Abstract

An interferometric method to study the induced variations of nonlinear parameters in bent optical fiber such as third-order susceptibility χ(3) and second-order refractive index n2 is presented. Due to the expected nonlinear response of the Young’s modulus of fiber material, the profiles of asymmetric variations of the two parameters with curvature are observed and calculated, revealing the high spatial and index resolution of the method. The investigation is done in single-mode optical fibers at the standard operating wavelengths of 1300 and 1550nm and at radii of curvature from 5 to 11mm. At the minimum radius of curvature R=5mm, the cladding χ(3)=4.131×1015esu on the tensile side, whereas on the compressed side it is 4.601×1015esu for λ=1300nm. On the tensile side n2=1.09×1013esu, whereas on the compressed side it is 1.216×1013esu. For λ=1550nm, the cladding χ(3) and n2 on the tensile side are 3.96×1015esu and 1.055×1013esu, whereas in the compressed cladding side they are 4.435×1015esu and 1.174×1013esu, respectively. At λ=1300nm and R=5mm, the core χ(3) is given by 4.631×1015esu on the tensile side and 4.649×1015esu on the compressed side. The asymmetry in n2 is given by 1.223×1013esu on the tensile side and by 1.227×1013esu on the compressed side. With λ=1550nm, the core χ(3) asymmetry is given by 4.46×1015esu on the tensile side and by 4.477×1015esu on the compressed side. For n2 its asymmetry is provided by 1.181×1013esu on the tensile side and by 1.185×1013esu on the compressed side.

© 2009 Optical Society of America

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References

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    [CrossRef]
  2. E. P. Ippen and R. H. Appli, “Stimulated Brillouin scattering in optical fibers,” Phys. Lett. 21, 539-541 (1972).
  3. R. H. Stolen and A. Ashkin, “Optical Kerr effect in glass waveguide,” Appl. Phys. Lett. 22, 294-296 (1973).
    [CrossRef]
  4. R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308-310 (1974).
    [CrossRef]
  5. R. H. Stolen, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” IEEE J. Quantum Electron. 11, 100-103 (1975).
    [CrossRef]
  6. E. P. Ippen, C. V. Shank, and T. K. Gustafson, “Self-phase modulation of picosecond pulses in optical fibers,” Appl. Phys. Lett. 24, 190-192 (1974).
    [CrossRef]
  7. R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448-1453 (1978).
    [CrossRef]
  8. L. F. Mollenauer and R. H. Stolen, “The soliton laser,” Opt. Lett. 9, 13-15 (1984).
    [CrossRef] [PubMed]
  9. A. S. Gouveia-Neto, A. S. L. Gomes, and J. R. Taylor, “Soliton Raman fibre-ring oscillators,” Opt. Quantum. Electron. 20, 165-174 (1988).
    [CrossRef]
  10. H. Nakatsuka, D. Grischkowsky, and A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion,” Phys. Rev. Lett. 47910-913 (1981).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. F. El-Diasty, “Fizeau interferometry-based measurement of the photoelastic coefficient and the cut-off wavelength in bent standard single-mode optical fiber,” Opt. Commun. 225, 61-70 (2003).
    [CrossRef]
  15. E. M. Vogel, M. J. Weber, and D. M. Krol, Phys. Chem. Glasses 32, 231-254 (1991).
  16. R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17-19 (1964).
    [CrossRef]
  17. R. C. O'Rourke, “Three-dimensional photoelasticity,” J. Appl. Phys. 22, 871-878 (1951).
    [CrossRef]
  18. 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]

2003

F. El-Diasty, “Fizeau interferometry-based measurement of the photoelastic coefficient and the cut-off wavelength in bent standard single-mode optical fiber,” Opt. Commun. 225, 61-70 (2003).
[CrossRef]

2001

2000

1991

E. M. Vogel, M. J. Weber, and D. M. Krol, Phys. Chem. Glasses 32, 231-254 (1991).

1988

A. S. L. Gomes, A. S. Gouveia-Neto, and J. R. Taylor, “Optical fibre-grating pulse compressors,” Opt. Quantum. Electron. 20, 95-112 (1988).
[CrossRef]

A. S. Gouveia-Neto, A. S. L. Gomes, and J. R. Taylor, “Soliton Raman fibre-ring oscillators,” Opt. Quantum. Electron. 20, 165-174 (1988).
[CrossRef]

1984

1981

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion,” Phys. Rev. Lett. 47910-913 (1981).
[CrossRef]

1978

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448-1453 (1978).
[CrossRef]

1975

R. H. Stolen, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” IEEE J. Quantum Electron. 11, 100-103 (1975).
[CrossRef]

1974

E. P. Ippen, C. V. Shank, and T. K. Gustafson, “Self-phase modulation of picosecond pulses in optical fibers,” Appl. Phys. Lett. 24, 190-192 (1974).
[CrossRef]

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308-310 (1974).
[CrossRef]

1973

R. H. Stolen and A. Ashkin, “Optical Kerr effect in glass waveguide,” Appl. Phys. Lett. 22, 294-296 (1973).
[CrossRef]

1972

R. H. Stolen, E. P. Ippen, and A. R. Tynes, “Raman oscillation in glass optical waveguide,” Appl. Phys. Lett. 20, 62-64 (1972).
[CrossRef]

E. P. Ippen and R. H. Appli, “Stimulated Brillouin scattering in optical fibers,” Phys. Lett. 21, 539-541 (1972).

1964

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17-19 (1964).
[CrossRef]

1951

R. C. O'Rourke, “Three-dimensional photoelasticity,” J. Appl. Phys. 22, 871-878 (1951).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995).

