Abstract

The simple structure of a tunable polarization mode dispersion (PMD) compensator based on a cantilever beam and a high-birefringence linearly chirped fiber Bragg grating is proposed. A cantilever structure is used to introduce a linear strain gradient on the grating, and we can tune the compensated differential group delay (DGD) at a fixed signal wavelength just by changing the displacement at the free end of the beam. Based on numerical simulations, the performance of the cantilever structure as a PMD compensator is assessed for 10-Gbits/s nonreturn-to-zero transmission systems with a large DGD. With this compensator, a significant improvement of system performance can be achieved in the eye pattern of a received signal.

© 2003 Optical Society of America

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References

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  1. C. D. Poole, R. W. Tkach, A. R. Chraplyvy, and D. A. Fishman, �??Fading in lightwave systems due to polarization-mode dispersion,�?? IEEE Photon. Technol. Lett. 3, 68�??70 (1991).
    [CrossRef]
  2. B. W. Hakki, �??Polarization mode dispersion in single mode fiber,�?? J. Lightwave Technol. 14, 2202�??2208 (1996).
    [CrossRef]
  3. D. Penninckx and S. Lanne, �??Reducing PMD impairments,�?? in Optical Fiber Communication Conference, (Optical Society of America, Washington, D.C., 2001), TUP1, pp. 1�??4.
  4. F. Heismann, D. A. Fishman, and D. L. Wilson, �??Automatic compensation of first order polarization mode dispersion in a 10 Gb/s transmission system,�?? in European Conference on Optical Communication, Madrid, Spain, 1998, pp. 529�??530.
  5. R. Noe, D. Sandel, M. Yoshida-Dierolf, S. Hinz, V. Mirvoda, A. Schopflin, C. Gungener, E. Gottwald, C. Scheerer, G. Fischer, T. Weyrauch, and W. Haase, �??Polarization mode dispersion compensation at 10, 20, and 40 Gb/s with various optical equalizers,�?? J. Lightwave Technol. 17, 1602 �??1616 (1999).
    [CrossRef]
  6. S. Lee, R. Khosravani, J. Peng, A. E. Willner, V. Grubsky, D. S. Starodubov, and J. Feinberg, �??Highbirefringence nonlinearly-chirped fiber Bragg grating for tunable compensation of polarization mode dispersion,�?? in Optical Fiber Communication Conference, OSA 1999 Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 272 �??274.
  7. K. M. Feng, J. X. Cai, V. Grubsky, D. S. Starodubov, M. I. Hayee, S. Lee, A. E. Willner, and J. Feiberg, �??Dynamic dispersion compensation in a 10-Gb/s optical system using a novel voltage tuned nonlinearly chirped fiber Bragg grating,�?? IEEE Photon. Technol. Lett. 11, 373�??375 (1999).
    [CrossRef]
  8. A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, �??Fiber grating sensors,�?? J. Lightwave Technol. 15, 1442�??1461 (1997).
    [CrossRef]
  9. D. Roylance, Mechanics of Materials (Wiley, New York, 1996).
  10. D. Garthe, R. E. Epworth, W. S. Lee, A. Hadjifotiou, C. P. Chew, T. Bricheno, A. Fielding, H. N. Rourke, S. R. Baker, K. C. Byron, R. S. Baulcomb, S. M. Ohja, and S. Clements, �??Adjustable dispersion equalizer for 10 and 20 Gbit/s over distances up to 160 km,�?? Electron. Lett. 30, 2159�??2160 (1994).
    [CrossRef]
  11. T. Erdogan, �??Fiber grating spectra,�?? J. Lightwave Technol. 15, 1277�??1294 (1997).
    [CrossRef]
  12. M. Yamada and K. Sakuda, �??Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach,�?? Appl. Opt. 26, 3474�??3478 (1987).
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  13. W. Du, X. Tao, and H. Tam, �??Fiber Bragg grating cavity sensor for simultaneous measurement of strain and temperature,�?? IEEE Photon. Technol. Lett. 11, 105-107 (1999).
    [CrossRef]
  14. D. Marcuse, C. R. Manyuk, and P. K. A. Wai, �??Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,�?? J. Lightwave Technol. 15, 1735 �??1746 (1997)
    [CrossRef]
  15. S. R. Desbruslais and P. R. Morkel, �??Simulation of polarization mode dispersion and its effects in long-haul optically amplified lightwave systems,�?? IEE Colloquium on International Transmission System, 6.1-6.6 (1994).

Appl. Opt. (1)

Electron. Lett. (1)

D. Garthe, R. E. Epworth, W. S. Lee, A. Hadjifotiou, C. P. Chew, T. Bricheno, A. Fielding, H. N. Rourke, S. R. Baker, K. C. Byron, R. S. Baulcomb, S. M. Ohja, and S. Clements, �??Adjustable dispersion equalizer for 10 and 20 Gbit/s over distances up to 160 km,�?? Electron. Lett. 30, 2159�??2160 (1994).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

K. M. Feng, J. X. Cai, V. Grubsky, D. S. Starodubov, M. I. Hayee, S. Lee, A. E. Willner, and J. Feiberg, �??Dynamic dispersion compensation in a 10-Gb/s optical system using a novel voltage tuned nonlinearly chirped fiber Bragg grating,�?? IEEE Photon. Technol. Lett. 11, 373�??375 (1999).
[CrossRef]

C. D. Poole, R. W. Tkach, A. R. Chraplyvy, and D. A. Fishman, �??Fading in lightwave systems due to polarization-mode dispersion,�?? IEEE Photon. Technol. Lett. 3, 68�??70 (1991).
[CrossRef]

