Abstract

High-spatial-resolution measurements of axial-stress profiles of UV-irradiated fibers are reported, providing diagnostic information and a technique for the direct observation of UV-written grating structures. Measurements have been made with a spatial resolution of ∼0.3 µm, which is capable of resolving detail within the pitch of the gratings.

© 1999 Optical Society of America

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References

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  1. K. W. Raine, “A microscope for measuring axial stress profiles with high spatial resolution and low noise,” in Proceedings of the Fourth Optical Fiber Measurement Conference, (National Physical Laboratory, Teddington, UK, 1997), pp. 269–272.
  2. P. Y. Fonjallaz, H. G. Limberger, R. P. Salathe, “Tension increase correlated to refractive index change in fibers containing UV written Bragg gratings,” Opt. Lett. 20, 1346–1348 (1995).
    [CrossRef] [PubMed]
  3. C. J. Koerster, “Optimum half shade angle in polarizing instrument,” J. Opt. Soc. Am. 49, 556–559 (1959).
    [CrossRef]
  4. W. Primak, D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
    [CrossRef]
  5. H. Poritsky, “Analysis of thermal stresses in sealed cylinders and the effect of viscous flow during anneal,” Physics. (New York) 5, 406–411 (1934).
  6. G. W. Scherer, “Thermal stresses in a cylinder: application to optical waveguide blanks,” J. Non-Cryst. Solids 34, 223–238 (1979).
    [CrossRef]
  7. G. W. Scherer, A. Cooper, “Thermal stresses in clad glass fibers,” J. Am. Ceram. Soc. 63, 346–347 (1980).
    [CrossRef]
  8. H. Bachmann, W. Hermann, H. Wehr, D. U. Wiechert, “Stress in optical waveguides 2: fibers,” Appl. Opt. 26, 1175–1182 (1987).
    [CrossRef] [PubMed]
  9. W. W. Morey, G. Meltz, G. A. Ball, J. R. Dunphy, F. X. D’Amato, “In fiber Bragg gratings,” in Proceedings of the Seventeenth Australian Conference on Optical Fiber Technology (Institution of Radio and Electronics Engineers, Australia, 1992), pp. 162–168.
  10. K. W. Raine, J. G. Baines, R. J. King, “Comparison of refractive index measurements of optical fibres by three methods,” IEE Proc. 135, 190–195 (1988).
  11. K. W. Raine, “Advances in the measurements of optical fibre refractive index and axial stress profiles,” Ph.D. thesis (London University, Kings College, UK, 1998), Chap. 7 (refracted near-field profiler), pp. 38–41, 242 (temperature difference in fiber).
  12. S. E. Miller, A. G. Chynoweth, eds., Optical Fiber Communications (Academic, New York, 1979), Chap. 7.
  13. S. Takahashi, S. Shibata, “Thermal variation of attenuation for optical fibers,” J. Non-Cryst. Solids 30, 359–370 (1979).
    [CrossRef]
  14. B. Malo, D. C. Johnson, F. Bilodeau, J. Albert, K. O. Hill, “Single-excimer-pulse writing of fiber gratings by use of a zero-order nulled phase mask: grating spectral response and visualisation of index perturbations,” Opt. Lett. 18, 1277–1279 (1993).
    [CrossRef] [PubMed]
  15. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993), p. 57.
  16. H. G. Limberger, P. Y. Fonjallaz, R. P. Salathe, F. Cochet, “Compaction and photoelastic-induced index changes in fiber Bragg gratings,” Appl. Phys. Lett. 68, 3068–3071 (1996).
    [CrossRef]

1996

H. G. Limberger, P. Y. Fonjallaz, R. P. Salathe, F. Cochet, “Compaction and photoelastic-induced index changes in fiber Bragg gratings,” Appl. Phys. Lett. 68, 3068–3071 (1996).
[CrossRef]

1995

1993

1988

K. W. Raine, J. G. Baines, R. J. King, “Comparison of refractive index measurements of optical fibres by three methods,” IEE Proc. 135, 190–195 (1988).

