Abstract

We present a simple variational method for the analysis of UV-side-illuminated single-mode fibers. We use a shiftable, two-dimensional elliptical Gaussian function as a field trial for the fundamental-mode. By this method, the actual UV-induced peak refractive-index increase can be quantitatively related to the measured effective-index increase. The asymmetry of the UV-induced refractive-index profile due to the absorption of the writing UV light causes both form birefringence and transition losses between UV-illuminated and non-illuminated fiber sections. These characteristics are easily calculated from the results of the variational method. We show that UV-illumination of the fiber from two opposite sides reduces both the form birefringence and the transition losses.

© Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, "Photosensitivity in optical waveguides: Application to reflection filter fabrication," Appl. Phys. Lett. 32, 647-649 (1978).
    [CrossRef]
  2. G. Meltz, W. W. Morey, and W. H. Glenn, "Formation of Bragg gratings in optical fibers by transverse holographic method," Opt. Lett. 14, 823-825 (1989).
    [CrossRef] [PubMed]
  3. F. Bilodeau, K. O. Hill, B. Malo, D. Johnson, and I. Skinner, "Efficient narrow-band LP01 LP02 mode convertors fabricated in photosensitive fiber: Spectral response," Electron. Lett. 27, 682-684 (1991).
    [CrossRef]
  4. A. M. Vengsarkar, P. L. Lemaire, J. B. Judkins, V. Bathia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band rejection filters," J. Lightwave Technol. 14, 58-65 (1996).
    [CrossRef]
  5. V. Mizrahi and J. E. Sipe, "Optical properties of photosensitive fiber phase gratings," J. Lightwave Technol. 11, 1513-1517 (1993).
    [CrossRef]
  6. D. Johlen, H. Renner, P. Klose, E. Brinkmeyer, "UV-Writing of Two-Mode Sections into Single-Mode Fibres for Hosting Mode-Converting Bragg Gratings," IEEE Photon. Technol. Lett. 11, 1015-1017 (1999).
    [CrossRef]
  7. R. Kashyap, Fiber Bragg Gratings (Academic Press, San Diego, 1999).
  8. E. Brinkmeyer, D. Johlen, F. Knappe, and H. Renner, "Methods for experimental characterization of UV-written gratings and waveguides," OSA Trends in Optics and Photonics Vol. 33, Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, pp. 155-175 (2000).
  9. D. Inniss, Q. Zhong, A. M. Vengsarkar, W. A. Reed, S. G. Kosinski, and P. L. Lemaire, "Atomic force microscopy study of uv-induced anisotropy in hydrogen-loaded germanosilicate fibers," Appl. Phys. Lett. 65, 1528-1530 (1994).
    [CrossRef]
  10. A. M. Vengsarkar, Q. Zhong, D. Inniss, W. A. Reed, P. L. Lemaire, and S. G. Kosinski, "Birefringence reduction in side-written photoinduced fiber devices by a dual-exposure method," Opt. Lett. 19, 1260-1262 (1994).
    [CrossRef]
  11. C. De Barros, I. Riant, T. Lopez, and P. Sansonetti, "Tapered slanted Bragg grating for low insertion loss gain equalizing filter," OSA Technical Digest: Conference on Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, Stresa, Italy, July 4-6 (paper JW1), (2001).
  12. H. Renner, D. Johlen, E. Brinkmeyer, "Modal field deformation and transition losses in UV side-written optical fibers," Appl. Opt. 39, 933-940 (2000).
    [CrossRef]
  13. D. Johlen, F. Knappe, H. Renner, and E. Brinkmeyer, "UV-Induced Absorption, Scattering and Transition Losses in UV Side-Written Fibers," Proc. Conf. Opt. Fiber Comm. (OFC), San Diego, CA, USA (paper ThD1), (1999).
  14. H. Renner, "Modes of UV-written planar waveguides," Opt. Lett. 23, 111-113 (1998).
    [CrossRef]
  15. S. Selleri und M. Zoboli, "Performance comparison of finite-element approaches for electromagnetic waveguides," J. Opt. Soc. Am. A 14, 1460-1466 (1997).
    [CrossRef]
  16. G. Tartarini und H. Renner, "Efficient Finite-Element Analysis of Tilted Open Anisotropic Optical Channel Waveguides," IEEE Microwave Guided Wave Lett. 9, 389-391 (1999).
    [CrossRef]
  17. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).
  18. Ph. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
  19. Ge-doped single-mode fiber, OFTC Sydney, Australia.
  20. H. Abramowitz and I. A. Stegun, Handbook of mathematical functions (US Government Printing Office, Washington, D. C., 1964).
  21. D. Johlen, H. Renner, A. Ewald, and E. Brinkmeyer : "Fiber Bragg grating Fabry-Perot interferometer for a precise measurement of the UV-induced index change," in Proc. ECOC"98, Madrid, 1998, Vol. 1, pp. 393-394.
  22. T. Erdogan and V. Mizrahi, "Characterization of UV-induced birefringence in photosensitive Ge-doped silica optical fibers," J. Opt. Soc. Am. B 11, 416-417 (1994).
    [CrossRef]
  23. O. Duhem and M. Douay, "Effect of birefringence on long-period-grating coupling characteristics," Electron. Lett. 36, 416-417 (2000).
    [CrossRef]
  24. M. Schiano and G. Zaffiro, "Polarisation mode dispersion in chirped fibre gratings," in Proc. ECOC"98, Madrid, 1998, Vol. 1, pp. 403-405.
  25. F. Oullette, "Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides," Opt. Lett. 12, 847-849 (1987).
    [CrossRef]
  26. J. L. Philipsen, M. O. Berendt, P. Varming, V. C. Lauridsen, J. H. Povlsen, J. Hubner, M. Kristensen, and B. Palsdottir, "Polarisation control of DFB fibre laser using UV-induced birefringent phase-shift," Electron. Lett. 34 678-679 (1998).
    [CrossRef]
  27. E.-G. Neumann, Single-Mode Fibers (Springer-Verlag, Berlin, 1988).
  28. H. Rosenfeldt, Ch. Knothe, R. Ulrich, E. Brinkmeyer, U. Feiste, C. Schubert, J. Berger, R. Ludwig, H. G. Weber, A. Ehrhardt, "Automatic PMD Compensation at 40 Gbit/s and 80 Gbit/s Using a 3-Dimensional DOP Evaluation for Feedback," Proc. Conf. Opt. Fiber Comm. (Optical Society of America, Washington, D.C., 2001) Postdeadline Paper PD27.
  29. K. O. Hill, B. Malo, K. Vineberg, F. Bilodeau, D. Johnson, and I. Skinner, "Efficient mode-conversion in telecommunication fiber using externally written gratings," Electron. Lett. 26, 1270-1272 (1990).
    [CrossRef]
  30. A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Henninot, J. F. Bayon, and L. Rivoallan, "Long-period fibre gratings as a wavelength selective polarisation element," Electron. Lett. 33, 616-617 (1997).
    [CrossRef]
  31. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), Sect. 13-6. 32.
  32. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), Sect. 17.
  33. M. Parent, J. Bures, S. Lacroix, and J. Lapierre, "Propri�t�s de polarisation des r�flecteurs de Bragg induits par photosensibilit� dans les fibres optiques monomodes," Appl. Opt. 24, 354-357 (1985).
    [CrossRef] [PubMed]
  34. J. Albert, B. Malo, D. C. Johnson, F. Bilodeau, K. O. Hill, J. L. Brebner, and G. Kajrys, "Dichroism in the absorption spectrum of photobleached ion-implanted silica," Opt. Lett. 18, 1126-1128 (1993).
    [CrossRef] [PubMed]
  35. T. Meyer, P.-A. Nicati, P. A. Robert, D. Varelas, H. G. Limberger and R. P. Salathe, "Birefringence writing and erasing in ultra-low-birefringence fibers by polarized UV side-exposure: origin and applications," Proc. 11th international Conference on Optical Fiber Sensors (OFS"96), Sapporo, Japan, 1997, vol. 1, pp. 368-371.

