms considering the refraction of the incident ray by the fiber,” Opt. Commun. 15, 131–138 (2002).

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

2001 (2)

F. El-Diasty, “Theory and measurement of Young’s modulus radial profiles of bent single-mode optical fibers with the multiple-beam interference technique,” J. Opt. Soc. Am. A 18, 1171–1175 (2001).
[CrossRef]

N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Gandoor, R. Hassan, F. El-Diasty, “Three-dimensional diffractive index of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
[CrossRef]

2000 (2)

1999 (3)

S. Yin, P. Purwosumarto, “Application of fiber specklergram sensor to fine angular alignment,” Opt. Commun. 170, 15–19 (1999).
[CrossRef]

K. Tsujikawa, K. Arakawa, K. Yoshida, “Reflection of light caused by sharp bends in optical fiber,” IEICE Trans. Electron. E82-C, 2105–2107 (1999).

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

1998 (4)

N. Barakat, H. A. El-Hannawi, F. El-Diasty, “Multiple-beam interference applied to GRIN optical fiber,” Appl. Opt. 27, 5090–5094 (1998).
[CrossRef]

V. V. Steblina, “Cladding mode degeneracy in bent W-fibers beyond cutoff,” Opt. Commun. 156, 271–278 (1998).
[CrossRef]

C. DeCusatis, “Optical data communication: fundamentals and future directions,” Opt. Eng. 37, 3082–3099 (1998).
[CrossRef]

B. H. Lee, J. Nishii, “Bending sensitivity of in-series long-period fiber gratings,” Opt. Lett. 23, 1624–1626 (1998).
[CrossRef]

1996 (2)

R. Henao, J. A. Pomarico, N. Russo, R. D. Torroba, M. Trivi, “Multimode optical fiber core measurement by speckle correlation,” Opt. Eng. 35, 26–30 (1996).
[CrossRef]

D. Z. Anderson, M. A. Bolshtyansky, B. Ya Zel’dovich, “Stabilization of the speckle pattern of a multimode fiber undergoing bending,” Opt. Lett. 21, 785–787 (1996).
[CrossRef] [PubMed]

1995 (1)

1993 (2)

1990 (1)

1989 (1)

M. A. El-Sherif, “On-fiber sensor and modulator,” IEEE Trans. Instrum. Meas. 38, 595–598 (1989).
[CrossRef]

1985 (1)

1984 (2)

G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramskov-Hansen, “Design and performance of tuned fiber coil isolators,” J. Lightwave Technol. LT-2, 56–60 (1984).
[CrossRef]

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

1981 (1)

1980 (2)

R. Ulrich, S. C. Rashleigh, W. Eichoff, “Bending-induced birefringence in single-mode fibers,” Opt. Lett. 5, 273–275 (1980).
[CrossRef] [PubMed]

H. C. Lefevre, “Single-mode fibre fractional wave devices and polarization controllers,” Electron. Lett. 16, 778–780 (1980).
[CrossRef]

1978 (1)

1977 (2)

1976 (4)

1975 (1)

1972 (1)

1951 (1)

R. C. O’Rourke, “Three-dimensional photoelasticity,” J. Appl. Phys. 22, 872–878 (1951).
[CrossRef]

Abd El-Ghafar, E. A.

M. A. Abd-El Rahman, E. A. Abd El-Ghafar, I. Nasser, “Angular dispersion of GRIN fiber using a laser sheet of light,” in Second International Conference on Experimental MechanicsF. S. Chau, C. Quan, eds. Proc. SPIE4317, 597–603 (2001).
[CrossRef]

Abd-El Rahman, M. A.

M. A. Abd-El Rahman, E. A. Abd El-Ghafar, I. Nasser, “Angular dispersion of GRIN fiber using a laser sheet of light,” in Second International Conference on Experimental MechanicsF. S. Chau, C. Quan, eds. Proc. SPIE4317, 597–603 (2001).
[CrossRef]

Anderson, D. Z.

Arakawa, K.

K. Tsujikawa, K. Arakawa, K. Yoshida, “Reflection of light caused by sharp bends in optical fiber,” IEICE Trans. Electron. E82-C, 2105–2107 (1999).

