Abstract

A novel technique for determining two-dimensional, cross-sectional stress distributions in optical fibers and fiber-based devices is presented. Use of the Brace–Köhler compensator technique and a polarization microscope for the measurement of retardation due to stress-induced birefringence is described, along with the tomographic reconstruction process for the determination of stress. Measurements are performed on Corning SMF-28 fiber in an unperturbed section, a section near a cleaved end-face, and a section exposed to CO2 laser radiation. Cross-sectional stress distributions are presented. Stress relaxation is quantified in the cleaved fiber and the fiber exposed to CO2 laser radiation.

© 2009 Optical Society of America

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2009

P. Kniazewski, T. Kozacki, and M. Kujawinska, “Inspection of axial stress and refractive index distribution in polarization-maintaining fiber with tomographic methods,” Opt. Lasers Eng. 47, 259-263 (2009).
[CrossRef]

2008

2006

C. C. Montarou, T. K. Gaylord, B. L. Bachim, A. I. Dachevski, and A. Agarwal, “Two-wave-plate compensator method for full-field retardation measurements,” Appl. Opt. 45, 271-280 (2006).
[CrossRef] [PubMed]

L. Bruno, L. Pagnotta, and A. Poggialini, “A full-field method for measuring residual stresses in optical fiber,” Opt. Lasers Eng. 44, 577-588 (2006).
[CrossRef]

C. C. Montarou, T. K. Gaylord, and A. I. Dachevski, “Residual stress profiles in optical fibers determined by the two-waveplate-compensator method,” Opt. Commun. 265, 29-32(2006).
[CrossRef]

2005

2004

C. C. Montarou and T. K. Gaylord, “Two-wave-plate compensator method for single-point retardation measurements,” Appl. Opt. 43, 6580-6595 (2004).
[CrossRef]

Y. Park, U.-C. Paek, S. Han, B.-H. Kim, C.-S. Kim, and D. Y. Kim, “Inelastic frozen-in stress in optical fibers,” Opt. Commun. 242, 431-436 (2004).
[CrossRef]

F. Durr, H. G. Limberger, R. P. Salathe, F. Hindle, M. Douay, E. Fertein, and C. Przygodzki, “Tomographic measurement of femtosecond-laser induced stress changes in optical fibers,” Appl. Phys. Lett. 84, 4983-4985 (2004).
[CrossRef]

A. D. Yablon, “Optical and mechanical effects of frozen-in stresses and strains in optical fibers,” IEEE J. Sel. Top. Quantum Electron. 10, 300-311 (2004).
[CrossRef]

2003

2002

2001

2000

S. Yamasaki, M. Akiyama, K. Nishide, A. Wada, and R. Yamauchi, “Characteristics of long-period fiber grating utilizing periodic stress relaxation,” IEICE Trans. Electron. E83-C, 440-443 (2000).

C.-S. Kim, Y. Han, B. H. Lee, W.-T. Han, U.-C. Paek, and Y. Chung, “Induction of the refractive index change in B-doped optical fibers through relaxation of the mechanical stress,” Opt. Commun. 185, 337-342 (2000).
[CrossRef]

1999

1998

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302-303 (1998).
[CrossRef]

1996

D. A. Viskoe and G. W. Donohoe, “Optimal computed tomography data acquisition techniques and filter selection for detection of small density variations,” IEEE Trans. Instrum. Meas. 45, 70-76 (1996).
[CrossRef]

1995

1989

Y. Hibino, F. Hanawa, and M. Horiguchi, “Drawing-induced residual stress effects on optical characteristics in pure-silica-core single-mode fibers,” J. Appl. Phys. 65, 30-34 (1989).
[CrossRef]

1986

1982

1980

Abe, T.

Aben, H.

H. Aben, Photoelasticity of Glass (Springer-Verlag, 1993).

Agarwal, A.

Ahn, T. J.

Ahn, T.-J.

Akiyama, M.

S. Yamasaki, M. Akiyama, K. Nishide, A. Wada, and R. Yamauchi, “Characteristics of long-period fiber grating utilizing periodic stress relaxation,” IEICE Trans. Electron. E83-C, 440-443 (2000).

Bachim, B. L.

Bruno, L.

L. Bruno, L. Pagnotta, and A. Poggialini, “A full-field method for measuring residual stresses in optical fiber,” Opt. Lasers Eng. 44, 577-588 (2006).
[CrossRef]

Buck, J. A.

J. A. Buck, Fundamentals of Optical Fibers (Wiley, 2004).

Busque, F.

