Abstract

We present an improved, high-resolution method for the measurement of phase retardation induced by the material birefringence of optical fibers. Such a method can be used to retrieve information about the spatial distribution of refractive index anisotropy in the fiber by comparing the accumulated phase of a polarization component oriented along the fiber transmission axis and another located in the transverse plane. The method is based on the nonlinear regression of a phase modulated signal of known modulation amplitude altered by the sample. Experimental results obtained with our method for a standard telecommunications fiber (the Corning SMF-28) as well as photosensitive fibers (Fibercore PS1250 and PS1500) are presented with a noise-limited phase resolution below 104 radians and a spatial resolution below 1μm. An analysis of the limitation of such measurement methods is also presented including diffraction by the fibers.

© 2008 Optical Society of America

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References

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  2. A. D. Yablon, “Optical and mechanical effects of frozen-in stresses and strains in optical fibers,” IEEE J. Sele. Top. Quantum Electron. 10, 300-311 (2004).
    [CrossRef]
  3. F. Dürr, H. G. Limberger, R. P. Salathé, and A. D. Yablon, “Inelastic strain birefringence in optical fibers,” in “Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference,” (Optical Society of America, 2006), paper OWA2.
    [CrossRef] [PubMed]
  4. J. H. Simmons, R. K. Mohr, and C. J. Montrose, “Non-Newtonian viscous flow in glass,” J. Appl. Phys. 53, 4075-4080 (1982).
    [CrossRef]
  5. Y. Park, U.-C. Paek, and D. Y. Kim, “Determination of stress-induced birefringence in a single-mode fiber by measurement of the two-dimensional stress profile,” Opt. Lett. 27, 1291-1293 (2002).
    [CrossRef]
  6. T. Rose, D. Spriegel, and J.-R. Kropp, “Fast photoelastic stress determination: application to monomode fibers and splices,” Meas. Sci. Technol. 4, 431-434 (1993).
    [CrossRef]
  7. Y. Park, S. Choi, U.-C. Paek, K. Oh, and D. Y. Kim, “Measurement method for profiling the residual stress of optical fibers: detailed analysis of off-focusing and beam-deflection effects,” Appl. Opt. 42, 1182-1190 (2003).
    [CrossRef] [PubMed]
  8. 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]
  9. K. W. Raine, “Advances in the measurement of optical fibre refractive index and axial stress profiles,” Ph.D. dissertation (Kings College, London, 1998).
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  11. 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]
  12. 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]
  13. C. C. Montarou, T. K. Gaylord, B. L. Bachim, A. I. Dachevski, and A. Agarwal, “Two-wave-plate compensator method for full-field retardation measurments,” Appl. Opt. 45, 271-280(2006).
    [CrossRef] [PubMed]
  14. C. C. Montarou and T. K. Gaylord, “Two-wave-plate compensator method for single point retardation measurments,” Appl. Opt. 43, 6580-6595 (2004).
    [CrossRef]
  15. M. Faucher, “Mesures de contraintes dans les fibres optiques et les composants tout-fibre,” Master's thesis (École Polytechnique de Montréal, 2003).
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    [CrossRef]
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    [PubMed]
  18. B. Sévigny, M. Faucher, N. Godbout, and S. Lacroix, “Drawing-induced index anisotropy in single-material endlessly single-mode microstructured optical fibers,” in “Conference on Lasers and Electro-Optics 2007,” (Optical Society of America, 2007).
    [CrossRef]
  19. 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]
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  22. P. Nebout, N. Godbout, S. Lacroix, X. Daxhelet, and J. Bures, “Tapered fiber diameter measurements,” in Symposium on Optical Fiber Measurements, Technical Digest (Optical Society of America, 1994), pp. 101-104.