Other (35)

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, "Photosensitivity in optical waveguides: Application to reflection filter fabrication," Appl. Phys. Lett. 32, 647-649 (1978).
[CrossRef]

G. Meltz, W. W. Morey, and W. H. Glenn, "Formation of Bragg gratings in optical fibers by transverse holographic method," Opt. Lett. 14, 823-825 (1989).
[CrossRef] [PubMed]

F. Bilodeau, K. O. Hill, B. Malo, D. Johnson, and I. Skinner, "Efficient narrow-band LP01 LP02 mode convertors fabricated in photosensitive fiber: Spectral response," Electron. Lett. 27, 682-684 (1991).
[CrossRef]

A. M. Vengsarkar, P. L. Lemaire, J. B. Judkins, V. Bathia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band rejection filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

V. Mizrahi and J. E. Sipe, "Optical properties of photosensitive fiber phase gratings," J. Lightwave Technol. 11, 1513-1517 (1993).
[CrossRef]

D. Johlen, H. Renner, P. Klose, E. Brinkmeyer, "UV-Writing of Two-Mode Sections into Single-Mode Fibres for Hosting Mode-Converting Bragg Gratings," IEEE Photon. Technol. Lett. 11, 1015-1017 (1999).
[CrossRef]

R. Kashyap, Fiber Bragg Gratings (Academic Press, San Diego, 1999).

E. Brinkmeyer, D. Johlen, F. Knappe, and H. Renner, "Methods for experimental characterization of UV-written gratings and waveguides," OSA Trends in Optics and Photonics Vol. 33, Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, pp. 155-175 (2000).