Choi, S.

Chu, P. L.

Chung, Y.

B. H. Kim, Y. Park, T. J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W. T. Han, “Residual stress relaxation in the core of optical fiber by CO2 laser irradiation,” Opt. Lett. 26, 1657-1659 (2001).
[CrossRef]

C.-S. Kim, Y. Han, B. H. Lee, W.-T. Han, U.-C. Paek, and Y. Chung, “Induction of the refractive index change in B-doped optical fibers through relaxation of the mechanical stress,” Opt. Commun. 185, 337-342 (2000).
[CrossRef]

Chung, Y. J.

Cochet, F.

Colomb, T.

Cuche, E.

Dachevski, A. I.

C. C. Montarou, T. K. Gaylord, B. L. Bachim, A. I. Dachevski, and A. Agarwal, “Two-wave-plate compensator method for full-field retardation measurements,” Appl. Opt. 45, 271-280 (2006).
[CrossRef] [PubMed]

C. C. Montarou, T. K. Gaylord, and A. I. Dachevski, “Residual stress profiles in optical fibers determined by the two-waveplate-compensator method,” Opt. Commun. 265, 29-32(2006).
[CrossRef]

Davis, D. D.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302-303 (1998).
[CrossRef]

Depeursinge, C.

Dianov, E. M.

Donohoe, G. W.

D. A. Viskoe and G. W. Donohoe, “Optimal computed tomography data acquisition techniques and filter selection for detection of small density variations,” IEEE Trans. Instrum. Meas. 45, 70-76 (1996).
[CrossRef]

Douay, M.

F. Durr, H. G. Limberger, R. P. Salathe, F. Hindle, M. Douay, E. Fertein, and C. Przygodzki, “Tomographic measurement of femtosecond-laser induced stress changes in optical fibers,” Appl. Phys. Lett. 84, 4983-4985 (2004).
[CrossRef]

Durr, F.

Faucher, M.

Feced, R.

Fertein, E.

F. Durr, H. G. Limberger, R. P. Salathe, F. Hindle, M. Douay, E. Fertein, and C. Przygodzki, “Tomographic measurement of femtosecond-laser induced stress changes in optical fibers,” Appl. Phys. Lett. 84, 4983-4985 (2004).
[CrossRef]

Fonjallaz, P. Y.

Gaylord, T. K.

C. C. Montarou, T. K. Gaylord, and A. I. Dachevski, “Residual stress profiles in optical fibers determined by the two-waveplate-compensator method,” Opt. Commun. 265, 29-32(2006).
[CrossRef]

C. C. Montarou, T. K. Gaylord, B. L. Bachim, A. I. Dachevski, and A. Agarwal, “Two-wave-plate compensator method for full-field retardation measurements,” Appl. Opt. 45, 271-280 (2006).
[CrossRef] [PubMed]

C. C. Montarou and T. K. Gaylord, “Two-wave-plate compensator method for single-point retardation measurements,” Appl. Opt. 43, 6580-6595 (2004).
[CrossRef]

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302-303 (1998).
[CrossRef]

Glytsis, E. N.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302-303 (1998).
[CrossRef]

Godbout, N.

Han, S.

Y. Park, U.-C. Paek, S. Han, B.-H. Kim, C.-S. Kim, and D. Y. Kim, “Inelastic frozen-in stress in optical fibers,” Opt. Commun. 242, 431-436 (2004).
[CrossRef]

Han, W. T.

Han, W.-T.

Y. Park, T.-J. Ahn, Y. H. Kim, W.-T. Han, U. C. Paek, and D. Y. Kim, “Measurement method for profiling the residual stress and the strain-optic coefficient of an optical fiber,” Appl. Opt. 41, 21-26 (2002).
[CrossRef] [PubMed]

C.-S. Kim, Y. Han, B. H. Lee, W.-T. Han, U.-C. Paek, and Y. Chung, “Induction of the refractive index change in B-doped optical fibers through relaxation of the mechanical stress,” Opt. Commun. 185, 337-342 (2000).
[CrossRef]

Han, Y.

C.-S. Kim, Y. Han, B. H. Lee, W.-T. Han, U.-C. Paek, and Y. Chung, “Induction of the refractive index change in B-doped optical fibers through relaxation of the mechanical stress,” Opt. Commun. 185, 337-342 (2000).
[CrossRef]

Hanawa, F.

Y. Hibino, F. Hanawa, and M. Horiguchi, “Drawing-induced residual stress effects on optical characteristics in pure-silica-core single-mode fibers,” J. Appl. Phys. 65, 30-34 (1989).
[CrossRef]

Handerek, V. A.