W. Du, X. Tao, and H. Tam, �??Fiber Bragg grating cavity sensor for simultaneous measurement of strain and temperature,�?? IEEE Photon. Technol. Lett. 11, 105-107 (1999).
[CrossRef]

J. Lightwave Technol. (5)

D. Marcuse, C. R. Manyuk, and P. K. A. Wai, �??Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,�?? J. Lightwave Technol. 15, 1735 �??1746 (1997)
[CrossRef]

R. Noe, D. Sandel, M. Yoshida-Dierolf, S. Hinz, V. Mirvoda, A. Schopflin, C. Gungener, E. Gottwald, C. Scheerer, G. Fischer, T. Weyrauch, and W. Haase, �??Polarization mode dispersion compensation at 10, 20, and 40 Gb/s with various optical equalizers,�?? J. Lightwave Technol. 17, 1602 �??1616 (1999).
[CrossRef]

B. W. Hakki, �??Polarization mode dispersion in single mode fiber,�?? J. Lightwave Technol. 14, 2202�??2208 (1996).
[CrossRef]

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, �??Fiber grating sensors,�?? J. Lightwave Technol. 15, 1442�??1461 (1997).
[CrossRef]

T. Erdogan, �??Fiber grating spectra,�?? J. Lightwave Technol. 15, 1277�??1294 (1997).
[CrossRef]

OFC (1)

S. Lee, R. Khosravani, J. Peng, A. E. Willner, V. Grubsky, D. S. Starodubov, and J. Feinberg, �??Highbirefringence nonlinearly-chirped fiber Bragg grating for tunable compensation of polarization mode dispersion,�?? in Optical Fiber Communication Conference, OSA 1999 Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 272 �??274.

Optical Fiber Communication Conference (1)

D. Penninckx and S. Lanne, �??Reducing PMD impairments,�?? in Optical Fiber Communication Conference, (Optical Society of America, Washington, D.C., 2001), TUP1, pp. 1�??4.

Other (3)

F. Heismann, D. A. Fishman, and D. L. Wilson, �??Automatic compensation of first order polarization mode dispersion in a 10 Gb/s transmission system,�?? in European Conference on Optical Communication, Madrid, Spain, 1998, pp. 529�??530.

D. Roylance, Mechanics of Materials (Wiley, New York, 1996).

S. R. Desbruslais and P. R. Morkel, �??Simulation of polarization mode dispersion and its effects in long-haul optically amplified lightwave systems,�?? IEE Colloquium on International Transmission System, 6.1-6.6 (1994).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Schematic diagram of the proposed strain gradient-induced cantilever structure. (b) Schematic structure of the Hi-Bi linearly chirped FBG. The reflected signal is introduced as a DGD between the ‘s’ (along the slow axis) and the ‘f’ (along the fast axis) polarization components.

Fig. 2.
Fig. 2.

Calculated (a) reflection spectra and (b) group delay curves under different conditions, Y=0 mm, 1 mm and 2 mm respectively. Solid line: fast axis; dotted line: slow axis. (c) DGD between two polarization axes of Hi-Bi nonlinearly chirped FBG as a function of displacement Y at a given signal wavelength λ 0=1550 nm.

Fig. 3.
Fig. 3.

Setup of the system simulation model to validate the effectiveness of the proposed PMD compensator, Hi-Bi linearly chirped FBG.

Fig. 4.
Fig. 4.

Eye diagrams of the 10-Gbits/s NRZ system model: (a) transmitter output; the received signal after 400-km transmission with PMD=0 ps; (b) DGD=40 ps (c) before and (d) after compensation; DGD=108 ps (e) before and (f) after compensation by use of the proposed PMD compensator.

Fig. 5
Fig. 5

EOP distribution (a) before and (b) after PMD compensation with a mean DGD of 60 ps

Fig. 6
Fig. 6

EOP at a probability of 10-3 in dependence of the mean DGD.

Tables (1)

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Table. 1 Parameters of the fibers

Equations (13)

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Λ ( z , ε ( z ) ) = ( Λ 0 + c 0 · z ) ( 1 + ε ( z ) ) ,
d n eff ( z ) n eff = ρ e · ε ( z ) ,
λ ( z ) = 2 n eff [ ( Λ 0 + c 0 z ) + ( Λ 0 + c 0 z ) ( 1 ρ e ) ε ( z ) ] .
ε ( z ) = 3 ( L z ) h Y ( 2 L 3 ) .
[ E j 1 + E j 1 ] = T ( j ) [ E j + E j ] = [ T 1 ( j ) T 2 ( j ) T 2 ( j ) * T 1 ( j ) * ] [ E j + E j ] ,
T 1 ( j ) = cosh ( γ Δ z ) i σ ̂ γ sinh ( γ Δ z ) ,
T 2 ( j ) = i κ γ sinh ( γ Δ z ) ,
γ = κ 2 σ ̂ 2 ,
σ ̂ = δ + 2 π λ δn ¯ eff 1 2 d φ ( z ) dz , κ = π λ δn ¯ eff ν g ( z ) ,
d φ ( z ) dz = 2 π z Λ 0 2 d Λ dz .
[ E 0 + E 0 ] = T ( 1 ) T ( 2 ) T ( j ) T ( M ) [ E M + E M ] = [ T 1 T 2 T 2 * T 1 * ] [ E M + E M ] .
DGD ( λ ) = G D s ( λ ) G D f ( λ )
EOP = 10 log ( B B 0 ) ,

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