Abstract

We clarify the relationship between group delay ripple and differential group delay in birefringent, chirped fiber Bragg gratings and relate this information to polarization mode dispersion. We illustrate that a grating can be characterized completely by measuring the grating phase ripple and fiber birefringence with careful selection of measurement system parameters. The impact of these imperfections on device performance as dispersion compensators in optical communications systems is explored with system testbed simulations and measurements.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. M. Schiano and G. Zaffiro, �??Polarisation mode dispersion in chirped fiber gratings,�?? in proceedings of the 24th European Conference on Optical Communication, Madrid, Spain, 20-24 September 1998, 403-404.
  2. T. Erdogan and V. Mizrahi, �??Characterization of UV induced birefringence in photosensitive Ge-doped silica optical fiber ,�?? J. Opt. Soc. Am. B 11, 2100-2105 (Oct. 1994).
    [CrossRef]
  3. O. Duhem and M. Douay, �??Effect of UV-induced birefringence on long-period grating coupling characteristics,�?? Electron. Lett. 36, 416-417 (Mar. 2000).
    [CrossRef]
  4. J. Albert, F. Bilodeau, D. C. Johnson, K.O. Hill, S.J. Mihailov, D. Stryckman, T. Kitagawa, and Y. Hibino, �??Polarisation-independent strong Bragg gratings in planar lightwave circuits,�?? Electron. Lett. 34, 485-486 (Mar. 1998).
    [CrossRef]
  5. 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 (OFMC �??97), Teddington, UK, 29 September �?? 1 October 1997, 10-13.
  6. L. Berthelot, J. Gourhant, I. Riant, P. Sansonetti, �??Vectorial model of Bragg gratings,�?? Electron. Lett. 36, 744-745 (April 2000).
    [CrossRef]
  7. E. Ciaramella, E. Riccardi, and M. Schiano, �??System penalties due to polarisation mode dispersion of chirped gratings,�?? in 24th European Conference on Optical Communication, 20-24 September 1998, Madrid, Spain, 515-516 (1998).
  8. L. C. B. Linares, A. O. Dal Forno, and J. P. von der Weid, �??Polarimetric measurements of PMD and differential group delay ripple in chirped fiber Bragg gratings,�?? Microwave Opt. Technol. Lett. 34, 270-3 (Aug. 2002).
    [CrossRef]
  9. LE Nelson, RM Jopson, H Kogelnik, and GJ Foschini, �??Measurement of depolarization and scaling associated with second-order polarization mode dispersion in optical fibers,�?? Photon. Tech. Letters 11(12), 1614-1616 (December 1999).
    [CrossRef]
  10. M. Eiselt, C. B. Clausen, and R. W. Tkach, �??Performance characterization of components with group delay fluctuations,�?? Photon. Tech. Lett. 15, 1076-1078 (2003). Also in proceedings of the Symposium on Optical Fiber Measurements (NIST, Boulder, CO, 2002), Session III.
    [CrossRef]
  11. X Fan and J F Brennan III, �??Performance effect in optical communication systems caused by phase ripple of dispersive components,�?? Appl. Opt. 43 (26), 5033- 5036 (2004).
    [CrossRef] [PubMed]
  12. P. A. Williams, �??Modulation phase-shift measurement of PMD using only four launched polarization states: a new algorithm,�?? Electron. Lett. 35, 1578-1579 (September 1999).
    [CrossRef]
  13. T. Niemi, M. Uusimma, and H. Ludvigsen, �??Limitations of phase-shift method in measuring dense group delay ripple of fiber Bragg gratings�??, Photon. Technol. Lett. 13, 1334-1336 (December 2001).
    [CrossRef]
  14. JF Brennan III, MR Matthews, WV Dower, DJ Treadwell, W Wang, J Porque, & X Fan, �??Dispersion correction with a robust fiber grating over the full C-band at 10 Gb/s rates with <0.3-dB power penalties�??, Photon. Technol. Lett. 15 (12), 1722-4 (December 2003).
    [CrossRef]
  15. G. P. Agrawal, Nonlinear fiber optics. (Academic Press, 1995), Chap 7.
  16. D. Marcuse, �??Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers,�?? J. Lightwave Technol. 8, 1816-1823 (December 1990).
    [CrossRef]
  17. C Scheerer, C Glingener, G Fischer, M Bohn, and W Rosenkranz, �??Influence of filter delay ripples on system performance,�?? in proceedings of 1999 European Conference on Optical Communication, Nice, France, Volume I, 410-411 (1999)
  18. M. R. Matthews, J. Porque, C. D. Hoyle, M. J. Vos, and T. L. Smith,"Simple model of errors in chirped fiber gratings," Opt. Express 12, 189-197 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-189">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-189</a>
    [CrossRef] [PubMed]