1987

1980

G. W. Scherer, A. Cooper, “Thermal stresses in clad glass fibers,” J. Am. Ceram. Soc. 63, 346–347 (1980).
[CrossRef]

1979

G. W. Scherer, “Thermal stresses in a cylinder: application to optical waveguide blanks,” J. Non-Cryst. Solids 34, 223–238 (1979).
[CrossRef]

S. Takahashi, S. Shibata, “Thermal variation of attenuation for optical fibers,” J. Non-Cryst. Solids 30, 359–370 (1979).
[CrossRef]

1959

C. J. Koerster, “Optimum half shade angle in polarizing instrument,” J. Opt. Soc. Am. 49, 556–559 (1959).
[CrossRef]

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

1934

H. Poritsky, “Analysis of thermal stresses in sealed cylinders and the effect of viscous flow during anneal,” Physics. (New York) 5, 406–411 (1934).

Albert, J.

Bachmann, H.

Baines, J. G.

K. W. Raine, J. G. Baines, R. J. King, “Comparison of refractive index measurements of optical fibres by three methods,” IEE Proc. 135, 190–195 (1988).

Ball, G. A.

W. W. Morey, G. Meltz, G. A. Ball, J. R. Dunphy, F. X. D’Amato, “In fiber Bragg gratings,” in Proceedings of the Seventeenth Australian Conference on Optical Fiber Technology (Institution of Radio and Electronics Engineers, Australia, 1992), pp. 162–168.

Bilodeau, F.

Cochet, F.

H. G. Limberger, P. Y. Fonjallaz, R. P. Salathe, F. Cochet, “Compaction and photoelastic-induced index changes in fiber Bragg gratings,” Appl. Phys. Lett. 68, 3068–3071 (1996).
[CrossRef]

Cooper, A.

G. W. Scherer, A. Cooper, “Thermal stresses in clad glass fibers,” J. Am. Ceram. Soc. 63, 346–347 (1980).
[CrossRef]

D’Amato, F. X.

W. W. Morey, G. Meltz, G. A. Ball, J. R. Dunphy, F. X. D’Amato, “In fiber Bragg gratings,” in Proceedings of the Seventeenth Australian Conference on Optical Fiber Technology (Institution of Radio and Electronics Engineers, Australia, 1992), pp. 162–168.

Dunphy, J. R.

W. W. Morey, G. Meltz, G. A. Ball, J. R. Dunphy, F. X. D’Amato, “In fiber Bragg gratings,” in Proceedings of the Seventeenth Australian Conference on Optical Fiber Technology (Institution of Radio and Electronics Engineers, Australia, 1992), pp. 162–168.

Fonjallaz, P. Y.

H. G. Limberger, P. Y. Fonjallaz, R. P. Salathe, F. Cochet, “Compaction and photoelastic-induced index changes in fiber Bragg gratings,” Appl. Phys. Lett. 68, 3068–3071 (1996).
[CrossRef]

P. Y. Fonjallaz, H. G. Limberger, R. P. Salathe, “Tension increase correlated to refractive index change in fibers containing UV written Bragg gratings,” Opt. Lett. 20, 1346–1348 (1995).
[CrossRef] [PubMed]

Hermann, W.

Hill, K. O.

Johnson, D. C.

King, R. J.

K. W. Raine, J. G. Baines, R. J. King, “Comparison of refractive index measurements of optical fibres by three methods,” IEE Proc. 135, 190–195 (1988).

Koerster, C. J.

Limberger, H. G.

H. G. Limberger, P. Y. Fonjallaz, R. P. Salathe, F. Cochet, “Compaction and photoelastic-induced index changes in fiber Bragg gratings,” Appl. Phys. Lett. 68, 3068–3071 (1996).
[CrossRef]

P. Y. Fonjallaz, H. G. Limberger, R. P. Salathe, “Tension increase correlated to refractive index change in fibers containing UV written Bragg gratings,” Opt. Lett. 20, 1346–1348 (1995).
[CrossRef] [PubMed]

Malo, B.

Meltz, G.