Appli, R. H.

E. P. Ippen and R. H. Appli, “Stimulated Brillouin scattering in optical fibers,” Phys. Lett. 21, 539-541 (1972).

Ashkin, A.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308-310 (1974).
[CrossRef]

R. H. Stolen and A. Ashkin, “Optical Kerr effect in glass waveguide,” Appl. Phys. Lett. 22, 294-296 (1973).
[CrossRef]

Balant, A. C.

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion,” Phys. Rev. Lett. 47910-913 (1981).
[CrossRef]

Bjorkholm, J. E.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308-310 (1974).
[CrossRef]

El-Diasty, F.

Gomes, A. S. L.

A. S. Gouveia-Neto, A. S. L. Gomes, and J. R. Taylor, “Soliton Raman fibre-ring oscillators,” Opt. Quantum. Electron. 20, 165-174 (1988).
[CrossRef]

A. S. L. Gomes, A. S. Gouveia-Neto, and J. R. Taylor, “Optical fibre-grating pulse compressors,” Opt. Quantum. Electron. 20, 95-112 (1988).
[CrossRef]

Gouveia-Neto, A. S.

A. S. L. Gomes, A. S. Gouveia-Neto, and J. R. Taylor, “Optical fibre-grating pulse compressors,” Opt. Quantum. Electron. 20, 95-112 (1988).
[CrossRef]

A. S. Gouveia-Neto, A. S. L. Gomes, and J. R. Taylor, “Soliton Raman fibre-ring oscillators,” Opt. Quantum. Electron. 20, 165-174 (1988).
[CrossRef]

Grischkowsky, D.

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion,” Phys. Rev. Lett. 47910-913 (1981).
[CrossRef]

Gustafson, T. K.

E. P. Ippen, C. V. Shank, and T. K. Gustafson, “Self-phase modulation of picosecond pulses in optical fibers,” Appl. Phys. Lett. 24, 190-192 (1974).
[CrossRef]

Ippen, E. P.

E. P. Ippen, C. V. Shank, and T. K. Gustafson, “Self-phase modulation of picosecond pulses in optical fibers,” Appl. Phys. Lett. 24, 190-192 (1974).
[CrossRef]

R. H. Stolen, E. P. Ippen, and A. R. Tynes, “Raman oscillation in glass optical waveguide,” Appl. Phys. Lett. 20, 62-64 (1972).
[CrossRef]

E. P. Ippen and R. H. Appli, “Stimulated Brillouin scattering in optical fibers,” Phys. Lett. 21, 539-541 (1972).

Krol, and D. M.

E. M. Vogel, M. J. Weber, and D. M. Krol, Phys. Chem. Glasses 32, 231-254 (1991).

Lin, C.

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448-1453 (1978).
[CrossRef]

Miller, R. C.

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17-19 (1964).
[CrossRef]

Mollenauer, L. F.

Nakatsuka, H.

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion,” Phys. Rev. Lett. 47910-913 (1981).
[CrossRef]

O'Rourke, R. C.

R. C. O'Rourke, “Three-dimensional photoelasticity,” J. Appl. Phys. 22, 871-878 (1951).
[CrossRef]

Shank, C. V.

E. P. Ippen, C. V. Shank, and T. K. Gustafson, “Self-phase modulation of picosecond pulses in optical fibers,” Appl. Phys. Lett. 24, 190-192 (1974).
[CrossRef]

Stolen, R. H.

L. F. Mollenauer and R. H. Stolen, “The soliton laser,” Opt. Lett. 9, 13-15 (1984).
[CrossRef] [PubMed]

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448-1453 (1978).
[CrossRef]

R. H. Stolen, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” IEEE J. Quantum Electron. 11, 100-103 (1975).
[CrossRef]

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308-310 (1974).
[CrossRef]

R. H. Stolen and A. Ashkin, “Optical Kerr effect in glass waveguide,” Appl. Phys. Lett. 22, 294-296 (1973).
[CrossRef]

R. H. Stolen, E. P. Ippen, and A. R. Tynes, “Raman oscillation in glass optical waveguide,” Appl. Phys. Lett. 20, 62-64 (1972).
[CrossRef]

Taylor, J. R.

A. S. Gouveia-Neto, A. S. L. Gomes, and J. R. Taylor, “Soliton Raman fibre-ring oscillators,” Opt. Quantum. Electron. 20, 165-174 (1988).
[CrossRef]

A. S. L. Gomes, A. S. Gouveia-Neto, and J. R. Taylor, “Optical fibre-grating pulse compressors,” Opt. Quantum. Electron. 20, 95-112 (1988).
[CrossRef]

Tynes, A. R.