24th ECOC 1998

M. Schiano and G. Zaffiro, �??Polarisation mode dispersion in chirped fiber gratings,�?? in proceedings of the 24th European Conference on Optical Communication, Madrid, Spain, 20-24 September 1998, 403-404.

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

Appl. Opt.

ECOC 1999

C Scheerer, C Glingener, G Fischer, M Bohn, and W Rosenkranz, �??Influence of filter delay ripples on system performance,�?? in proceedings of 1999 European Conference on Optical Communication, Nice, France, Volume I, 410-411 (1999)

Electron. Lett.

P. A. Williams, �??Modulation phase-shift measurement of PMD using only four launched polarization states: a new algorithm,�?? Electron. Lett. 35, 1578-1579 (September 1999).
[CrossRef]

L. Berthelot, J. Gourhant, I. Riant, P. Sansonetti, �??Vectorial model of Bragg gratings,�?? Electron. Lett. 36, 744-745 (April 2000).
[CrossRef]

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

J. Albert, F. Bilodeau, D. C. Johnson, K.O. Hill, S.J. Mihailov, D. Stryckman, T. Kitagawa, and Y. Hibino, �??Polarisation-independent strong Bragg gratings in planar lightwave circuits,�?? Electron. Lett. 34, 485-486 (Mar. 1998).
[CrossRef]

J. Lightwave Technol.

D. Marcuse, �??Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers,�?? J. Lightwave Technol. 8, 1816-1823 (December 1990).
[CrossRef]

J. Opt. Soc. Am. B =

T. Erdogan and V. Mizrahi, �??Characterization of UV induced birefringence in photosensitive Ge-doped silica optical fiber ,�?? J. Opt. Soc. Am. B 11, 2100-2105 (Oct. 1994).
[CrossRef]

Microwave Opt. Technol. Lett.

L. C. B. Linares, A. O. Dal Forno, and J. P. von der Weid, �??Polarimetric measurements of PMD and differential group delay ripple in chirped fiber Bragg gratings,�?? Microwave Opt. Technol. Lett. 34, 270-3 (Aug. 2002).
[CrossRef]

OFMC 1997

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 (OFMC �??97), Teddington, UK, 29 September �?? 1 October 1997, 10-13.

Opt. Express

Photon. Tech. Lett.

M. Eiselt, C. B. Clausen, and R. W. Tkach, �??Performance characterization of components with group delay fluctuations,�?? Photon. Tech. Lett. 15, 1076-1078 (2003). Also in proceedings of the Symposium on Optical Fiber Measurements (NIST, Boulder, CO, 2002), Session III.
[CrossRef]

Photon. Tech. Letters

LE Nelson, RM Jopson, H Kogelnik, and GJ Foschini, �??Measurement of depolarization and scaling associated with second-order polarization mode dispersion in optical fibers,�?? Photon. Tech. Letters 11(12), 1614-1616 (December 1999).
[CrossRef]

Photon. Technol. Lett.

T. Niemi, M. Uusimma, and H. Ludvigsen, �??Limitations of phase-shift method in measuring dense group delay ripple of fiber Bragg gratings�??, Photon. Technol. Lett. 13, 1334-1336 (December 2001).
[CrossRef]

JF Brennan III, MR Matthews, WV Dower, DJ Treadwell, W Wang, J Porque, & X Fan, �??Dispersion correction with a robust fiber grating over the full C-band at 10 Gb/s rates with <0.3-dB power penalties�??, Photon. Technol. Lett. 15 (12), 1722-4 (December 2003).
[CrossRef]

Other

G. P. Agrawal, Nonlinear fiber optics. (Academic Press, 1995), Chap 7.

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 (9)

Fig. 1.
Fig. 1.

