Abstract

We examine both theoretically and experimentally rapid polarization transients generated by mechanical impacts on dispersion compensation modules (DCMs). In our experiments, the transient response of the output polarization to sudden mechanical impacts is found to remain constant among successive measurements. That is, the Stokes vector traces the same path over the Poincaré sphere provided that the interval of time between measurements is less than the time associated with the slow thermal drift of the fiber birefringence profile. Experimentally we can measure angular velocities (AVs) of the Stokes vector over the Poincaré sphere exceeding 100krads. We demonstrate theoretically with a simple model for the excitation that the patterns of the AV observed in experiments can be reproduced through simulation and that the amplitude of the AV increases with the volume of the fiber affected by the impact. Our model is sufficiently simple to be employed in system simulations.

© 2010 Optical Society of America

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References

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  1. N. G. Walker and G. R. Walker, “Polarization control for coherent communications,” J. Lightwave Technol. 8, 438–458 (1990).
    [CrossRef]
  2. B. Koch, A. Hidayat, H. Zhang, V. Mirvoda, M. Lichtinger, D. Sandel, and R. Noe, “Optical endless polarization stabilization at 9 krad∕s with FPGA based controller,” IEEE Photonics Technol. Lett. 20, 961–963, (2008).
    [CrossRef]
  3. P. Krummrich and K. Kotten, “Extremely fast (microsecond timescale) polarization changes in high-speed long haul WDM transmission systems,” in Optical Fiber Communication Conference ’04 Technical Digest (2004), vol. 2, paper OWI40.
  4. M. Reimer, D. Dumas, G. Soliman, D. Yevick, and M. O’Sullivan, “Polarization evolution in polarization compensation modules,” In Optical Fiber Communication Conference ’09 Technical Digest (2004), paper OWD4.
  5. K. Roberts, M. O’Sullivan, K. Wu, H. Sun, A. Awadalla, D. J. Krauss, and Charles Laperle, “Performance of dual-polarization QPSK for optical transport systems,” J. Lightwave Technol. 27, 3546–3559, (2009).
    [CrossRef]
  6. J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization-mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. , 97, 4541, (2000).
    [CrossRef] [PubMed]
  7. W. Shieh and H. Kogelnik, “Dynamic eigenstates of polarization,” IEEE Photon. Technol. Lett. 13, 40–42 (2001).
    [CrossRef]
  8. P. K. A. Wai and C. R. Menyuk, “Polarization decorrelation in optical fibers with randomly varying birefringence,” Opt. Lett. 19, pp. 1517–1519, (1994).
    [CrossRef] [PubMed]
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    [CrossRef]
  11. Karl E. Graff, Wave Motion in Elastic Solids (Dover, 1975), Chaps. 2, 3.
  12. B. M. Beadle and J. Jarzynski, “Measurement of speed and attenuation of longitudinal elastic waves in optical fibers,” Opt. Eng. 40, 2115–2119 (2001).
    [CrossRef]
  13. C.-L. Shen, Foundations for Guided Wave Optics (Wiley, 2007), Chap. 11.
  14. R. Ulrich, S. C. Rashleigh and W. Eickhoff, “Bending-induced birefringence in single mode fibers,” Opt. Lett. 5, 273–275 (1980).
    [CrossRef] [PubMed]
  15. A. Galtarossa, L. Palmieri, M. Schiano and T. Tambosso, “Measurements of beat length and perturbation length in long single mode fibers,” Opt. Lett. 25, 384–386 (2000).
    [CrossRef]

2009 (1)

2008 (1)

B. Koch, A. Hidayat, H. Zhang, V. Mirvoda, M. Lichtinger, D. Sandel, and R. Noe, “Optical endless polarization stabilization at 9 krad∕s with FPGA based controller,” IEEE Photonics Technol. Lett. 20, 961–963, (2008).
[CrossRef]

2007 (1)

C.-L. Shen, Foundations for Guided Wave Optics (Wiley, 2007), Chap. 11.

