Abstract

In this paper, we completely study the wavelength dependency of differential group delay (DGD) in uniform fiber Bragg gratings (FBG) exhibiting birefringence. An analytical expression of DGD is established. We analyze the impact of grating parameters (physical length, index modulation and apodization profile) on the wavelength dependency of DGD. Experimental results complete the paper. A very good agreement between theory and experience is reported.

© 2005 Optical Society of America

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References

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  1. A. Othonos and K. Kalli , Fiber Bragg gratings: fundamentals and applications in telecommunications and sensing ( Artech House, Norwood, MA , 1999 ).
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    [Crossref]
  3. A. M. Vengsarkar , Q. Zhong , D. Inniss , W. A. Reed , P. 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] [PubMed]
  4. N. Gisin and B. Huttner , “ Combined effects of polarization mode dispersion and polarization dependent losses in optical fibers ,” Opt. Commun.   142 , 119 – 125 ( 1997 ).
    [Crossref]
  5. S.T. Oh , W.T. Han , U.C. Paek , and Y. Chung , “ Discrimination of temperature and strain with a single FBG based on the birefringence effect ,” Opt. Express   12 , 724 – 729 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-724
    [Crossref] [PubMed]
  6. Z. Yihong , E. Simova , P. Berini , and C.P. Grover , “ A comparison of wavelength dependent polarization dependent loss measurements in fiber gratings ,” IEEE Trans. Instrum. Meas.   49 , 1231 – 1239 ( 2000 ).
    [Crossref]
  7. E. Ciaramella , E. Riccardi , and M. Schiano , “ System penalties due to polarisation mode dispersion of chirped gratings ,” in Prooceedings of 24th European Conference on Optical Communication 1 , 20–24 September, Madrid, Spain, 515 – 516 ( 1998 ).
  8. I. Riant , J. Gourhant , and P. Sansonetti , “ Polarization mode dispersion analysis in fibre chromatic dispersion compensators ,” in Prooceedings of Optical Fiber Communication Conference 1 , 21–26 February, 269 – 271 ( 1999 ).
  9. M. Schiano and G. Zaffiro , “ Polarisation mode dispersion in chirped fiber gratings ,” in Proceedings of the 24th European Conference on Optical Communication 1 , 20–24 September, Madrid, Spain, 403 – 404 ( 1998 ).
  10. S. Bonino , M. Norgia , E. Riccardi , and M. Schiano , “ Measurement of polarization properties of chirped fiber gratings ,” in Proceedings of 1997 Optical Fiber Measurement Conference, 29 September - 1 October, Teddington, UK, 10 – 13 ( 1997 ).
  11. S. Bette , C. Caucheteur , M. Wuilpart , O. Deparis , M. Blondel , and P. Mégret , “ Relationship Between Group Delay And Stokes Parameters In Fiber Bragg Gratings ,” in Proceedings of Conference on Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, Sydney, AU, 4–6 July, paper on CD ROM ( 2005 ).
  12. T. Erdogan , “ Fiber Grating Spectra ,” J. Lightwave Technol.   15 , 1277 – 1294 ( 1997 ).
    [Crossref]
  13. M. Yamada and K. Sakuda , “ Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach ,” Appl. Opt.   26 , 3474 – 3478 ( 1987 ).
    [Crossref] [PubMed]
  14. D. Pastor , J. Capmany , D. Ortega , V. Tatay , and J. Marti , “ Design of apodized linearly chirped fiber gratings for dispersion compensation ,” J. Lightwave Technol.   14 , 2581 – 2588 ( 1996 ).
    [Crossref]
  15. F. Lhommé , C. Caucheteur , K. Chah , M. Blondel , and P. Mégret , “ Synthesis of fiber Bragg grating parameters from experimental reflectivity: a simplex approach and its application to the determination of temperature-dependent properties ,” Appl. Opt.   44 , 493 – 497 ( 2005 ).
    [Crossref] [PubMed]
  16. D. Derikson , Fiber optic test and measurement ( Prentice Hall PTR, New Jersey , 1998 ).