W. W. Morey, G. Meltz, G. A. Ball, J. R. Dunphy, F. X. D’Amato, “In fiber Bragg gratings,” in Proceedings of the Seventeenth Australian Conference on Optical Fiber Technology (Institution of Radio and Electronics Engineers, Australia, 1992), pp. 162–168.

Morey, W. W.

W. W. Morey, G. Meltz, G. A. Ball, J. R. Dunphy, F. X. D’Amato, “In fiber Bragg gratings,” in Proceedings of the Seventeenth Australian Conference on Optical Fiber Technology (Institution of Radio and Electronics Engineers, Australia, 1992), pp. 162–168.

Poritsky, H.

H. Poritsky, “Analysis of thermal stresses in sealed cylinders and the effect of viscous flow during anneal,” Physics. (New York) 5, 406–411 (1934).

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]

Raine, K. W.

K. W. Raine, J. G. Baines, R. J. King, “Comparison of refractive index measurements of optical fibres by three methods,” IEE Proc. 135, 190–195 (1988).

K. W. Raine, “Advances in the measurements of optical fibre refractive index and axial stress profiles,” Ph.D. thesis (London University, Kings College, UK, 1998), Chap. 7 (refracted near-field profiler), pp. 38–41, 242 (temperature difference in fiber).

K. W. Raine, “A microscope for measuring axial stress profiles with high spatial resolution and low noise,” in Proceedings of the Fourth Optical Fiber Measurement Conference, (National Physical Laboratory, Teddington, UK, 1997), pp. 269–272.

Salathe, R. P.

H. G. Limberger, P. Y. Fonjallaz, R. P. Salathe, F. Cochet, “Compaction and photoelastic-induced index changes in fiber Bragg gratings,” Appl. Phys. Lett. 68, 3068–3071 (1996).
[CrossRef]

P. Y. Fonjallaz, H. G. Limberger, R. P. Salathe, “Tension increase correlated to refractive index change in fibers containing UV written Bragg gratings,” Opt. Lett. 20, 1346–1348 (1995).
[CrossRef] [PubMed]

Scherer, G. W.

G. W. Scherer, A. Cooper, “Thermal stresses in clad glass fibers,” J. Am. Ceram. Soc. 63, 346–347 (1980).
[CrossRef]

G. W. Scherer, “Thermal stresses in a cylinder: application to optical waveguide blanks,” J. Non-Cryst. Solids 34, 223–238 (1979).
[CrossRef]

Shibata, S.

S. Takahashi, S. Shibata, “Thermal variation of attenuation for optical fibers,” J. Non-Cryst. Solids 30, 359–370 (1979).
[CrossRef]

Takahashi, S.

S. Takahashi, S. Shibata, “Thermal variation of attenuation for optical fibers,” J. Non-Cryst. Solids 30, 359–370 (1979).
[CrossRef]

Wehr, H.

Wiechert, D. U.

Yeh, P.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993), p. 57.

Appl. Opt.

Appl. Phys. Lett.

H. G. Limberger, P. Y. Fonjallaz, R. P. Salathe, F. Cochet, “Compaction and photoelastic-induced index changes in fiber Bragg gratings,” Appl. Phys. Lett. 68, 3068–3071 (1996).
[CrossRef]

IEE Proc.

K. W. Raine, J. G. Baines, R. J. King, “Comparison of refractive index measurements of optical fibres by three methods,” IEE Proc. 135, 190–195 (1988).

J. Am. Ceram. Soc.

G. W. Scherer, A. Cooper, “Thermal stresses in clad glass fibers,” J. Am. Ceram. Soc. 63, 346–347 (1980).
[CrossRef]

J. Appl. Phys.

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

J. Non-Cryst. Solids

G. W. Scherer, “Thermal stresses in a cylinder: application to optical waveguide blanks,” J. Non-Cryst. Solids 34, 223–238 (1979).
[CrossRef]

S. Takahashi, S. Shibata, “Thermal variation of attenuation for optical fibers,” J. Non-Cryst. Solids 30, 359–370 (1979).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Physics. (New York)

H. Poritsky, “Analysis of thermal stresses in sealed cylinders and the effect of viscous flow during anneal,” Physics. (New York) 5, 406–411 (1934).