Barakat, N.

Barlow, A. J.

G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramskov-Hansen, “Design and performance of tuned fiber coil isolators,” J. Lightwave Technol. LT-2, 56–60 (1984).
[CrossRef]

Beck, Th.

Th. Beck, N. Reng, H. Weber, “Optical fibers for material processing lasers,” Opt. Laser Eng. 34, 255–272 (2000).
[CrossRef]

Bolshtyansky, M. A.

Brown, D. A.

Chen, Y.-X.

G.-Y. He, Y.-X. Chen, E.-Y. Qi, “Numerical aperture of multimode fibers with curvature, a new theory formula,” in Fiber Optic Sensors V, K. D. Bennett, B.-Y. Kim, Y.-B. Liao, eds., Proc. SPIE2895, 552–558 (1996).
[CrossRef]

Chernikov, S. V.

S. V. Chernikov, F. Koch, J. R. Taylor, L. Gruner-Nielsen, “Measurement of the effect of bending on dispersion in dispersion-compensating fibers,” in Proceeding of OFC’98, Optical Fiber Communication Conference and Exhibition, (Optical Society of American Washington, D.C., 1998), p. 23–24.

Culshaw, B.

B. Culshaw, Optical Fiber Sensing and Signal Processing,1st ed. (Peregrinus, London, 1984).

Day, G. W.

G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramskov-Hansen, “Design and performance of tuned fiber coil isolators,” J. Lightwave Technol. LT-2, 56–60 (1984).
[CrossRef]

DeCusatis, C.

C. DeCusatis, “Optical data communication: fundamentals and future directions,” Opt. Eng. 37, 3082–3099 (1998).
[CrossRef]

Djambova, T. V.

T. Mizunami, T. Niiho, T. V. Djambova, “Multimode fiber Bragg gratings for fiber-optic bending sensors,” 13th International Conference on Optical Fiber Sensors, B. Kim, K. Hotate, eds. Proc. SPIE3746, 216–219 (1999).

Drinkmeyer, E.

Eichoff, W.

El-Diasty, F.

F. El-Diasty, “Application of Fizeau fringes with bending technique to determine the shear modulus of the cladding material of single-mode optical fibers through the mechanically induced change of refractive index,” Opt. Commun. 212, 267–274 (2002).
[CrossRef]

F. El-Diasty, “Theory and measurement of Young’s modulus radial profiles of bent single-mode optical fibers with the multiple-beam interference technique,” J. Opt. Soc. Am. A 18, 1171–1175 (2001).
[CrossRef]

N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Gandoor, R. Hassan, F. El-Diasty, “Three-dimensional diffractive index of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
[CrossRef]

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]

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

N. Barakat, H. A. El-Hannawi, F. El-Diasty, “Multiple-beam interference applied to GRIN optical fiber,” Appl. Opt. 27, 5090–5094 (1998).
[CrossRef]

El-Gandoor, H.

N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Gandoor, R. Hassan, F. El-Diasty, “Three-dimensional diffractive index of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
[CrossRef]

El-Ghafar, E. A.

N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Gandoor, R. Hassan, F. El-Diasty, “Three-dimensional diffractive index of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
[CrossRef]

El-Hannawi, H. A.

El-Hennawi, H. A.

N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Gandoor, R. Hassan, F. El-Diasty, “Three-dimensional diffractive index of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
[CrossRef]

El-Sherif, M. A.

M. A. El-Sherif, “On-fiber sensor and modulator,” IEEE Trans. Instrum. Meas. 38, 595–598 (1989).
[CrossRef]

Frocht, M. M.

M. M. Frocht, “Photoelasticity,” vol. 1, 1941; “Photoelasticity,” vol. 2, 1948 (Wiley, New York).

Galliot, E. A. C.

M. J. Gander, E. A. C. Galliot, R. McBride, J. D. C. Jones, “Bend measurement using multicore optical fiber,” in proceeding of the 12th International Conference on Optical Fiber Sensors, (Williamsburg, Virginia, 1997), p. 166–169.

Gambling, W. A.

Gander, M. J.