2005 (1)

2004 (1)

2000 (1)

Z. Yihong , E. Simova , P. Berini , and C.P. Grover , “ A comparison of wavelength dependent polarization dependent loss measurements in fiber gratings ,” IEEE Trans. Instrum. Meas.   49 , 1231 – 1239 ( 2000 ).
[Crossref]

1997 (2)

T. Erdogan , “ Fiber Grating Spectra ,” J. Lightwave Technol.   15 , 1277 – 1294 ( 1997 ).
[Crossref]

N. Gisin and B. Huttner , “ Combined effects of polarization mode dispersion and polarization dependent losses in optical fibers ,” Opt. Commun.   142 , 119 – 125 ( 1997 ).
[Crossref]

1996 (1)

D. Pastor , J. Capmany , D. Ortega , V. Tatay , and J. Marti , “ Design of apodized linearly chirped fiber gratings for dispersion compensation ,” J. Lightwave Technol.   14 , 2581 – 2588 ( 1996 ).
[Crossref]

1994 (2)

1987 (1)

Berini, P.

Z. Yihong , E. Simova , P. Berini , and C.P. Grover , “ A comparison of wavelength dependent polarization dependent loss measurements in fiber gratings ,” IEEE Trans. Instrum. Meas.   49 , 1231 – 1239 ( 2000 ).
[Crossref]

Bette, S.

S. Bette , C. Caucheteur , M. Wuilpart , O. Deparis , M. Blondel , and P. Mégret , “ Relationship Between Group Delay And Stokes Parameters In Fiber Bragg Gratings ,” in Proceedings of Conference on Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, Sydney, AU, 4–6 July, paper on CD ROM ( 2005 ).

Blondel, M.

F. Lhommé , C. Caucheteur , K. Chah , M. Blondel , and P. Mégret , “ Synthesis of fiber Bragg grating parameters from experimental reflectivity: a simplex approach and its application to the determination of temperature-dependent properties ,” Appl. Opt.   44 , 493 – 497 ( 2005 ).
[Crossref] [PubMed]

S. Bette , C. Caucheteur , M. Wuilpart , O. Deparis , M. Blondel , and P. Mégret , “ Relationship Between Group Delay And Stokes Parameters In Fiber Bragg Gratings ,” in Proceedings of Conference on Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, Sydney, AU, 4–6 July, paper on CD ROM ( 2005 ).

Bonino, S.

S. Bonino , M. Norgia , E. Riccardi , and M. Schiano , “ Measurement of polarization properties of chirped fiber gratings ,” in Proceedings of 1997 Optical Fiber Measurement Conference, 29 September - 1 October, Teddington, UK, 10 – 13 ( 1997 ).

Capmany, J.

D. Pastor , J. Capmany , D. Ortega , V. Tatay , and J. Marti , “ Design of apodized linearly chirped fiber gratings for dispersion compensation ,” J. Lightwave Technol.   14 , 2581 – 2588 ( 1996 ).
[Crossref]

Caucheteur, C.

F. Lhommé , C. Caucheteur , K. Chah , M. Blondel , and P. Mégret , “ Synthesis of fiber Bragg grating parameters from experimental reflectivity: a simplex approach and its application to the determination of temperature-dependent properties ,” Appl. Opt.   44 , 493 – 497 ( 2005 ).
[Crossref] [PubMed]

S. Bette , C. Caucheteur , M. Wuilpart , O. Deparis , M. Blondel , and P. Mégret , “ Relationship Between Group Delay And Stokes Parameters In Fiber Bragg Gratings ,” in Proceedings of Conference on Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, Sydney, AU, 4–6 July, paper on CD ROM ( 2005 ).

Chah, K.

Chung, Y.

Ciaramella, E.