D. Inniss, Q. Zhong, A. M. Vengsarkar, W. A. Reed, S. G. Kosinski, and P. L. Lemaire, "Atomic force microscopy study of uv-induced anisotropy in hydrogen-loaded germanosilicate fibers," Appl. Phys. Lett. 65, 1528-1530 (1994).
[CrossRef]

A. M. Vengsarkar, Q. Zhong, D. Inniss, W. A. Reed, P. L. Lemaire, and S. G. Kosinski, "Birefringence reduction in side-written photoinduced fiber devices by a dual-exposure method," Opt. Lett. 19, 1260-1262 (1994).
[CrossRef]

C. De Barros, I. Riant, T. Lopez, and P. Sansonetti, "Tapered slanted Bragg grating for low insertion loss gain equalizing filter," OSA Technical Digest: Conference on Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, Stresa, Italy, July 4-6 (paper JW1), (2001).

H. Renner, D. Johlen, E. Brinkmeyer, "Modal field deformation and transition losses in UV side-written optical fibers," Appl. Opt. 39, 933-940 (2000).
[CrossRef]

D. Johlen, F. Knappe, H. Renner, and E. Brinkmeyer, "UV-Induced Absorption, Scattering and Transition Losses in UV Side-Written Fibers," Proc. Conf. Opt. Fiber Comm. (OFC), San Diego, CA, USA (paper ThD1), (1999).

H. Renner, "Modes of UV-written planar waveguides," Opt. Lett. 23, 111-113 (1998).
[CrossRef]

S. Selleri und M. Zoboli, "Performance comparison of finite-element approaches for electromagnetic waveguides," J. Opt. Soc. Am. A 14, 1460-1466 (1997).
[CrossRef]

G. Tartarini und H. Renner, "Efficient Finite-Element Analysis of Tilted Open Anisotropic Optical Channel Waveguides," IEEE Microwave Guided Wave Lett. 9, 389-391 (1999).
[CrossRef]

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

Ph. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Ge-doped single-mode fiber, OFTC Sydney, Australia.

H. Abramowitz and I. A. Stegun, Handbook of mathematical functions (US Government Printing Office, Washington, D. C., 1964).

D. Johlen, H. Renner, A. Ewald, and E. Brinkmeyer : "Fiber Bragg grating Fabry-Perot interferometer for a precise measurement of the UV-induced index change," in Proc. ECOC"98, Madrid, 1998, Vol. 1, pp. 393-394.

T. Erdogan and V. Mizrahi, "Characterization of UV-induced birefringence in photosensitive Ge-doped silica optical fibers," J. Opt. Soc. Am. B 11, 416-417 (1994).
[CrossRef]

O. Duhem and M. Douay, "Effect of birefringence on long-period-grating coupling characteristics," Electron. Lett. 36, 416-417 (2000).
[CrossRef]

M. Schiano and G. Zaffiro, "Polarisation mode dispersion in chirped fibre gratings," in Proc. ECOC"98, Madrid, 1998, Vol. 1, pp. 403-405.

F. Oullette, "Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides," Opt. Lett. 12, 847-849 (1987).
[CrossRef]

J. L. Philipsen, M. O. Berendt, P. Varming, V. C. Lauridsen, J. H. Povlsen, J. Hubner, M. Kristensen, and B. Palsdottir, "Polarisation control of DFB fibre laser using UV-induced birefringent phase-shift," Electron. Lett. 34 678-679 (1998).
[CrossRef]

E.-G. Neumann, Single-Mode Fibers (Springer-Verlag, Berlin, 1988).

H. Rosenfeldt, Ch. Knothe, R. Ulrich, E. Brinkmeyer, U. Feiste, C. Schubert, J. Berger, R. Ludwig, H. G. Weber, A. Ehrhardt, "Automatic PMD Compensation at 40 Gbit/s and 80 Gbit/s Using a 3-Dimensional DOP Evaluation for Feedback," Proc. Conf. Opt. Fiber Comm. (Optical Society of America, Washington, D.C., 2001) Postdeadline Paper PD27.