(a) Low-bandwidth measurement of DGD across the bandwidth of a chirped fiber grating in reflection. The thick line corresponds to a 20 GHz moving-window average. (b) The corresponding position of the PMD vector in Poincaré space. The solid diamond is the angle θ on the sphere horizontal plane; the open square, the azimuth angle φ. (c) Q-penalty due to the grating in a 10 Gb/s communications system. Error bars indicate the penalty variation with launch polarization at each wavelength.

Fig. 2.
Fig. 2.

Orientation of the PMD vector across the bandwidth of the grating in Poincaré space.

Fig. 3.
Fig. 3.

GDR along each birefringent axes of a grating (upper curves), and the lower curve is the difference between them, i.e. DGD with sign.

Fig. 4.
Fig. 4.

The angles θ and φ (a) and magnitude (b) of the 1st-order PMD vector in Poincaré space measured with high-frequency MPS methods. The thick line in (b) is the 1st-order PMD calculated with the fiber birefringence and grating dispersion.

Fig. 5.
Fig. 5.

Comparison of PMD measurements made with MPS (black solid line) and Jones eigen-analysis (grey dashed line) methods when care is taken to use equivalent bandwidths.

Fig. 6.
Fig. 6.

Grating DGD measured with the MPS method at a 10 GHz modulation frequency (diamond demarcated line) compared with that calculated by taking the vector average of the data in Fig. 1(a)

Fig. 7.
Fig. 7.

Simulations of pulse distortion when the PMD is modeled as a vector, the input pulse (solid line) is not distorted after propagating through the grating (open circles), but the pulse is distorted significantly when the scalar average is used (filled circles).

Fig. 8.
Fig. 8.

Pulse width within the original time slot as a function of the ripple frequency normalized to the standard deviation of the pulse spectrum.

Fig. 9.
Fig. 9.

(a) Simulations of Q-penalty induced by rapidly varying DGD when the input signal polarization is aligned with X (solid line) or Y birefringence axis (dotted line). (b) Penalty variation when the polarization alignment of the input signal changes gradually from the X to the Y birefringence axis. The penalty offset is caused by noise added to the simulations.

Equations (18)

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

ϕ x ( ω ) = β x · L x ( ω ) = n x ω c · L x ( ω ) ,
2 · ( n + Δ n ) Λ 2 · n · Λ = λ + Δ λ λ = ω ω + Δ ω
Δ n n = Δ λ λ Δ ω ω .
ϕ y ( ω ) = n y ω c · L y ( ω ) = ( n x + Δ n ) ω c · L x ( ω + Δ ω )
= ( n x + Δ n ) · ω c · { L x ( ω ) + Δ ω · L ˙ x ( ω ) + 1 2 Δ ω 2 · L ̈ x ( ω ) + }
= ϕ x ( ω ) + Δ ϕ
Δ ϕ Δ n · ω c · L x ( ω ) + ( n x + Δ n ) · ω c · { Δ ω · L ˙ x ( ω ) + 1 2 Δ ω 2 · L x ̈ ( ω ) + }
Δ n · ω c · L x ( ω ) + ( n x + Δ n ) · ω c · Δ L ( ω )
ϕ y ( ω ) = ( n x + Δ n n x ) · ( ω ω + Δ ω ) · ϕ x ( ω + Δ ω )
= ( n x + Δ n n x ) 2 · ϕ x ( ω + Δ ω )
ϕ y ( ω ) ϕ x ( ω + Δ ω )
t g = L v g L · ( β ω ) ,
Δ t Δ n c · L x ( ω ) + n x c · Δ L ( ω ) ,
Δ t ω Δ n c · L ˙ x ( ω ) + n x c · Δ L ˙ ( ω ) .
e i ϕ x ( ω ) [ 1 0 0 e i Δ ϕ ] [ e i ϕ x R ( ω ) 0 0 e i ϕ x R ( ω + Δ ω ) ] ,
e i { ϕ x ( ω ) + ϕ x R ( ω ) } [ 1 0 0 e i { Δ ϕ + Δ ϕ R } ]
DGD ( ω ) D · Δ λ + GDR x ( ω + Δ ω ) GDR x ( ω ) ,
Ω Δ τ x ( ω ) · i ̂ x + Δ τ y ( ω ) · i ̂ y + Δ τ z ( ω ) · i ̂ z

Metrics