Hibino, Y.

Y. Hibino, F. Hanawa, and M. Horiguchi, “Drawing-induced residual stress effects on optical characteristics in pure-silica-core single-mode fibers,” J. Appl. Phys. 65, 30-34 (1989).
[CrossRef]

Hindle, F.

F. Durr, H. G. Limberger, R. P. Salathe, F. Hindle, M. Douay, E. Fertein, and C. Przygodzki, “Tomographic measurement of femtosecond-laser induced stress changes in optical fibers,” Appl. Phys. Lett. 84, 4983-4985 (2004).
[CrossRef]

Horiguchi, M.

Y. Hibino, F. Hanawa, and M. Horiguchi, “Drawing-induced residual stress effects on optical characteristics in pure-silica-core single-mode fibers,” J. Appl. Phys. 65, 30-34 (1989).
[CrossRef]

Hsieh, J.

J. Hsieh, Computed Tomography: Principles, Design, Artifacts, and Recent Advances (SPIE Press, 2003).

Kanellopoulos, S. E.

Kang, M. S.

D. I. Yeom, H. S. Kim, M. S. Kang, H. S. Park, and B. Y. Kim, “Narrow-bandwidth all-fiber acoustooptic tunable filter with low polarization-sensitivity,” IEEE Photon. Technol. Lett. 17, 2646-2648 (2005).
[CrossRef]

Kim, B. H.

Kim, B. Y.

D. I. Yeom, H. S. Kim, M. S. Kang, H. S. Park, and B. Y. Kim, “Narrow-bandwidth all-fiber acoustooptic tunable filter with low polarization-sensitivity,” IEEE Photon. Technol. Lett. 17, 2646-2648 (2005).
[CrossRef]

Kim, B.-H.

Y. Park, U.-C. Paek, S. Han, B.-H. Kim, C.-S. Kim, and D. Y. Kim, “Inelastic frozen-in stress in optical fibers,” Opt. Commun. 242, 431-436 (2004).
[CrossRef]

Kim, C.-S.

Y. Park, U.-C. Paek, S. Han, B.-H. Kim, C.-S. Kim, and D. Y. Kim, “Inelastic frozen-in stress in optical fibers,” Opt. Commun. 242, 431-436 (2004).
[CrossRef]

C.-S. Kim, Y. Han, B. H. Lee, W.-T. Han, U.-C. Paek, and Y. Chung, “Induction of the refractive index change in B-doped optical fibers through relaxation of the mechanical stress,” Opt. Commun. 185, 337-342 (2000).
[CrossRef]

Kim, D. Y.

I. H. Shin, B. H. Kim, S. P. Veetil, W. T. Han, and D. Y. Kim, “Residual stress relaxation in cleaved fibers,” Opt. Commun. 281, 75-79 (2008).
[CrossRef]

Y. Park, U.-C. Paek, S. Han, B.-H. Kim, C.-S. Kim, and D. Y. Kim, “Inelastic frozen-in stress in optical fibers,” Opt. Commun. 242, 431-436 (2004).
[CrossRef]

H. S. Ryu, Y. Park, S. T. Oh, Y. J. Chung, and D. Y. Kim, “Effect of asymmetric stress relaxation on the polarization-dependent transmission characteristics of a CO2 laser-written long-period fiber grating,” Opt. Lett. 28, 155-157 (2003).
[CrossRef] [PubMed]

Y. Park, S. Choi, U.-C. Paek, K. Oh, and D. Y. Kim, “Measurement method for profiling the residual stress of an optical fiber: detailed analysis of off-focusing and beam-deflection effects,” Appl. Opt. 42, 1182-1190 (2003).
[CrossRef] [PubMed]

Y. Park, U.-C. Paek, and D. Y. Kim, “Characterization of a stress-applied polarization-maintaining (PM) fiber through photoelastic tomography,” J. Lightwave Technol. 21, 997-1004(2003).
[CrossRef]

Y. Park, U.-C. Paek, and D. Y. Kim, “Complete determination of the stress tensor of a polarization-maintaining fiber by photoelastic tomography,” Opt. Lett. 27, 1217-1219 (2002).
[CrossRef]

Y. Park, U.-C. Paek, and D. Y. Kim, “Determination of stress-induced intrinsic birefringence in a single-mode fiber by measurement of the two-dimensional stress profile,” Opt. Lett. 27, 1291-1293 (2002).
[CrossRef]