E. Ciaramella , E. Riccardi , and M. Schiano , “ System penalties due to polarisation mode dispersion of chirped gratings ,” in Prooceedings of 24th European Conference on Optical Communication 1 , 20–24 September, Madrid, Spain, 515 – 516 ( 1998 ).

Deparis, O.

S. Bette , C. Caucheteur , M. Wuilpart , O. Deparis , M. Blondel , and P. Mégret , “ Relationship Between Group Delay And Stokes Parameters In Fiber Bragg Gratings ,” in Proceedings of Conference on Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, Sydney, AU, 4–6 July, paper on CD ROM ( 2005 ).

Derikson, D.

D. Derikson , Fiber optic test and measurement ( Prentice Hall PTR, New Jersey , 1998 ).

Erdogan, T.

Gisin, N.

N. Gisin and B. Huttner , “ Combined effects of polarization mode dispersion and polarization dependent losses in optical fibers ,” Opt. Commun.   142 , 119 – 125 ( 1997 ).
[Crossref]

Gourhant, J.

I. Riant , J. Gourhant , and P. Sansonetti , “ Polarization mode dispersion analysis in fibre chromatic dispersion compensators ,” in Prooceedings of Optical Fiber Communication Conference 1 , 21–26 February, 269 – 271 ( 1999 ).

Grover, C.P.

Z. Yihong , E. Simova , P. Berini , and C.P. Grover , “ A comparison of wavelength dependent polarization dependent loss measurements in fiber gratings ,” IEEE Trans. Instrum. Meas.   49 , 1231 – 1239 ( 2000 ).
[Crossref]

Han, W.T.

Huttner, B.

N. Gisin and B. Huttner , “ Combined effects of polarization mode dispersion and polarization dependent losses in optical fibers ,” Opt. Commun.   142 , 119 – 125 ( 1997 ).
[Crossref]

Inniss, D.

Kalli, K.

A. Othonos and K. Kalli , Fiber Bragg gratings: fundamentals and applications in telecommunications and sensing ( Artech House, Norwood, MA , 1999 ).

Kosinski, S. G.

Lemaire, P.

Lhommé, F.

Marti, J.

D. Pastor , J. Capmany , D. Ortega , V. Tatay , and J. Marti , “ Design of apodized linearly chirped fiber gratings for dispersion compensation ,” J. Lightwave Technol.   14 , 2581 – 2588 ( 1996 ).
[Crossref]

Mégret, P.

F. Lhommé , C. Caucheteur , K. Chah , M. Blondel , and P. Mégret , “ Synthesis of fiber Bragg grating parameters from experimental reflectivity: a simplex approach and its application to the determination of temperature-dependent properties ,” Appl. Opt.   44 , 493 – 497 ( 2005 ).
[Crossref] [PubMed]

S. Bette , C. Caucheteur , M. Wuilpart , O. Deparis , M. Blondel , and P. Mégret , “ Relationship Between Group Delay And Stokes Parameters In Fiber Bragg Gratings ,” in Proceedings of Conference on Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, Sydney, AU, 4–6 July, paper on CD ROM ( 2005 ).

Mizrahi, V.

Norgia, M.

S. Bonino , M. Norgia , E. Riccardi , and M. Schiano , “ Measurement of polarization properties of chirped fiber gratings ,” in Proceedings of 1997 Optical Fiber Measurement Conference, 29 September - 1 October, Teddington, UK, 10 – 13 ( 1997 ).

Oh, S.T.

Ortega, D.

D. Pastor , J. Capmany , D. Ortega , V. Tatay , and J. Marti , “ Design of apodized linearly chirped fiber gratings for dispersion compensation ,” J. Lightwave Technol.   14 , 2581 – 2588 ( 1996 ).
[Crossref]

Othonos, A.

A. Othonos and K. Kalli , Fiber Bragg gratings: fundamentals and applications in telecommunications and sensing ( Artech House, Norwood, MA , 1999 ).

Paek, U.C.

Pastor, D.