K. O. Hill, B. Malo, K. Vineberg, F. Bilodeau, D. Johnson, and I. Skinner, "Efficient mode-conversion in telecommunication fiber using externally written gratings," Electron. Lett. 26, 1270-1272 (1990).
[CrossRef]

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Henninot, J. F. Bayon, and L. Rivoallan, "Long-period fibre gratings as a wavelength selective polarisation element," Electron. Lett. 33, 616-617 (1997).
[CrossRef]

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), Sect. 13-6. 32.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), Sect. 17.

M. Parent, J. Bures, S. Lacroix, and J. Lapierre, "Propri�t�s de polarisation des r�flecteurs de Bragg induits par photosensibilit� dans les fibres optiques monomodes," Appl. Opt. 24, 354-357 (1985).
[CrossRef] [PubMed]

J. Albert, B. Malo, D. C. Johnson, F. Bilodeau, K. O. Hill, J. L. Brebner, and G. Kajrys, "Dichroism in the absorption spectrum of photobleached ion-implanted silica," Opt. Lett. 18, 1126-1128 (1993).
[CrossRef] [PubMed]

T. Meyer, P.-A. Nicati, P. A. Robert, D. Varelas, H. G. Limberger and R. P. Salathe, "Birefringence writing and erasing in ultra-low-birefringence fibers by polarized UV side-exposure: origin and applications," Proc. 11th international Conference on Optical Fiber Sensors (OFS"96), Sapporo, Japan, 1997, vol. 1, pp. 368-371.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

a) UV-illumination of a photosensitive fiber from the left and resulting non-symmetric refractive-index profile. b) UV-illumination from two opposite sides and resulting non-homogeneous, but symmetric refractive-index profile.

Fig. 2.
Fig. 2.

UV-induced refractive-index increase δn̂+ versus effective-index increase δne for one-sided UV-illumination of the fiber. The dashed line marks the effective-index increase itself.

Fig. 3.
Fig. 3.

Field shift -s (dotted lines) and field widths wx (solid lines) and wy (dashed lines) versus effective-index increase δne for α=0, 1/4ρ, 1/2ρ, and 1/ρ. a) UV-illumination from one horizontal side of the fiber. b) Equal UV-illumination from two opposite horizontal sides, resulting in s≡0. The arrows in both figures give the direction of growing α. For α=0, the field is circular and concentric to the fiber core, i.e. wx =wy and s=0.

Fig. 4.
Fig. 4.

Birefringence in a UV-illuminated fiber for various values of the UV-attenuation constant. a) UV-illumination from one horizontal side of the fiber. b) UV-illumination from two opposite horizontal sides.

Fig. 5.
Fig. 5.

Transition loss between a UV-illuminated and a non-illuminated fiber section for various values of the UV-attenuation constant. a) UV-illumination from one side of the fiber. b) UV-illumination from two opposite sides.

Equations (51)