B. H. Kim, Y. Park, D. Y. Kim, U. C. Paek, and W. T. Han, “Observation and analysis of residual stress development resulting from OH impurity in optical fibers,” Opt. Lett. 27, 806-808 (2002).
[CrossRef]

Y. Park, T.-J. Ahn, Y. H. Kim, W.-T. Han, U. C. Paek, and D. Y. Kim, “Measurement method for profiling the residual stress and the strain-optic coefficient of an optical fiber,” Appl. Opt. 41, 21-26 (2002).
[CrossRef] [PubMed]

B. H. Kim, Y. Park, T. J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W. T. Han, “Residual stress relaxation in the core of optical fiber by CO2 laser irradiation,” Opt. Lett. 26, 1657-1659 (2001).
[CrossRef]

Kim, H. S.

D. I. Yeom, H. S. Kim, M. S. Kang, H. S. Park, and B. Y. Kim, “Narrow-bandwidth all-fiber acoustooptic tunable filter with low polarization-sensitivity,” IEEE Photon. Technol. Lett. 17, 2646-2648 (2005).
[CrossRef]

Kim, Y. H.

Kniazewski, P.

P. Kniazewski, T. Kozacki, and M. Kujawinska, “Inspection of axial stress and refractive index distribution in polarization-maintaining fiber with tomographic methods,” Opt. Lasers Eng. 47, 259-263 (2009).
[CrossRef]

Koga, H.

Kosinski, S. G.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302-303 (1998).
[CrossRef]

Kozacki, T.

P. Kniazewski, T. Kozacki, and M. Kujawinska, “Inspection of axial stress and refractive index distribution in polarization-maintaining fiber with tomographic methods,” Opt. Lasers Eng. 47, 259-263 (2009).
[CrossRef]

Kujawinska, M.

P. Kniazewski, T. Kozacki, and M. Kujawinska, “Inspection of axial stress and refractive index distribution in polarization-maintaining fiber with tomographic methods,” Opt. Lasers Eng. 47, 259-263 (2009).
[CrossRef]

Lacroix, S.

Lee, B. H.

B. H. Kim, Y. Park, T. J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W. T. Han, “Residual stress relaxation in the core of optical fiber by CO2 laser irradiation,” Opt. Lett. 26, 1657-1659 (2001).
[CrossRef]

C.-S. Kim, Y. Han, B. H. Lee, W.-T. Han, U.-C. Paek, and Y. Chung, “Induction of the refractive index change in B-doped optical fibers through relaxation of the mechanical stress,” Opt. Commun. 185, 337-342 (2000).
[CrossRef]

Leuenberger, B.

Limberger, H. G.

Marques, P. V. S.

Marquet, P.

Mettler, S. C.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302-303 (1998).
[CrossRef]

Mitsunaga, Y.

Montarou, C. C.

Nishide, K.

S. Yamasaki, M. Akiyama, K. Nishide, A. Wada, and R. Yamauchi, “Characteristics of long-period fiber grating utilizing periodic stress relaxation,” IEICE Trans. Electron. E83-C, 440-443 (2000).

Oh, K.

Oh, S. T.

Paek, U. C.

Paek, U.-C.

Pagnotta, L.

L. Bruno, L. Pagnotta, and A. Poggialini, “A full-field method for measuring residual stresses in optical fiber,” Opt. Lasers Eng. 44, 577-588 (2006).
[CrossRef]

Park, H. S.

D. I. Yeom, H. S. Kim, M. S. Kang, H. S. Park, and B. Y. Kim, “Narrow-bandwidth all-fiber acoustooptic tunable filter with low polarization-sensitivity,” IEEE Photon. Technol. Lett. 17, 2646-2648 (2005).
[CrossRef]

Park, Y.

Y. Park, U.-C. Paek, S. Han, B.-H. Kim, C.-S. Kim, and D. Y. Kim, “Inelastic frozen-in stress in optical fibers,” Opt. Commun. 242, 431-436 (2004).
[CrossRef]

Y. Park, U.-C. Paek, and D. Y. Kim, “Characterization of a stress-applied polarization-maintaining (PM) fiber through photoelastic tomography,” J. Lightwave Technol. 21, 997-1004(2003).
[CrossRef]

H. S. Ryu, Y. Park, S. T. Oh, Y. J. Chung, and D. Y. Kim, “Effect of asymmetric stress relaxation on the polarization-dependent transmission characteristics of a CO2 laser-written long-period fiber grating,” Opt. Lett. 28, 155-157 (2003).
[CrossRef] [PubMed]