M. J. Gander, E. A. C. Galliot, R. McBride, J. D. C. Jones, “Bend measurement using multicore optical fiber,” in proceeding of the 12th International Conference on Optical Fiber Sensors, (Williamsburg, Virginia, 1997), p. 166–169.

Geneid, A. S.

Gloge, D.

Gorski, W.

W. Gorski, “The influence of diffraction in microinterferometry and microtomography of optical fibers,” Opt. Laser Eng. (in press).

Goure, J. P.

Gruner-Nielsen, L.

S. V. Chernikov, F. Koch, J. R. Taylor, L. Gruner-Nielsen, “Measurement of the effect of bending on dispersion in dispersion-compensating fibers,” in Proceeding of OFC’98, Optical Fiber Communication Conference and Exhibition, (Optical Society of American Washington, D.C., 1998), p. 23–24.

Hamza, A. A.

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, M. A. Shams-Eldin, “Determination of GR-IN optical fiber parameters from transverse interferograms considering the refraction of the incident ray by the fiber,” Opt. Commun. 15, 131–138 (2002).

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

Hannay, J. H.

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

Hassan, R.

N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Gandoor, R. Hassan, F. El-Diasty, “Three-dimensional diffractive index of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
[CrossRef]

He, G.-Y.

G.-Y. He, Y.-X. Chen, E.-Y. Qi, “Numerical aperture of multimode fibers with curvature, a new theory formula,” in Fiber Optic Sensors V, K. D. Bennett, B.-Y. Kim, Y.-B. Liao, eds., Proc. SPIE2895, 552–558 (1996).
[CrossRef]

Hefferon, J. E.

J. E. Hefferon, “Calculating bend and twist stress in optical fibers,” in Components for Fiber Optic Applications, V. J. Tekippe, ed., Proc. SPIE, 722, 108–110 (1986).
[CrossRef]

Henao, R.

R. Henao, J. A. Pomarico, N. Russo, R. D. Torroba, M. Trivi, “Multimode optical fiber core measurement by speckle correlation,” Opt. Eng. 35, 26–30 (1996).
[CrossRef]

Hlubina, P.

P. Hlubina, T. Martynkien, W. Urbanczyk, “Measurements of intermodal dispersion in few-mode optical fibers using a spectral-domain white-light interferometric method,” Meas. Sci. Technol. 14, 784–789 (2003).
[CrossRef]

Hotate, K.

Hubner, J.

J. Rathji, M. Kristensen, J. Hubner, “Effect of core concentricity error on bend direction asymmetry for long-period fiber gratings,” Conference on Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, (Optical Society of America, Washington D.C.1999), p. 283–285.

Ikeda, M.

Ishigure, T.

T. Ishigure, M. Sato, E. Nihei, Y. Koike, “High-bandwidth and high-thermal stability graded-index polymer optical fiber,” in Polymer Photonic Devices, B. Kippelen, D. D. Bradley, eds., Proc. SPIE, 328166–74 (1998).
[CrossRef]

Jones, J. D. C.

M. J. Gander, E. A. C. Galliot, R. McBride, J. D. C. Jones, “Bend measurement using multicore optical fiber,” in proceeding of the 12th International Conference on Optical Fiber Sensors, (Williamsburg, Virginia, 1997), p. 166–169.

Kawakami, S.

King, R.

R. King, R. Michalzik, “VCSEL arrays for fiber optical interconnections,” Annual Report1999, Department of Optoelectronics, University of Ulm.

Kitayama, K.

Koch, F.

S. V. Chernikov, F. Koch, J. R. Taylor, L. Gruner-Nielsen, “Measurement of the effect of bending on dispersion in dispersion-compensating fibers,” in Proceeding of OFC’98, Optical Fiber Communication Conference and Exhibition, (Optical Society of American Washington, D.C., 1998), p. 23–24.

Koike, Y.

T. Ishigure, M. Sato, E. Nihei, Y. Koike, “High-bandwidth and high-thermal stability graded-index polymer optical fiber,” in Polymer Photonic Devices, B. Kippelen, D. D. Bradley, eds., Proc. SPIE, 328166–74 (1998).
[CrossRef]

Kristensen, M.