2005 (1)

Jay N. Damask, Polarization Optics in Telecommunications (Springer, 2005), Chap. 9, p. 391.

2004 (2)

P. Krummrich and K. Kotten, “Extremely fast (microsecond timescale) polarization changes in high-speed long haul WDM transmission systems,” in Optical Fiber Communication Conference ’04 Technical Digest (2004), vol. 2, paper OWI40.

M. Reimer, D. Dumas, G. Soliman, D. Yevick, and M. O’Sullivan, “Polarization evolution in polarization compensation modules,” In Optical Fiber Communication Conference ’09 Technical Digest (2004), paper OWD4.

2001 (2)

B. M. Beadle and J. Jarzynski, “Measurement of speed and attenuation of longitudinal elastic waves in optical fibers,” Opt. Eng. 40, 2115–2119 (2001).
[CrossRef]

W. Shieh and H. Kogelnik, “Dynamic eigenstates of polarization,” IEEE Photon. Technol. Lett. 13, 40–42 (2001).
[CrossRef]

2000 (2)

A. Galtarossa, L. Palmieri, M. Schiano and T. Tambosso, “Measurements of beat length and perturbation length in long single mode fibers,” Opt. Lett. 25, 384–386 (2000).
[CrossRef]

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization-mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. , 97, 4541, (2000).
[CrossRef] [PubMed]

1994 (1)

1990 (1)

N. G. Walker and G. R. Walker, “Polarization control for coherent communications,” J. Lightwave Technol. 8, 438–458 (1990).
[CrossRef]

1988 (1)

H. E. Engan, B. Y. Kim, J. N. Blake, and H. J. Shaw, “Propagation and optical interaction of guided acoustic waves in two-mode optical fibers,” J. Lightwave Technol. 6, 428–436 (1988).
[CrossRef]

1980 (1)

1975 (1)

Karl E. Graff, Wave Motion in Elastic Solids (Dover, 1975), Chaps. 2, 3.

Awadalla, A.

Beadle, B. M.

B. M. Beadle and J. Jarzynski, “Measurement of speed and attenuation of longitudinal elastic waves in optical fibers,” Opt. Eng. 40, 2115–2119 (2001).
[CrossRef]

Blake, J. N.

H. E. Engan, B. Y. Kim, J. N. Blake, and H. J. Shaw, “Propagation and optical interaction of guided acoustic waves in two-mode optical fibers,” J. Lightwave Technol. 6, 428–436 (1988).
[CrossRef]

Damask, Jay N.

Jay N. Damask, Polarization Optics in Telecommunications (Springer, 2005), Chap. 9, p. 391.

Dumas, D.

M. Reimer, D. Dumas, G. Soliman, D. Yevick, and M. O’Sullivan, “Polarization evolution in polarization compensation modules,” In Optical Fiber Communication Conference ’09 Technical Digest (2004), paper OWD4.

Eickhoff, W.

Engan, H. E.

H. E. Engan, B. Y. Kim, J. N. Blake, and H. J. Shaw, “Propagation and optical interaction of guided acoustic waves in two-mode optical fibers,” J. Lightwave Technol. 6, 428–436 (1988).
[CrossRef]

Galtarossa, A.

Gordon, J. P.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization-mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. , 97, 4541, (2000).
[CrossRef] [PubMed]

Graff, Karl E.

Karl E. Graff, Wave Motion in Elastic Solids (Dover, 1975), Chaps. 2, 3.

Hidayat, A.

B. Koch, A. Hidayat, H. Zhang, V. Mirvoda, M. Lichtinger, D. Sandel, and R. Noe, “Optical endless polarization stabilization at 9 krad∕s with FPGA based controller,” IEEE Photonics Technol. Lett. 20, 961–963, (2008).
[CrossRef]

Jarzynski, J.

B. M. Beadle and J. Jarzynski, “Measurement of speed and attenuation of longitudinal elastic waves in optical fibers,” Opt. Eng. 40, 2115–2119 (2001).
[CrossRef]

Kim, B. Y.