Y. Park, S. Choi, U.-C. Paek, K. Oh, and D. Y. Kim, “Measurement method for profiling the residual stress of an optical fiber: detailed analysis of off-focusing and beam-deflection effects,” Appl. Opt. 42, 1182-1190 (2003).
[CrossRef] [PubMed]

Y. Park, U.-C. Paek, and D. Y. Kim, “Determination of stress-induced intrinsic birefringence in a single-mode fiber by measurement of the two-dimensional stress profile,” Opt. Lett. 27, 1291-1293 (2002).
[CrossRef]

Y. Park, U.-C. Paek, and D. Y. Kim, “Complete determination of the stress tensor of a polarization-maintaining fiber by photoelastic tomography,” Opt. Lett. 27, 1217-1219 (2002).
[CrossRef]

B. H. Kim, Y. Park, D. Y. Kim, U. C. Paek, and W. T. Han, “Observation and analysis of residual stress development resulting from OH impurity in optical fibers,” Opt. Lett. 27, 806-808 (2002).
[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Configuration of fiber illumination for birefringence measurements.

Fig. 2
Fig. 2

Arrangement of the polarization microscope optical components and a fiber sample used for full-field retardation measurements. Rotation of the compensator during a full-field measurement is indicated by θ c . Axial rotation of the fiber between full-field measurements is indicated by θ f .

Fig. 3
Fig. 3

Flow chart of the measurement process for determination of cross-sectional axial stress distributions. The dashed enclosed portion represents the image acquisition process for a full-field retardation measurement.

Fig. 4
Fig. 4

Grayscale plot of a typical cross-sectional axial stress distribution in an unperturbed Corning SMF-28 fiber.

Fig. 5
Fig. 5

Average radial profile of the stress distribution of the unperturbed Corning SMF-28 fiber (solid line) and the stress distribution 10 μm from the cleaved end-face (dotted line). Both profiles indicate peaks of compressive stress near the boundary between the core and cladding.

Fig. 6
Fig. 6

Grayscale plot of the cross-sectional axial stress distribution 10 μm from the cleaved end-face of Corning SMF-28 fiber. For comparison to the unperturbed Corning SMF-28 fiber, the range of axial stress values shown is identical to that in Fig. 4. When compared to the unperturbed fiber, stress relaxation is evident throughout the fiber cross section.

Fig. 7
Fig. 7

Mean axial stress inside the fiber at various lengths from the cleaved end-face of the Corning SMF-28 fiber (solid curve). For comparison, the mean axial stress inside the unperturbed Corning SMF-28 fiber is shown (dashed line).

Fig. 8
Fig. 8

Grayscale plots of the cross-sectional axial stress distribution at the center of a region of Corning SMF-28 fiber exposed to CO 2 laser radiation. The full range of axial stress values present in the fiber is shown in (a). The range of axial stress values is reduced in (b) to highlight the azimuthal asymmetry in the stress distribution. The dot-dashed center line indicates the radial direction along which the asymmetry is strongest.

Fig. 9
Fig. 9

Radial profile of the axial stress along the dot–dashed center line in Fig. 8b (solid line) and a typical radial profile of the axial stress in the unperturbed Corning SMF-28 fiber (dotted line).

Fig. 10
Fig. 10

Mean axial stress inside the fiber exposed to CO 2 laser radiation at various lengths along the fiber axis (solid curve). For comparison, the mean axial stress inside the unperturbed Corning SMF-28 fiber is shown (dashed line).

Equations (19)

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n x = n 0 + C 1 σ x + C 2 ( σ y + σ z ) , n y = n 0 + C 1 σ y + C 2 ( σ x + σ z ) , n z = n 0 + C 1 σ z + C 2 ( σ x + σ y ) ,
n z n x = C ( σ z σ x ) ,
45 °
R ( x , θ f ) = C [ σ z ( x , y ) σ x ( x , y ) ] d y .
R ( x , θ f ) = C σ z ( x , y ) d y .
180 °
R ˜ ( s , θ f ) = C σ ˜ z ( s cos θ f , s sin θ f ) ,
180 °
C σ z ( x , y ) = 0 π [ R ˜ ( s , θ f ) | s | e i 2 π s x d s ] d θ .
45 °
R s = | R c sin 2 θ c | ,
0.5 °
180 °
2 °
2 °
180 °
2 °
178 °
σ ¯ z = 0 2 π 0 a σ z ( r , θ ) r d r d θ 0 2 π 0 a r d r d θ ,

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