J. Rathji, M. Kristensen, J. Hubner, “Effect of core concentricity error on bend direction asymmetry for long-period fiber gratings,” Conference on Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, (Optical Society of America, Washington D.C.1999), p. 283–285.

Lee, B. H.

Lefevre, H. C.

H. C. Lefevre, “Single-mode fibre fractional wave devices and polarization controllers,” Electron. Lett. 16, 778–780 (1980).
[CrossRef]

Lehman, R. L.

R. L. Lehman, “Developments in fiber optic sensor design,” in Proceedings of the 40th Electronic Components and Technology Conference, (Las Vegas, Nevada, 1990) pp. 60–63.
[CrossRef]

Mabrouk, M. A.

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, M. A. Shams-Eldin, “Determination of GR-IN optical fiber parameters from transverse interferograms considering the refraction of the incident ray by the fiber,” Opt. Commun. 15, 131–138 (2002).

Marcuse, D.

Martynkien, T.

P. Hlubina, T. Martynkien, W. Urbanczyk, “Measurements of intermodal dispersion in few-mode optical fibers using a spectral-domain white-light interferometric method,” Meas. Sci. Technol. 14, 784–789 (2003).
[CrossRef]

Matsumura, H.

McBride, R.

M. J. Gander, E. A. C. Galliot, R. McBride, J. D. C. Jones, “Bend measurement using multicore optical fiber,” in proceeding of the 12th International Conference on Optical Fiber Sensors, (Williamsburg, Virginia, 1997), p. 166–169.

Medhat, M.

M. Medhat, S. Y. Zaiat, A. Radi, M. Omer, “Application of fringes of equal chromatic order for investigating the effect of temperature on optical parameters of a GRIN optical fibre,” J. Opt. A: Pure Appl. Opt. 4, 174–179 (2002).
[CrossRef]

Michalzik, R.

R. King, R. Michalzik, “VCSEL arrays for fiber optical interconnections,” Annual Report1999, Department of Optoelectronics, University of Ulm.

Mizunami, T.

T. Mizunami, T. Niiho, T. V. Djambova, “Multimode fiber Bragg gratings for fiber-optic bending sensors,” 13th International Conference on Optical Fiber Sensors, B. Kim, K. Hotate, eds. Proc. SPIE3746, 216–219 (1999).

Morse, T. F.

Murakami, Y.

Nagano, K.

Nasser, I.

M. A. Abd-El Rahman, E. A. Abd El-Ghafar, I. Nasser, “Angular dispersion of GRIN fiber using a laser sheet of light,” in Second International Conference on Experimental MechanicsF. S. Chau, C. Quan, eds. Proc. SPIE4317, 597–603 (2001).
[CrossRef]

Nihei, E.

T. Ishigure, M. Sato, E. Nihei, Y. Koike, “High-bandwidth and high-thermal stability graded-index polymer optical fiber,” in Polymer Photonic Devices, B. Kippelen, D. D. Bradley, eds., Proc. SPIE, 328166–74 (1998).
[CrossRef]

Niiho, T.

T. Mizunami, T. Niiho, T. V. Djambova, “Multimode fiber Bragg gratings for fiber-optic bending sensors,” 13th International Conference on Optical Fiber Sensors, B. Kim, K. Hotate, eds. Proc. SPIE3746, 216–219 (1999).

Nishida, S.

Nishii, J.

O’Rourke, R. C.

R. C. O’Rourke, “Three-dimensional photoelasticity,” J. Appl. Phys. 22, 872–878 (1951).
[CrossRef]

Okashi, T.

Omer, M.

M. Medhat, S. Y. Zaiat, A. Radi, M. Omer, “Application of fringes of equal chromatic order for investigating the effect of temperature on optical parameters of a GRIN optical fibre,” J. Opt. A: Pure Appl. Opt. 4, 174–179 (2002).
[CrossRef]

Payne, D. N.

G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramskov-Hansen, “Design and performance of tuned fiber coil isolators,” J. Lightwave Technol. LT-2, 56–60 (1984).
[CrossRef]

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

Pomarico, J. A.

R. Henao, J. A. Pomarico, N. Russo, R. D. Torroba, M. Trivi, “Multimode optical fiber core measurement by speckle correlation,” Opt. Eng. 35, 26–30 (1996).
[CrossRef]

Purwosumarto, P.