R. H. Stolen, E. P. Ippen, and A. R. Tynes, “Raman oscillation in glass optical waveguide,” Appl. Phys. Lett. 20, 62-64 (1972).
[CrossRef]

Vogel, E. M.

E. M. Vogel, M. J. Weber, and D. M. Krol, Phys. Chem. Glasses 32, 231-254 (1991).

Weber, M. J.

E. M. Vogel, M. J. Weber, and D. M. Krol, Phys. Chem. Glasses 32, 231-254 (1991).

Appl. Opt.

Appl. Phys. Lett.

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17-19 (1964).
[CrossRef]

R. H. Stolen, E. P. Ippen, and A. R. Tynes, “Raman oscillation in glass optical waveguide,” Appl. Phys. Lett. 20, 62-64 (1972).
[CrossRef]

R. H. Stolen and A. Ashkin, “Optical Kerr effect in glass waveguide,” Appl. Phys. Lett. 22, 294-296 (1973).
[CrossRef]

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308-310 (1974).
[CrossRef]

E. P. Ippen, C. V. Shank, and T. K. Gustafson, “Self-phase modulation of picosecond pulses in optical fibers,” Appl. Phys. Lett. 24, 190-192 (1974).
[CrossRef]

IEEE J. Quantum Electron.

R. H. Stolen, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” IEEE J. Quantum Electron. 11, 100-103 (1975).
[CrossRef]

J. Appl. Phys.

R. C. O'Rourke, “Three-dimensional photoelasticity,” J. Appl. Phys. 22, 871-878 (1951).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

F. El-Diasty, “Fizeau interferometry-based measurement of the photoelastic coefficient and the cut-off wavelength in bent standard single-mode optical fiber,” Opt. Commun. 225, 61-70 (2003).
[CrossRef]

Opt. Lett.

Opt. Quantum. Electron.

A. S. Gouveia-Neto, A. S. L. Gomes, and J. R. Taylor, “Soliton Raman fibre-ring oscillators,” Opt. Quantum. Electron. 20, 165-174 (1988).
[CrossRef]

A. S. L. Gomes, A. S. Gouveia-Neto, and J. R. Taylor, “Optical fibre-grating pulse compressors,” Opt. Quantum. Electron. 20, 95-112 (1988).
[CrossRef]

Phys. Chem. Glasses

E. M. Vogel, M. J. Weber, and D. M. Krol, Phys. Chem. Glasses 32, 231-254 (1991).

Phys. Lett.

E. P. Ippen and R. H. Appli, “Stimulated Brillouin scattering in optical fibers,” Phys. Lett. 21, 539-541 (1972).

Phys. Rev. A

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448-1453 (1978).
[CrossRef]

Phys. Rev. Lett.

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion,” Phys. Rev. Lett. 47910-913 (1981).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995).

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Figures (9)

Fig. 1
Fig. 1

Schematic representation of birefringence in bent fiber and its fringe shape.

Fig. 2
Fig. 2

Experimental setup: S is a monochromatic light source, L 1 is a lens with a short focal length ( 5 cm ), L 2 is a lens with long focal length ( 20 cm ), P 1 is a bin hole, P 2 is a polarizer, M is a microscope, and W is a wedge interferometer.

Fig. 3
Fig. 3

Digital interferogram of the parallel component of induced phase shift in bent optical fiber.

Fig. 4
Fig. 4

Radial profiles of the nonlinear third-order susceptibility in the cladding of bent single-mode optical fibers at different radii of curvature.

Fig. 5
Fig. 5

Radial profiles of the second-order nonlinear refractive index in the cladding of bent single-mode optical fibers at different radii of curvature.

Fig. 6
Fig. 6

Asymmetry in the nonlinear third-order susceptibility of the bent fiber cladding versus radius of curvature.

Fig. 7
Fig. 7

Asymmetry in the second-order nonlinear refractive index of the cladding of bent fiber versus radius of curvature.

Fig. 8
Fig. 8

Asymmetry in the nonlinear third-order susceptibility of the core of bent fiber versus radius of curvature.

Fig. 9
Fig. 9

Asymmetry in the second-order nonlinear refractive index of the core of bent fiber versus radius of curvature.

Equations (8)

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

λ 3 2 π c 2 d 2 n ( R ) d λ 2 .
2 E 1 c 2 2 E t 2 = μ 0 2 P L t 2 + μ 0 2 P NL t 2 ,
N = n + n 2 I .
n 2 = 12 π n 0 χ ( 3 ) ,
χ ( 3 ) = ( n 2 1 4 π ) 4 × 10 10 .
z ( x ) = 4 λ Δ z ( n o n L ) ( r 2 x 2 ) 1 / 2 .
n II = n 0 + z ( x ) λ 4 Δ z ( r 2 x 2 ) 1 / 2 .
n II = n 0 z ( x ) λ 4 Δ z ( r 2 x 2 ) 1 / 2 .

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