2006 (3)

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, B. L. Bachim, A. I. Dachevski, and A. Agarwal, “Two-wave-plate compensator method for full-field retardation measurments,” 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]

2004 (3)

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

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

2003 (1)

2002 (2)

1999 (1)

1993 (1)

T. Rose, D. Spriegel, and J.-R. Kropp, “Fast photoelastic stress determination: application to monomode fibers and splices,” Meas. Sci. Technol. 4, 431-434 (1993).
[CrossRef]

1987 (1)

1982 (1)

J. H. Simmons, R. K. Mohr, and C. J. Montrose, “Non-Newtonian viscous flow in glass,” J. Appl. Phys. 53, 4075-4080 (1982).
[CrossRef]

1978 (1)

Appl. Opt. (7)

IEEE J. Sele. Top. Quantum Electron. (1)

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

J. Appl. Phys. (1)

J. H. Simmons, R. K. Mohr, and C. J. Montrose, “Non-Newtonian viscous flow in glass,” J. Appl. Phys. 53, 4075-4080 (1982).
[CrossRef]

Meas. Sci. Technol. (1)

T. Rose, D. Spriegel, and J.-R. Kropp, “Fast photoelastic stress determination: application to monomode fibers and splices,” Meas. Sci. Technol. 4, 431-434 (1993).
[CrossRef]

Opt. Commun. (2)

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. 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]

Opt. Lasers Eng. (1)

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]

Opt. Lett. (1)

Other (8)

F. Dürr, H. G. Limberger, R. P. Salathé, and A. D. Yablon, “Inelastic strain birefringence in optical fibers,” in “Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference,” (Optical Society of America, 2006), paper OWA2.
[CrossRef] [PubMed]

K. W. Raine, “Advances in the measurement of optical fibre refractive index and axial stress profiles,” Ph.D. dissertation (Kings College, London, 1998).

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw-Hill, 1970).

P. Nebout, N. Godbout, S. Lacroix, X. Daxhelet, and J. Bures, “Tapered fiber diameter measurements,” in Symposium on Optical Fiber Measurements, Technical Digest (Optical Society of America, 1994), pp. 101-104.

M. Faucher, “Mesures de contraintes dans les fibres optiques et les composants tout-fibre,” Master's thesis (École Polytechnique de Montréal, 2003).

D. M. Bates and D. G. Watts, Nonlinear Regression and its Applications (Wiley, 1988).
[CrossRef]

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999).
[PubMed]

B. Sévigny, M. Faucher, N. Godbout, and S. Lacroix, “Drawing-induced index anisotropy in single-material endlessly single-mode microstructured optical fibers,” in “Conference on Lasers and Electro-Optics 2007,” (Optical Society of America, 2007).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Illustration of the small birefringence measurement setup. This setup is based on a crossed polarizers scheme combined with a phase modulator and an imaging system. The probe beam is sent transversally through the fiber with a polarization state oriented at 45 ° from the fiber axis z.

Fig. 2
Fig. 2

Examples of the polarization state after passing through the modulator and sample. The modulator produces an elliptically polarized state with known ellipticity. When the light subsequently passes through the sample, its polarization state is altered. The solid curve illustrates a modulated polarization state in the case where the phase retardation induced by the modulator and sample is subtractive. The dashed curve indicates a modulated state for the case where the phase retardation induced by the sample and by the modulator is additive. The output elliptical state of light is measured to deduce the phase retardation induced by the sample. This operation is performed for every coordinate y.

Fig. 3
Fig. 3

Arrangement of two almost compensating quarter waveplates used as a phase modulator. The modulation amplitude Ω is equal to 2 α , α being the angular offset between the compensated refractive index axes. The angle θ is the rotation angle of the whole structure with respect to an arbitrary reference axis.

Fig. 4
Fig. 4

Polarization path of the modulator on the Poincaré sphere for different angular offsets α (in radians) and θ [ 0 , π ] . The input polarization is S = [ 0 , 1 , 0 ] . We notice that the modulation amplitude is indeed Ω = 2 α and that the polarization state rotates by angle α. To compensate for that rotation and to preserve the 45 ° polarization orientation with respect to the fiber axis, the polarizer can be rotated by an angle α .

Fig. 5
Fig. 5

Simulation of the signal captured for each pixel. Here, fiber phase retardation of 0 and 5 degrees is illustrated. The phase modulation amplitude Ω = 2 α is set to 10 degrees.