S. Yin, P. Purwosumarto, “Application of fiber specklergram sensor to fine angular alignment,” Opt. Commun. 170, 15–19 (1999).
[CrossRef]

Qi, E.-Y.

G.-Y. He, Y.-X. Chen, E.-Y. Qi, “Numerical aperture of multimode fibers with curvature, a new theory formula,” in Fiber Optic Sensors V, K. D. Bennett, B.-Y. Kim, Y.-B. Liao, eds., Proc. SPIE2895, 552–558 (1996).
[CrossRef]

Radi, A.

M. Medhat, S. Y. Zaiat, A. Radi, M. Omer, “Application of fringes of equal chromatic order for investigating the effect of temperature on optical parameters of a GRIN optical fibre,” J. Opt. A: Pure Appl. Opt. 4, 174–179 (2002).
[CrossRef]

Ramadan, W. A.

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, M. A. Shams-Eldin, “Determination of GR-IN optical fiber parameters from transverse interferograms considering the refraction of the incident ray by the fiber,” Opt. Commun. 15, 131–138 (2002).

Ramskov-Hansen, J. J.

G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramskov-Hansen, “Design and performance of tuned fiber coil isolators,” J. Lightwave Technol. LT-2, 56–60 (1984).
[CrossRef]

Rashleigh, S. C.

Rathji, J.

J. Rathji, M. Kristensen, J. Hubner, “Effect of core concentricity error on bend direction asymmetry for long-period fiber gratings,” Conference on Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, (Optical Society of America, Washington D.C.1999), p. 283–285.

Reinhart, I. J.

Reng, N.

Th. Beck, N. Reng, H. Weber, “Optical fibers for material processing lasers,” Opt. Laser Eng. 34, 255–272 (2000).
[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]

Russo, N.

R. Henao, J. A. Pomarico, N. Russo, R. D. Torroba, M. Trivi, “Multimode optical fiber core measurement by speckle correlation,” Opt. Eng. 35, 26–30 (1996).
[CrossRef]

Sato, M.

T. Ishigure, M. Sato, E. Nihei, Y. Koike, “High-bandwidth and high-thermal stability graded-index polymer optical fiber,” in Polymer Photonic Devices, B. Kippelen, D. D. Bradley, eds., Proc. SPIE, 328166–74 (1998).
[CrossRef]

Shams-Eldin, M. A.

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, M. A. Shams-Eldin, “Determination of GR-IN optical fiber parameters from transverse interferograms considering the refraction of the incident ray by the fiber,” Opt. Commun. 15, 131–138 (2002).

Srubshchik, L. S.

L. S. Srubshchik, “Strength measurement of optical fibers by bending,” in Optical Wireless Communications, E. J. Kovovaas, ed., Proc. SPIE3532, 114–121 (1998).
[CrossRef]

Steblina, V. V.

V. V. Steblina, “Cladding mode degeneracy in bent W-fibers beyond cutoff,” Opt. Commun. 156, 271–278 (1998).
[CrossRef]

Suhir, E.

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]

Taylor, H. F.

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

Taylor, J. R.

S. V. Chernikov, F. Koch, J. R. Taylor, L. Gruner-Nielsen, “Measurement of the effect of bending on dispersion in dispersion-compensating fibers,” in Proceeding of OFC’98, Optical Fiber Communication Conference and Exhibition, (Optical Society of American Washington, D.C., 1998), p. 23–24.

Torroba, R. D.

R. Henao, J. A. Pomarico, N. Russo, R. D. Torroba, M. Trivi, “Multimode optical fiber core measurement by speckle correlation,” Opt. Eng. 35, 26–30 (1996).
[CrossRef]

Trivi, M.

R. Henao, J. A. Pomarico, N. Russo, R. D. Torroba, M. Trivi, “Multimode optical fiber core measurement by speckle correlation,” Opt. Eng. 35, 26–30 (1996).
[CrossRef]

Tsujikawa, K.

K. Tsujikawa, K. Arakawa, K. Yoshida, “Reflection of light caused by sharp bends in optical fiber,” IEICE Trans. Electron. E82-C, 2105–2107 (1999).