D. Pastor , J. Capmany , D. Ortega , V. Tatay , and J. Marti , “ Design of apodized linearly chirped fiber gratings for dispersion compensation ,” J. Lightwave Technol.   14 , 2581 – 2588 ( 1996 ).
[Crossref]

Reed, W. A.

Riant, I.

I. Riant , J. Gourhant , and P. Sansonetti , “ Polarization mode dispersion analysis in fibre chromatic dispersion compensators ,” in Prooceedings of Optical Fiber Communication Conference 1 , 21–26 February, 269 – 271 ( 1999 ).

Riccardi, E.

S. Bonino , M. Norgia , E. Riccardi , and M. Schiano , “ Measurement of polarization properties of chirped fiber gratings ,” in Proceedings of 1997 Optical Fiber Measurement Conference, 29 September - 1 October, Teddington, UK, 10 – 13 ( 1997 ).

E. Ciaramella , E. Riccardi , and M. Schiano , “ System penalties due to polarisation mode dispersion of chirped gratings ,” in Prooceedings of 24th European Conference on Optical Communication 1 , 20–24 September, Madrid, Spain, 515 – 516 ( 1998 ).

Sakuda, K.

Sansonetti, P.

I. Riant , J. Gourhant , and P. Sansonetti , “ Polarization mode dispersion analysis in fibre chromatic dispersion compensators ,” in Prooceedings of Optical Fiber Communication Conference 1 , 21–26 February, 269 – 271 ( 1999 ).

Schiano, M.

M. Schiano and G. Zaffiro , “ Polarisation mode dispersion in chirped fiber gratings ,” in Proceedings of the 24th European Conference on Optical Communication 1 , 20–24 September, Madrid, Spain, 403 – 404 ( 1998 ).

E. Ciaramella , E. Riccardi , and M. Schiano , “ System penalties due to polarisation mode dispersion of chirped gratings ,” in Prooceedings of 24th European Conference on Optical Communication 1 , 20–24 September, Madrid, Spain, 515 – 516 ( 1998 ).

S. Bonino , M. Norgia , E. Riccardi , and M. Schiano , “ Measurement of polarization properties of chirped fiber gratings ,” in Proceedings of 1997 Optical Fiber Measurement Conference, 29 September - 1 October, Teddington, UK, 10 – 13 ( 1997 ).

Simova, E.

Z. Yihong , E. Simova , P. Berini , and C.P. Grover , “ A comparison of wavelength dependent polarization dependent loss measurements in fiber gratings ,” IEEE Trans. Instrum. Meas.   49 , 1231 – 1239 ( 2000 ).
[Crossref]

Tatay, V.

D. Pastor , J. Capmany , D. Ortega , V. Tatay , and J. Marti , “ Design of apodized linearly chirped fiber gratings for dispersion compensation ,” J. Lightwave Technol.   14 , 2581 – 2588 ( 1996 ).
[Crossref]

Vengsarkar, A. M.

Wuilpart, M.

S. Bette , C. Caucheteur , M. Wuilpart , O. Deparis , M. Blondel , and P. Mégret , “ Relationship Between Group Delay And Stokes Parameters In Fiber Bragg Gratings ,” in Proceedings of Conference on Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, Sydney, AU, 4–6 July, paper on CD ROM ( 2005 ).

Yamada, M.

Yihong, Z.

Z. Yihong , E. Simova , P. Berini , and C.P. Grover , “ A comparison of wavelength dependent polarization dependent loss measurements in fiber gratings ,” IEEE Trans. Instrum. Meas.   49 , 1231 – 1239 ( 2000 ).
[Crossref]

Zaffiro, G.

M. Schiano and G. Zaffiro , “ Polarisation mode dispersion in chirped fiber gratings ,” in Proceedings of the 24th European Conference on Optical Communication 1 , 20–24 September, Madrid, Spain, 403 – 404 ( 1998 ).

Zhong, Q.