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

n ¯ 2 ( x , y ) = { n 1 2 0 r < ρ , ( core ) , n 2 2 = n 1 2 Δ n ¯ 2 ρ < r < , ( cladding ) ,
n 2 ( x , y ) = n ¯ 2 ( x , y ) + δ n + 2 ( x , y ) + δ n 2 ( x , y ) ,
δ n ± 2 ( x , y ) = { δ n ̂ ± 2 exp [ 2 α ( ± x + ρ 2 y 2 ) ] , 0 r < ρ , 0 , ρ < r < .
{ 2 x 2 + 2 y 2 + [ k 2 n 2 ( x , y ) β 2 ] } Ψ ( x , y ) = 0 .
γ 2 = β 2 k 2 n 2 2
= 1 N [ ( t Ψ ) 2 + k 2 Δ n 2 ( x , y ) Ψ 2 ] d x d y
N = Ψ 2 d x d y
Δ n 2 ( x , y ) = n 2 ( x , y ) n 2 2
Ψ ( x , y ) = Ψ 0 exp { 1 2 [ ( x s ) 2 w x 2 + y 2 w y 2 ] } .
γ 2 = 1 2 w x 2 1 2 w y 2
+ k 2 π w x w y Δ n 2 ( x , y ) exp { [ ( x s ) 2 w x 2 + y 2 w y 2 ] } d x d y
γ 2 w x = 0 , γ 2 w y = 0 , γ 2 s = 0 ,
w x = k 2 π w y
× Δ n 2 ( x , y ) [ w x 2 2 ( x s ) 2 ] exp { [ ( x s ) 2 w x 2 + y 2 w y 2 ] } d x d y ,
w y = k 2 π w x
× Δ n 2 ( x , y ) [ w y 2 2 y 2 ] exp { [ ( x s ) 2 w x 2 + y 2 w y 2 ] } d x d y ,
Δ n 2 ( x , y ) ( x s ) exp { [ ( x s ) 2 w x 2 + y 2 w y 2 ] } d x d y = 0 .
γ 2 = 1 2 w x 2 1 2 w y 2
+ k 2 Δ n ¯ 2 π w y 0 ρ exp ( y 2 w y 2 ) [ erf ( s + ρ 2 y 2 w x ) erf ( s ρ 2 y 2 w x ) ] d y
+ k 2 δ n ̂ + 2 π w y exp ( α 2 w x 2 2 α s ) 0 ρ exp ( 2 α ρ 2 y 2 y 2 w y 2 ) ×
× [ erf ( s α w x 2 + ρ 2 y 2 w x ) erf ( s α w x 2 ρ 2 y 2 w x ) ] d y
+ k 2 δ n ̂ + 2 π w y exp ( α 2 w x 2 + 2 α s ) 0 ρ exp ( 2 α ρ 2 y 2 y 2 w y 2 ) ×
× [ erf ( s + α w x 2 + ρ 2 y 2 w x ) erf ( s + α w x 2 ρ 2 y 2 w x ) ] d y .
γ 2 = 1 2 w x 2 1 2 w y 2 + 2 k 2 Δ n ¯ 2 π w y y = 0 ρ exp ( y 2 w y 2 ) erf ( ρ 2 y 2 w x ) d y
+ 2 k 2 δ n ̂ 2 π w y exp ( α 2 w x 2 ) y = 0 ρ exp ( 2 α ρ 2 y 2 y 2 w y 2 ) ×
× [ erf ( ρ 2 y 2 + α w x 2 w x ) + erf ( ρ 2 y 2 α w x 2 w x ) ] d y .
B = β x β y k = n x n y ,
2 π Λ = 2 β ( λ B ) ,
2 π Λ = 2 β x ( λ B x ) = 2 β y ( λ B y ) .
λ y n x ( λ B x ) = λ x n y ( λ B y ) .
λ B x = λ m + Δ λ B 2 , λ B y = λ m Δ λ B 2 ,
n x ( λ B x ) = n x ( λ m ) + n x ( λ m ) Δ λ B 2 ,
n y ( λ B y ) = n y ( λ m ) n y ( λ m ) Δ λ B 2
Δ λ B = 2 λ ( n x n y ) n g x + n g y λ = λ m ,
Δ λ B λ m n x ( λ m ) n y ( λ m ) n g ( λ m ) λ m B ( λ m ) n 2 .
2 π Λ ( z x , y ) = 2 β x , y ( λ ) ,
2 π Λ = β 0 ( λ L ) β h ( λ L ) ,
Δ λ L = 2 λ ( B 0 B h ) n g 0 x + n g 0 y ( n gh x + n gh y ) λ = λ m ,
Δ λ L λ m B 0 ( λ m ) n g 0 ( λ m ) n 2 .
{ t 2 + k 2 n 2 ( x , y ) β ξ 2 } E t = ( E t · t n 2 ( x , y ) n 2 ( x , y ) ) .
E t ( x , y ) = ξ Ψ ( x , y ) , ξ = x , y
δ β ξ = 1 2 k n 1 3 N Δ n 2 ( x , y ) ξ Ψ Ψ ξ d x d y , ξ = x , y ,
δ β ξ = 1 4 k n 1 3 N Δ n 2 ( x , y ) 2 Ψ 2 ξ 2 d x d y .
1 N 2 Ψ 2 x 2 = 4 ( x s ) 2 2 w x 2 π w x 5 w y exp { [ ( x s ) 2 w x 2 + y 2 w y 2 ] }
1 N 2 Ψ 2 y 2 = 4 y 2 2 w y 2 π w x w y 5 exp { [ ( x s ) 2 w x 2 + y 2 w y 2 ] }
δ β x = 1 2 k 3 n 1 3 w x 4 , δ β y = 1 2 k 3 n 1 3 w y 4 .
B = β x β y k = δ β x δ β y k = 1 2 k 4 n 1 3 ( 1 w y 4 1 w x 4 ) .
T = 10 log ( C 2 ) ,
C = Ψ Ψ ¯ d x d y ( Ψ 2 d x d y Ψ ¯ 2 d x d y ) 1 2
Ψ ¯ ( x , y ) = Ψ ¯ 0 exp { 1 2 ( x 2 + y 2 w ¯ 2 ) } ,
C = 2 exp [ s 2 2 ( w ¯ 2 + w x 2 ) ] w ¯ 2 w x w y ( w ¯ 2 + w x 2 ) ( w ¯ 2 + w y 2 )

Metrics