Uang, C. M.

Ulrich, R.

Urbanczyk, W.

P. Hlubina, T. Martynkien, W. Urbanczyk, “Measurements of intermodal dispersion in few-mode optical fibers using a spectral-domain white-light interferometric method,” Meas. Sci. Technol. 14, 784–789 (2003).
[CrossRef]

Verrier, I.

Weber, H.

Th. Beck, N. Reng, H. Weber, “Optical fibers for material processing lasers,” Opt. Laser Eng. 34, 255–272 (2000).
[CrossRef]

Wen, M.

Ya Zel’dovich, B.

Yen, Y.

Yin, S.

S. Yin, P. Purwosumarto, “Application of fiber specklergram sensor to fine angular alignment,” Opt. Commun. 170, 15–19 (1999).
[CrossRef]

F. S. Yu, M. Wen, S. Yin, C. M. Uang, “Submicrometer displacement sensing using inner-product multimode fiber speckle field,” Appl. Opt. 32, 4685–4891 (1993).
[CrossRef] [PubMed]

Yoshida, K.

K. Tsujikawa, K. Arakawa, K. Yoshida, “Reflection of light caused by sharp bends in optical fiber,” IEICE Trans. Electron. E82-C, 2105–2107 (1999).

Yu, F. S.

Zaiat, S. Y.

M. Medhat, S. Y. Zaiat, A. Radi, M. Omer, “Application of fringes of equal chromatic order for investigating the effect of temperature on optical parameters of a GRIN optical fibre,” J. Opt. A: Pure Appl. Opt. 4, 174–179 (2002).
[CrossRef]

Zhang, Q.

Appl. Opt. (12)

F. S. Yu, M. Wen, S. Yin, C. M. Uang, “Submicrometer displacement sensing using inner-product multimode fiber speckle field,” Appl. Opt. 32, 4685–4891 (1993).
[CrossRef] [PubMed]

K. Nagano, S. Kawakami, S. Nishida, “Change of the refractive index in an optucal fiber due to external forces,” Appl. Opt. 17, 2080–2085 (1978).
[CrossRef] [PubMed]

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

S. Kawakami, “Mode conversion losses of randomly bent, singly and doubly clad waveguides for single mode transmission,” Appl. Opt. 15, 2778–2784 (1976).
[CrossRef] [PubMed]

M. Ikeda, Y. Murakami, K. Kitayama, “Mode scrambler for optical fibers,” Appl. Opt. 16, 1045–1049 (1977).
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[CrossRef] [PubMed]

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

N. Barakat, H. A. El-Hannawi, F. El-Diasty, “Multiple-beam interference applied to GRIN optical fiber,” Appl. Opt. 27, 5090–5094 (1998).
[CrossRef]

T. Okashi, K. Hotate, “Refractive index profile of an optical fibre: Its measurement by the scattering-pattern method,” Appl. Opt. 15, 2756–2764 (1976).
[CrossRef]

E. Drinkmeyer, “Refractive-index profile determination of optical fibers from the diffraction pattern,” Appl. Opt. 16, 2802–2807 (1977).
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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]

E. Suhir, “Effect of the nonlinear stress-strain relationship on the maximum stress in silica fibers subjected to two-point bending,” Appl. Opt. 32, 1567–1572 (1993).
[CrossRef] [PubMed]

Electron. Lett. (2)

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

H. C. Lefevre, “Single-mode fibre fractional wave devices and polarization controllers,” Electron. Lett. 16, 778–780 (1980).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

M. A. El-Sherif, “On-fiber sensor and modulator,” IEEE Trans. Instrum. Meas. 38, 595–598 (1989).
[CrossRef]

IEICE Trans. Electron. (1)

K. Tsujikawa, K. Arakawa, K. Yoshida, “Reflection of light caused by sharp bends in optical fiber,” IEICE Trans. Electron. E82-C, 2105–2107 (1999).