H. E. Engan, B. Y. Kim, J. N. Blake, and H. J. Shaw, “Propagation and optical interaction of guided acoustic waves in two-mode optical fibers,” J. Lightwave Technol. 6, 428–436 (1988).
[CrossRef]

Koch, B.

B. Koch, A. Hidayat, H. Zhang, V. Mirvoda, M. Lichtinger, D. Sandel, and R. Noe, “Optical endless polarization stabilization at 9 krad∕s with FPGA based controller,” IEEE Photonics Technol. Lett. 20, 961–963, (2008).
[CrossRef]

Kogelnik, H.

W. Shieh and H. Kogelnik, “Dynamic eigenstates of polarization,” IEEE Photon. Technol. Lett. 13, 40–42 (2001).
[CrossRef]

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization-mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. , 97, 4541, (2000).
[CrossRef] [PubMed]

Kotten, K.

P. Krummrich and K. Kotten, “Extremely fast (microsecond timescale) polarization changes in high-speed long haul WDM transmission systems,” in Optical Fiber Communication Conference ’04 Technical Digest (2004), vol. 2, paper OWI40.

Krauss, D. J.

Krummrich, P.

P. Krummrich and K. Kotten, “Extremely fast (microsecond timescale) polarization changes in high-speed long haul WDM transmission systems,” in Optical Fiber Communication Conference ’04 Technical Digest (2004), vol. 2, paper OWI40.

Laperle, Charles

Lichtinger, M.

B. Koch, A. Hidayat, H. Zhang, V. Mirvoda, M. Lichtinger, D. Sandel, and R. Noe, “Optical endless polarization stabilization at 9 krad∕s with FPGA based controller,” IEEE Photonics Technol. Lett. 20, 961–963, (2008).
[CrossRef]

Menyuk, C. R.

Mirvoda, V.

B. Koch, A. Hidayat, H. Zhang, V. Mirvoda, M. Lichtinger, D. Sandel, and R. Noe, “Optical endless polarization stabilization at 9 krad∕s with FPGA based controller,” IEEE Photonics Technol. Lett. 20, 961–963, (2008).
[CrossRef]

Noe, R.

B. Koch, A. Hidayat, H. Zhang, V. Mirvoda, M. Lichtinger, D. Sandel, and R. Noe, “Optical endless polarization stabilization at 9 krad∕s with FPGA based controller,” IEEE Photonics Technol. Lett. 20, 961–963, (2008).
[CrossRef]

O’Sullivan, M.

K. Roberts, M. O’Sullivan, K. Wu, H. Sun, A. Awadalla, D. J. Krauss, and Charles Laperle, “Performance of dual-polarization QPSK for optical transport systems,” J. Lightwave Technol. 27, 3546–3559, (2009).
[CrossRef]

M. Reimer, D. Dumas, G. Soliman, D. Yevick, and M. O’Sullivan, “Polarization evolution in polarization compensation modules,” In Optical Fiber Communication Conference ’09 Technical Digest (2004), paper OWD4.

Palmieri, L.

Rashleigh, S. C.

Reimer, M.

M. Reimer, D. Dumas, G. Soliman, D. Yevick, and M. O’Sullivan, “Polarization evolution in polarization compensation modules,” In Optical Fiber Communication Conference ’09 Technical Digest (2004), paper OWD4.

Roberts, K.

Sandel, D.

B. Koch, A. Hidayat, H. Zhang, V. Mirvoda, M. Lichtinger, D. Sandel, and R. Noe, “Optical endless polarization stabilization at 9 krad∕s with FPGA based controller,” IEEE Photonics Technol. Lett. 20, 961–963, (2008).
[CrossRef]

Schiano, M.

Shaw, H. J.

