Abstract

We employ a modified version of the multicanonical algorithm to evaluate the system penalties and outage probabilities of different polarization-mode dispersion compensators. The procedure determines the optimal operating conditions for each compensator architecture far more efficiently than the standard Monte Carlo algorithm.

© 2005 Optical Society of America

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References

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  1. D. Yevick, “Multicanonical communication system modeling—application to PMD statistics,” IEEE Photon. Technol. Lett. 14, 1512–1514 (2002).
    [CrossRef]
  2. D. Yevick, “The accuracy of multicanonical system models,” IEEE Photon. Technol. Lett. 15, 224–226 (2003).
    [CrossRef]
  3. D. Yevick, “Multicanonical evaluation of joint probability density functions in communication system modeling,” IEEE Photon. Technol. Lett. 15, 1540–1542 (2003).
    [CrossRef]
  4. D. Yevick, W. Bardyszewski, “A random walk procedure for evaluating probability distribution functions in communication systems,” IEEE Photon. Technol. Lett. 16, 108–110 (2004).
    [CrossRef]
  5. T. Lu, D. O. Yevick, L. Yan, B. Zhang, A. E. Willner, “An experimental approach to multicanonical sampling,” IEEE Photon. Technol. Lett. 16, 1978–1980 (2004).
    [CrossRef]
  6. I. Kaminow and T. Li, eds., Systems and Impairments, Vol. IVB of Optical Fiber Telecommunications (Academic, 2002).
  7. J. N. Damask, G. Gray, P. Leo, G. Simer, K. Rochford, D. Veasey, “Method to measure and estimate total outage probability for PMD-impaired systems,” IEEE Photon. Technol. Lett. 15, 48–50 (2003).
    [CrossRef]
  8. Q. Yu, L.-S. Yan, Y. Xie, M. Hauer, A. E. Willner, “Higher order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay,” IEEE Photon. Technol. Lett. 13, 863–865 (2001).
    [CrossRef]
  9. D. O. Yevick, M. Chanachowicz, M. Reimer, M. O’Sullivan, W. Huang, T. Lu, “Chebyshev and Taylor approximations of polarization mode dispersion for improved compensation bandwidth,” J. Opt. Soc. Am. A 22, 1662–1667 (2005).
    [CrossRef]
  10. A. Eyal, W. K. Marshall, M. Tur, A. Yariv, “Representation of second-order polarization mode dispersion,” Electron. Lett. 35, 1658–1659 (1999).
    [CrossRef]
  11. T. Lu, D. O. Yevick, “Efficient multicanonical algorithms,” IEEE Photon. Technol. Lett. 17, 861–863 (2005).
    [CrossRef]
  12. B. A. Berg, “Introduction to multicanonical Monte Carlo simulations,” Fields Inst. Commun. 26, 1–24 (2000).

2005

2004

D. Yevick, W. Bardyszewski, “A random walk procedure for evaluating probability distribution functions in communication systems,” IEEE Photon. Technol. Lett. 16, 108–110 (2004).
[CrossRef]

T. Lu, D. O. Yevick, L. Yan, B. Zhang, A. E. Willner, “An experimental approach to multicanonical sampling,” IEEE Photon. Technol. Lett. 16, 1978–1980 (2004).
[CrossRef]

2003

J. N. Damask, G. Gray, P. Leo, G. Simer, K. Rochford, D. Veasey, “Method to measure and estimate total outage probability for PMD-impaired systems,” IEEE Photon. Technol. Lett. 15, 48–50 (2003).
[CrossRef]

D. Yevick, “The accuracy of multicanonical system models,” IEEE Photon. Technol. Lett. 15, 224–226 (2003).
[CrossRef]

D. Yevick, “Multicanonical evaluation of joint probability density functions in communication system modeling,” IEEE Photon. Technol. Lett. 15, 1540–1542 (2003).
[CrossRef]

2002

D. Yevick, “Multicanonical communication system modeling—application to PMD statistics,” IEEE Photon. Technol. Lett. 14, 1512–1514 (2002).
[CrossRef]

2001

Q. Yu, L.-S. Yan, Y. Xie, M. Hauer, A. E. Willner, “Higher order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay,” IEEE Photon. Technol. Lett. 13, 863–865 (2001).
[CrossRef]

2000

B. A. Berg, “Introduction to multicanonical Monte Carlo simulations,” Fields Inst. Commun. 26, 1–24 (2000).

1999

A. Eyal, W. K. Marshall, M. Tur, A. Yariv, “Representation of second-order polarization mode dispersion,” Electron. Lett. 35, 1658–1659 (1999).
[CrossRef]

Bardyszewski, W.

D. Yevick, W. Bardyszewski, “A random walk procedure for evaluating probability distribution functions in communication systems,” IEEE Photon. Technol. Lett. 16, 108–110 (2004).
[CrossRef]

Berg, B. A.