J. Appl. Phys. (1)

R. C. O’Rourke, “Three-dimensional photoelasticity,” J. Appl. Phys. 22, 872–878 (1951).
[CrossRef]

J. Lightwave Technol. (2)

G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramskov-Hansen, “Design and performance of tuned fiber coil isolators,” J. Lightwave Technol. LT-2, 56–60 (1984).
[CrossRef]

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

J. Opt. A: Pure Appl. Opt. (1)

M. Medhat, S. Y. Zaiat, A. Radi, M. Omer, “Application of fringes of equal chromatic order for investigating the effect of temperature on optical parameters of a GRIN optical fibre,” J. Opt. A: Pure Appl. Opt. 4, 174–179 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (1)

P. Hlubina, T. Martynkien, W. Urbanczyk, “Measurements of intermodal dispersion in few-mode optical fibers using a spectral-domain white-light interferometric method,” Meas. Sci. Technol. 14, 784–789 (2003).
[CrossRef]

Opt. Commun. (5)

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, M. A. Shams-Eldin, “Determination of GR-IN optical fiber parameters from transverse interferograms considering the refraction of the incident ray by the fiber,” Opt. Commun. 15, 131–138 (2002).

F. El-Diasty, “Application of Fizeau fringes with bending technique to determine the shear modulus of the cladding material of single-mode optical fibers through the mechanically induced change of refractive index,” Opt. Commun. 212, 267–274 (2002).
[CrossRef]

S. Yin, P. Purwosumarto, “Application of fiber specklergram sensor to fine angular alignment,” Opt. Commun. 170, 15–19 (1999).
[CrossRef]

V. V. Steblina, “Cladding mode degeneracy in bent W-fibers beyond cutoff,” Opt. Commun. 156, 271–278 (1998).
[CrossRef]

N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Gandoor, R. Hassan, F. El-Diasty, “Three-dimensional diffractive index of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
[CrossRef]

Opt. Eng. (2)

C. DeCusatis, “Optical data communication: fundamentals and future directions,” Opt. Eng. 37, 3082–3099 (1998).
[CrossRef]

R. Henao, J. A. Pomarico, N. Russo, R. D. Torroba, M. Trivi, “Multimode optical fiber core measurement by speckle correlation,” Opt. Eng. 35, 26–30 (1996).
[CrossRef]

Opt. Fiber Technol. (1)

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

Opt. Laser Eng. (1)

Th. Beck, N. Reng, H. Weber, “Optical fibers for material processing lasers,” Opt. Laser Eng. 34, 255–272 (2000).
[CrossRef]

Opt. Lett. (6)

Pure Appl. Opt. (1)

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

Other (14)

W. Gorski, “The influence of diffraction in microinterferometry and microtomography of optical fibers,” Opt. Laser Eng. (in press).

M. A. Abd-El Rahman, E. A. Abd El-Ghafar, I. Nasser, “Angular dispersion of GRIN fiber using a laser sheet of light,” in Second International Conference on Experimental MechanicsF. S. Chau, C. Quan, eds. Proc. SPIE4317, 597–603 (2001).
[CrossRef]

M. M. Frocht, “Photoelasticity,” vol. 1, 1941; “Photoelasticity,” vol. 2, 1948 (Wiley, New York).

J. Rathji, M. Kristensen, J. Hubner, “Effect of core concentricity error on bend direction asymmetry for long-period fiber gratings,” Conference on Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, (Optical Society of America, Washington D.C.1999), p. 283–285.

T. Mizunami, T. Niiho, T. V. Djambova, “Multimode fiber Bragg gratings for fiber-optic bending sensors,” 13th International Conference on Optical Fiber Sensors, B. Kim, K. Hotate, eds. Proc. SPIE3746, 216–219 (1999).

G.-Y. He, Y.-X. Chen, E.-Y. Qi, “Numerical aperture of multimode fibers with curvature, a new theory formula,” in Fiber Optic Sensors V, K. D. Bennett, B.-Y. Kim, Y.-B. Liao, eds., Proc. SPIE2895, 552–558 (1996).
[CrossRef]

J. E. Hefferon, “Calculating bend and twist stress in optical fibers,” in Components for Fiber Optic Applications, V. J. Tekippe, ed., Proc. SPIE, 722, 108–110 (1986).
[CrossRef]

L. S. Srubshchik, “Strength measurement of optical fibers by bending,” in Optical Wireless Communications, E. J. Kovovaas, ed., Proc. SPIE3532, 114–121 (1998).
[CrossRef]

M. J. Gander, E. A. C. Galliot, R. McBride, J. D. C. Jones, “Bend measurement using multicore optical fiber,” in proceeding of the 12th International Conference on Optical Fiber Sensors, (Williamsburg, Virginia, 1997), p. 166–169.