H. E. Engan, B. Y. Kim, J. N. Blake, and H. J. Shaw, “Propagation and optical interaction of guided acoustic waves in two-mode optical fibers,” J. Lightwave Technol. 6, 428–436 (1988).
[CrossRef]

Shen, C.-L.

C.-L. Shen, Foundations for Guided Wave Optics (Wiley, 2007), Chap. 11.

Shieh, W.

W. Shieh and H. Kogelnik, “Dynamic eigenstates of polarization,” IEEE Photon. Technol. Lett. 13, 40–42 (2001).
[CrossRef]

Soliman, G.

M. Reimer, D. Dumas, G. Soliman, D. Yevick, and M. O’Sullivan, “Polarization evolution in polarization compensation modules,” In Optical Fiber Communication Conference ’09 Technical Digest (2004), paper OWD4.

Sun, H.

Tambosso, T.

Ulrich, R.

Wai, P. K. A.

Walker, G. R.

N. G. Walker and G. R. Walker, “Polarization control for coherent communications,” J. Lightwave Technol. 8, 438–458 (1990).
[CrossRef]

Walker, N. G.

N. G. Walker and G. R. Walker, “Polarization control for coherent communications,” J. Lightwave Technol. 8, 438–458 (1990).
[CrossRef]

Wu, K.

Yevick, D.

M. Reimer, D. Dumas, G. Soliman, D. Yevick, and M. O’Sullivan, “Polarization evolution in polarization compensation modules,” In Optical Fiber Communication Conference ’09 Technical Digest (2004), paper OWD4.

Zhang, H.

B. Koch, A. Hidayat, H. Zhang, V. Mirvoda, M. Lichtinger, D. Sandel, and R. Noe, “Optical endless polarization stabilization at 9 krad∕s with FPGA based controller,” IEEE Photonics Technol. Lett. 20, 961–963, (2008).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

W. Shieh and H. Kogelnik, “Dynamic eigenstates of polarization,” IEEE Photon. Technol. Lett. 13, 40–42 (2001).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

B. Koch, A. Hidayat, H. Zhang, V. Mirvoda, M. Lichtinger, D. Sandel, and R. Noe, “Optical endless polarization stabilization at 9 krad∕s with FPGA based controller,” IEEE Photonics Technol. Lett. 20, 961–963, (2008).
[CrossRef]

J. Lightwave Technol. (3)

H. E. Engan, B. Y. Kim, J. N. Blake, and H. J. Shaw, “Propagation and optical interaction of guided acoustic waves in two-mode optical fibers,” J. Lightwave Technol. 6, 428–436 (1988).
[CrossRef]

N. G. Walker and G. R. Walker, “Polarization control for coherent communications,” J. Lightwave Technol. 8, 438–458 (1990).
[CrossRef]

K. Roberts, M. O’Sullivan, K. Wu, H. Sun, A. Awadalla, D. J. Krauss, and Charles Laperle, “Performance of dual-polarization QPSK for optical transport systems,” J. Lightwave Technol. 27, 3546–3559, (2009).
[CrossRef]

Opt. Eng. (1)

B. M. Beadle and J. Jarzynski, “Measurement of speed and attenuation of longitudinal elastic waves in optical fibers,” Opt. Eng. 40, 2115–2119 (2001).
[CrossRef]

Opt. Lett. (3)

Proc. Natl. Acad. Sci. (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization-mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. , 97, 4541, (2000).
[CrossRef] [PubMed]

Other (5)

C.-L. Shen, Foundations for Guided Wave Optics (Wiley, 2007), Chap. 11.

Karl E. Graff, Wave Motion in Elastic Solids (Dover, 1975), Chaps. 2, 3.

P. Krummrich and K. Kotten, “Extremely fast (microsecond timescale) polarization changes in high-speed long haul WDM transmission systems,” in Optical Fiber Communication Conference ’04 Technical Digest (2004), vol. 2, paper OWI40.

M. Reimer, D. Dumas, G. Soliman, D. Yevick, and M. O’Sullivan, “Polarization evolution in polarization compensation modules,” In Optical Fiber Communication Conference ’09 Technical Digest (2004), paper OWD4.