Other

K. W. Raine, “A microscope for measuring axial stress profiles with high spatial resolution and low noise,” in Proceedings of the Fourth Optical Fiber Measurement Conference, (National Physical Laboratory, Teddington, UK, 1997), pp. 269–272.

W. W. Morey, G. Meltz, G. A. Ball, J. R. Dunphy, F. X. D’Amato, “In fiber Bragg gratings,” in Proceedings of the Seventeenth Australian Conference on Optical Fiber Technology (Institution of Radio and Electronics Engineers, Australia, 1992), pp. 162–168.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993), p. 57.

K. W. Raine, “Advances in the measurements of optical fibre refractive index and axial stress profiles,” Ph.D. thesis (London University, Kings College, UK, 1998), Chap. 7 (refracted near-field profiler), pp. 38–41, 242 (temperature difference in fiber).

S. E. Miller, A. G. Chynoweth, eds., Optical Fiber Communications (Academic, New York, 1979), Chap. 7.

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of microscope for measuring birefringence. The field of view shown at the top shows how a small rotation of the quarter-wave plate, from the balance setting, appears to the observer.

Fig. 2
Fig. 2

Refractive-index profile of fiber with a core doped with germania and boric oxide.

Fig. 3
Fig. 3

Full width axial-stress profiles of a fiber doped with germania and a boric oxide-doped fiber with the refractive-index profile shown in Fig. 2.

Fig. 4
Fig. 4

(a) Calculated axial-stress components: thermal, dashed curve; mechanical, solid curve. (b) Calculated radial stress (solid curve) and circumferential stress (dashed curve).

Fig. 5
Fig. 5

Axial-stress profiles after exposure to UV radiation with a wavelength of 193 nm.

Fig. 6
Fig. 6

Axial-stress profiles after exposure to UV radiation with a wavelength of 248 nm.

Fig. 7
Fig. 7

Axial-stress profiles made across the grating at positions of maximum and minimum birefringence with a spatial resolution of 0.3 µm. The mean fluence was 400 J/cm2 at a wavelength of 193 nm.

Fig. 8
Fig. 8

Birefringence profiles obtained from measurements made along directions parallel to the axis of the grating made by exposure to UV radiation with a wavelength of 193 nm, also shown in Fig. 7.

Fig. 9
Fig. 9

Birefringent image of an asymmetric grating and the estimated axial-stress profile sampled as shown.

Fig. 10
Fig. 10

Axial-stress profiles of a standard single-mode fiber with a refractive-index difference of ∼0.005. A truncated profile of the exposed fiber is shown below the full profile of the unexposed fiber. The profile of the exposed fiber shows a small decrease, ∼3 MPa, in compressive stress after exposure to 400 J/cm2 at the wavelength of 193 nm.

Fig. 11
Fig. 11

Refractive-index profile of a multimode step-index fiber.

Fig. 12
Fig. 12

Axial-stress profiles of a hydrogenated multimode fiber before and after exposure to UV radiation with a wavelength of 248 nm. The lower UV-exposed plot is discontinued near the origin for clarity.

Equations (13)

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I  ±H+0.5uδ+θ2,
ΔI  uHδ+2Hθ,
σzr=-λ2π2BrRdδx/dxdxx2-r21/2,
σzr=EΔT1-υαr-2R20R αrrdr,
σrr=1r20r σzρρdρ,  σθr=σzr-σrr.
σz,r,θ=3ΔαΔTh1K+3rd21-2υ+2R21+υER2-rd2,
σzhr=-rd2P/R2-rd2,
σrhr=-rd2P/R2-rd21-R2/r2,
σθr=σrr-2σzr.
σz,cl=ΔσzAd/A,  σz,d=-ΔσzAcl/A,
δnz=-B1σz-B2σθ+σr,  δnr=-B1σr-B2σθ+σz,  δnθ=-B1σθ-B2σr+σz,
R=tanh2πδnLλm
m=2nΛ/λ.

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