S. V. Chernikov, F. Koch, J. R. Taylor, L. Gruner-Nielsen, “Measurement of the effect of bending on dispersion in dispersion-compensating fibers,” in Proceeding of OFC’98, Optical Fiber Communication Conference and Exhibition, (Optical Society of American Washington, D.C., 1998), p. 23–24.

B. Culshaw, Optical Fiber Sensing and Signal Processing,1st ed. (Peregrinus, London, 1984).

R. L. Lehman, “Developments in fiber optic sensor design,” in Proceedings of the 40th Electronic Components and Technology Conference, (Las Vegas, Nevada, 1990) pp. 60–63.
[CrossRef]

T. Ishigure, M. Sato, E. Nihei, Y. Koike, “High-bandwidth and high-thermal stability graded-index polymer optical fiber,” in Polymer Photonic Devices, B. Kippelen, D. D. Bradley, eds., Proc. SPIE, 328166–74 (1998).
[CrossRef]

R. King, R. Michalzik, “VCSEL arrays for fiber optical interconnections,” Annual Report1999, Department of Optoelectronics, University of Ulm.

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the optical setup.

Fig. 2
Fig. 2

Interference pattern of Fizeau fringes at a transmission crossing transversally a strain-free straight GRIN fiber immersed in nonmatching liquid, n L < n clad.

Fig. 3
Fig. 3

Microinterferogram of a set of Fizeau fringes at a transmission crossing of a strain-free straight fiber immersed in matching liquid.

Fig. 4
Fig. 4

Interferogram of the birefringence component n for light vibrating in a direction parallel to the optical axis of a bent GRIN fiber (shifted component).

Fig. 5
Fig. 5

Interferogram of the birefringence component of light vibrating in a perpendicular direction to the fiber axis, n (unshifted component).

Fig. 6
Fig. 6

Variation of the acceptance angle vs. the radius of curvature R in both the (a) compressed side and (b) tensile side at radial position x = a and x max.

Fig. 7
Fig. 7

Variation of the numerical aperture NA vs. the radius of curvature R in both the (a) compressed side and (b) tensile side at radial position x = a and x max.

Fig. 8
Fig. 8

Variation of the V number vs. the radius of curvature R in both the (a) compressed side and (b) tensile side at radial position x = a and x max.

Fig. 9
Fig. 9

Plots of the variation of the fraction mode loss ΔP vs. the radius of curvature R in the compressed side of the fiber at a different value of the index difference Δn. The lower curve is deduced in the case of a constant Δn ignoring the variation of the index difference due to bending.

Tables (2)

Tables Icon

Table 1 GRIN Fiber Specifications

Tables Icon

Table 2 Summary of the Shifted Components n of Birefringence of the Cladding Via Different Very Small Radii of Curvature R (i.e., a Few Millimeters). The Birefringence Components at Both the Fiber Compressed Side and the Tensile Side are Measured at the Core-Cladding Interface, x = a, and at the Radial Distance x Corresponding to the Maximum Fringe Shift, x max

Equations (14)

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

θc=1-ncladnc21/22Δn1/2.
nx=nc1-2Δnx2a21/2 for x  a.
Δn=nc2-nclad22nc2.
V=ka NA=kanc2-nclad2,
P=14aknθc2=akn2Δn2.
ΔP=2aRΔn.
zx=4Δzλnclad-nLr2-x21/2+Δna2-x21/2-Δnaα0a2-x21/2x2+y2α/2dy,
δn=C1-C2σz,
δn=no32ρ121-ν-νρ11xR,
nclad=nL+zxλ4Δzr2-x2-1/2,
nclad=nL-zxλ4Δzr2-x2-1/2.
δn=zxλ4Δzr2-x2-1/2.
Δn=nc2-no+δn22nc2,
Δn=nc2-no-δn22nc2,

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