Jay N. Damask, Polarization Optics in Telecommunications (Springer, 2005), Chap. 9, p. 391.

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Figures (16)

Fig. 1
Fig. 1

In our experiments, a steel ball is secured and later released onto a DCM by an electromagnet generating fast polarization changes. The acoustic signal from the impact is detected by a microphone and employed to trigger the scope, which then samples the output from a fast polarimeter.

Fig. 2
Fig. 2

Different impact positions on the DCM as follows: points 1–4 are located 1.5 cm , 3 cm , 4.5 cm , and 6 cm from the inner core. Points 6 and 8 and 10 and 12 are at the same radial distances as points 2 and 4 but displaced at 45° and 90° angles.

Fig. 3
Fig. 3

Ten successive measurements of the S 1 component. The inset displays the region from 0.7 ms to 0.74 ms showing the individual measurement curves.

Fig. 4
Fig. 4

Mean squared error versus drop height for different DCMs for impact location 1. The error is largest for a height of 9 cm .

Fig. 5
Fig. 5

Geometry of the DCM. Our model assumes that the steel ball impacts a certain area of the DCM, resulting in the oscillation of the fiber coils beneath it. Here R in = 5.25 cm and R out = 12.4 cm . H = 4 cm .

Fig. 6
Fig. 6

AV for DCM10 with impact location 1 and release height 3 cm .

Fig. 7
Fig. 7

AV for DCM20 with impact location 1 and release height 3 cm .

Fig. 8
Fig. 8

AV for DCM40 with impact location 1 and release height 3 cm .

Fig. 9
Fig. 9

AV for DCM100 with impact location 1 and release height 3 cm .

Fig. 10
Fig. 10

Time dependence of the simulated birefringence. The behavior in the first 5 ms generates the largest AV.

Fig. 11
Fig. 11

Simulated AV of fiber B for an active length of 600 m , z i 1 = 100 m .

Fig. 12
Fig. 12

Simulated AV for fiber B, for active length equal to the total fiber length.

Fig. 13
Fig. 13

S parameters for fiber C with an active length of 20 m and z i 1 = 200 m . The fluctuations are clearly very small compared to the experimental measurements (Fig. 3).

Fig. 14
Fig. 14

Dependence of the arc length on the angular velocity for different lengths of fiber B.

Fig. 15
Fig. 15

Dependence of the experimental arc length on the angular velocity for DCM10 with a ball release height of 9 cm .

Fig. 16
Fig. 16

Experimental arc length for impact location 1, a release height of 9 cm , and different DCM structures.

Equations (13)

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

d s ̂ ( z , t ) d z = β ( z , t ) × s ̂ ( z , t ) .
ω × = d R d t R T
ω ( z , t ) z = β t + ω ( z , t ) × β .
d β i d z = β i L c + g ( z ) , i = x , y ,
δ β ( z , t ) = 5.11 × 10 5 ( a cl r ) 2 1.8 × 10 6 a cl r u z ( z , t ) z .
δ β ( z , t ) = 1.8 × 10 6 a cl r u z ( z , t ) z .
u z = q ( t ) F ( z ) = q ( t ) sin ( 2 π z λ ) W ( z ) = q ( t ) sin ( 2 π z λ ) ( tanh ( z z i 1 ) tanh ( z z i 2 ) ) 2 ,
2 f z 2 = 1 v g 2 2 f t 2 + b f t ,
q ̈ + 2 ξ ω o q ̇ + ω o 2 q = 0 ,
r ( z ) = R 1 + ( R 2 R 1 ) L z .
β = ( β x ( z ) β p β y ( z ) 0 ) .
β p = 5.11 × 10 5 ( a cl r ) 2 + 1.8 × 10 6 A ( e α 1 t e α 2 t ) a cl r F z ,
a l ( ω o ) = o T | ω | θ ( | ω | ω o ) d t ,

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