Fig. 6
Fig. 6

Phase retardation of the SMF-28 telecommunications fiber: (a) the oil refractive index is not matched with the index of the cladding, (b) the oil refractive index is matched with the index of the cladding. We see that fringes are still visible in the fiber core region. Note that this fiber has a 125 μm diameter cladding and an approximately 9 μm diameter, Ge-doped core ( N . A . = 0.12 ). Regions with different dopant compositions are separated by vertical dashed lines.

Fig. 7
Fig. 7

Phase retardation of the photosensitive fiber Fibercore PS1250. This fiber has an intermediate buried cladding that is clearly visible on the retardation profile. Notches in the cladding, visible around 45 μm , are presumably due to the interface of the hollow silica tube used to manufacture the preform. Note that this fiber has a 125 μm diameter cladding and an approximately 9 μm diameter core ( N . A . = 0.14 ) surrounded by the low-index intermediate cladding about 32 μm in diameter. Regions with different dopant compositions are separated by vertical dashed lines.

Fig. 8
Fig. 8

Phase retardation of the photosensitive fiber Fibercore PS1500. Notches in the cladding, visible around 35 μm , are presumably due to the interface of the hollow silica tube used to manufacture the preform. One can also notice diffraction fringes due to the refractive index difference between the fiber core and cladding. Note that this fiber has a 125 μm diameter cladding and an approximately 9 μm diameter core ( N . A . = 0.11 ). Regions with different dopant compositions are separated by vertical dashed lines.

Fig. 9
Fig. 9

Plane-wave BPM simulation of diffraction by a standard telecommunications fiber (Corning SMF-28): (a) difference between the oil refractive index and the fiber cladding refractive index is Δ n = n clad n oil = 3 × 10 3 , (b) the refractive index difference is one order of magnitude lower, Δ n = 3 × 10 4 . The fringe contrast is diminished at the cladding–oil interface when the refractive index difference is smaller. Diffraction by the fiber core–cladding interface is not significantly altered whether the oil–cladding index difference is small or not.

Fig. 10
Fig. 10

Example of phase noise added to the wavefront in the BPM analysis in an attempt to model the contribution of the diffuser to the lowering of the visibility of the diffraction fringes from the fiber. This profile was generated from 10 uniformly distributed random phase points in the range [ 0 , 2 π ] . Those phase points are uniformly spaced along the wavefront and are interconnected with a cubic spline for smooth variation.

Fig. 11
Fig. 11

Illustration of the average (in intensity) of multiple BPM runs, each affected with a random phase pattern as shown in Fig. 10. This result represents the contribution of the rotating diffuser in the lowering of the visibility of the diffraction fringes from the fiber. As we can see, it has little or no effect, which is in accordance with our experimental data.

Equations (7)

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R - π / 4 R θ W π / 2 R α W π / 2 R α 1 R θ 1 R π / 4 = R θ R α W 2 α R θ 1 ,
I t ( y ) = I 0 ( y ) { [ sin ( ϕ ( y ) 2 ) sin ( Ω 2 ) cos ( 2 θ ) ] 2 + [ sin ( ϕ ( y ) 2 ) cos ( Ω 2 ) + sin ( Ω 2 ) cos ( ϕ ( y ) 2 ) sin ( 2 θ ) ] 2 } ,
ϕ ( y ) = 2 π λ R f 2 y 2 R f 2 y 2 [ C σ z ( x , y ) + P Δ ϵ res ( x , y ) ] d x ,
σ z ( r ) = E Δ T 1 ν [ 2 R f 2 0 R f α ( r ) r d r α ( r ) ] .
ϕ ( y ) 2 π λ R f 2 y 2 R f 2 y 2 C σ z ( x , y ) d x .
ϕ ( y ) = 4 π C σ z , clad λ R f 2 y 2 ,
A σ z d A = 0 R f R f λ 2 π ϕ ( y ) d y = A P Δ ϵ res d A ,

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