Appl. Opt. (2)

IEEE Trans. Instrum. Meas. (1)

Z. Yihong , E. Simova , P. Berini , and C.P. Grover , “ A comparison of wavelength dependent polarization dependent loss measurements in fiber gratings ,” IEEE Trans. Instrum. Meas.   49 , 1231 – 1239 ( 2000 ).
[Crossref]

J. Lightwave Technol. (2)

D. Pastor , J. Capmany , D. Ortega , V. Tatay , and J. Marti , “ Design of apodized linearly chirped fiber gratings for dispersion compensation ,” J. Lightwave Technol.   14 , 2581 – 2588 ( 1996 ).
[Crossref]

T. Erdogan , “ Fiber Grating Spectra ,” J. Lightwave Technol.   15 , 1277 – 1294 ( 1997 ).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

N. Gisin and B. Huttner , “ Combined effects of polarization mode dispersion and polarization dependent losses in optical fibers ,” Opt. Commun.   142 , 119 – 125 ( 1997 ).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Other (7)

E. Ciaramella , E. Riccardi , and M. Schiano , “ System penalties due to polarisation mode dispersion of chirped gratings ,” in Prooceedings of 24th European Conference on Optical Communication 1 , 20–24 September, Madrid, Spain, 515 – 516 ( 1998 ).

I. Riant , J. Gourhant , and P. Sansonetti , “ Polarization mode dispersion analysis in fibre chromatic dispersion compensators ,” in Prooceedings of Optical Fiber Communication Conference 1 , 21–26 February, 269 – 271 ( 1999 ).

M. Schiano and G. Zaffiro , “ Polarisation mode dispersion in chirped fiber gratings ,” in Proceedings of the 24th European Conference on Optical Communication 1 , 20–24 September, Madrid, Spain, 403 – 404 ( 1998 ).

S. Bonino , M. Norgia , E. Riccardi , and M. Schiano , “ Measurement of polarization properties of chirped fiber gratings ,” in Proceedings of 1997 Optical Fiber Measurement Conference, 29 September - 1 October, Teddington, UK, 10 – 13 ( 1997 ).

S. Bette , C. Caucheteur , M. Wuilpart , O. Deparis , M. Blondel , and P. Mégret , “ Relationship Between Group Delay And Stokes Parameters In Fiber Bragg Gratings ,” in Proceedings of Conference on Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, Sydney, AU, 4–6 July, paper on CD ROM ( 2005 ).

A. Othonos and K. Kalli , Fiber Bragg gratings: fundamentals and applications in telecommunications and sensing ( Artech House, Norwood, MA , 1999 ).

D. Derikson , Fiber optic test and measurement ( Prentice Hall PTR, New Jersey , 1998 ).

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Figures (4)

Fig. 1.
Fig. 1.

Wavelength dependency of DGD and transmission coefficient as a function of Δn

Fig. 2.
Fig. 2.

Wavelength dependency of DGD as a function of L (a) and δn (b)

Fig. 3.
Fig. 3.

Transmission spectrum (a) and wavelength dependency of DGD (b) as a function of the apodization

Fig. 4.
Fig. 4.

Evolution with wavelength of DGD: experimental and simulation results for (a) strong grating and (b) weak grating

Equations (7)

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

n eff , x = n eff + Δn 2 ; n eff , y = n eff Δn 2
E i , x E i , y = M x e j ξ x M y e j ξ y
E t , x E t , y = J . E i , x E i , y = t x M x e j ξ x t y M y e j ξ y with J = t x 0 0 t y
t x ( y ) = j α x ( y ) σ x ( y ) sinh ( α x ( y ) L ) j α x ( y ) cosh ( α x ( y ) L )
τ x ( y ) = n eff , x ( y ) c κ 2 α x ( y ) σ x ( y ) 2 sinh ( α x ( y ) L ) cosh ( α x ( y ) L ) L κ 2 σ x ( y ) 2 cosh 2 ( α x ( y ) L ) 1
Δ τ = Arg ( ρ 1 ρ 2 ) Δω
T ( ω + Δω ) . T 1 ( ω )

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