B. A. Berg, “Introduction to multicanonical Monte Carlo simulations,” Fields Inst. Commun. 26, 1–24 (2000).

Chanachowicz, M.

Damask, J. N.

J. N. Damask, G. Gray, P. Leo, G. Simer, K. Rochford, D. Veasey, “Method to measure and estimate total outage probability for PMD-impaired systems,” IEEE Photon. Technol. Lett. 15, 48–50 (2003).
[CrossRef]

Eyal, A.

A. Eyal, W. K. Marshall, M. Tur, A. Yariv, “Representation of second-order polarization mode dispersion,” Electron. Lett. 35, 1658–1659 (1999).
[CrossRef]

Gray, G.

J. N. Damask, G. Gray, P. Leo, G. Simer, K. Rochford, D. Veasey, “Method to measure and estimate total outage probability for PMD-impaired systems,” IEEE Photon. Technol. Lett. 15, 48–50 (2003).
[CrossRef]

Hauer, M.

Q. Yu, L.-S. Yan, Y. Xie, M. Hauer, A. E. Willner, “Higher order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay,” IEEE Photon. Technol. Lett. 13, 863–865 (2001).
[CrossRef]

Huang, W.

Leo, P.

J. N. Damask, G. Gray, P. Leo, G. Simer, K. Rochford, D. Veasey, “Method to measure and estimate total outage probability for PMD-impaired systems,” IEEE Photon. Technol. Lett. 15, 48–50 (2003).
[CrossRef]

Lu, T.

D. O. Yevick, M. Chanachowicz, M. Reimer, M. O’Sullivan, W. Huang, T. Lu, “Chebyshev and Taylor approximations of polarization mode dispersion for improved compensation bandwidth,” J. Opt. Soc. Am. A 22, 1662–1667 (2005).
[CrossRef]

T. Lu, D. O. Yevick, “Efficient multicanonical algorithms,” IEEE Photon. Technol. Lett. 17, 861–863 (2005).
[CrossRef]

T. Lu, D. O. Yevick, L. Yan, B. Zhang, A. E. Willner, “An experimental approach to multicanonical sampling,” IEEE Photon. Technol. Lett. 16, 1978–1980 (2004).
[CrossRef]

Marshall, W. K.

A. Eyal, W. K. Marshall, M. Tur, A. Yariv, “Representation of second-order polarization mode dispersion,” Electron. Lett. 35, 1658–1659 (1999).
[CrossRef]

O’Sullivan, M.

Reimer, M.

Rochford, K.

J. N. Damask, G. Gray, P. Leo, G. Simer, K. Rochford, D. Veasey, “Method to measure and estimate total outage probability for PMD-impaired systems,” IEEE Photon. Technol. Lett. 15, 48–50 (2003).
[CrossRef]

Simer, G.

J. N. Damask, G. Gray, P. Leo, G. Simer, K. Rochford, D. Veasey, “Method to measure and estimate total outage probability for PMD-impaired systems,” IEEE Photon. Technol. Lett. 15, 48–50 (2003).
[CrossRef]

Tur, M.

A. Eyal, W. K. Marshall, M. Tur, A. Yariv, “Representation of second-order polarization mode dispersion,” Electron. Lett. 35, 1658–1659 (1999).
[CrossRef]

Veasey, D.

J. N. Damask, G. Gray, P. Leo, G. Simer, K. Rochford, D. Veasey, “Method to measure and estimate total outage probability for PMD-impaired systems,” IEEE Photon. Technol. Lett. 15, 48–50 (2003).
[CrossRef]

Willner, A. E.

T. Lu, D. O. Yevick, L. Yan, B. Zhang, A. E. Willner, “An experimental approach to multicanonical sampling,” IEEE Photon. Technol. Lett. 16, 1978–1980 (2004).
[CrossRef]

Q. Yu, L.-S. Yan, Y. Xie, M. Hauer, A. E. Willner, “Higher order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay,” IEEE Photon. Technol. Lett. 13, 863–865 (2001).
[CrossRef]

Xie, Y.

Q. Yu, L.-S. Yan, Y. Xie, M. Hauer, A. E. Willner, “Higher order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay,” IEEE Photon. Technol. Lett. 13, 863–865 (2001).
[CrossRef]

Yan, L.

T. Lu, D. O. Yevick, L. Yan, B. Zhang, A. E. Willner, “An experimental approach to multicanonical sampling,” IEEE Photon. Technol. Lett. 16, 1978–1980 (2004).
[CrossRef]

Yan, L.-S.

Q. Yu, L.-S. Yan, Y. Xie, M. Hauer, A. E. Willner, “Higher order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay,” IEEE Photon. Technol. Lett. 13, 863–865 (2001).
[CrossRef]

Yariv, A.

A. Eyal, W. K. Marshall, M. Tur, A. Yariv, “Representation of second-order polarization mode dispersion,” Electron. Lett. 35, 1658–1659 (1999).
[CrossRef]

Yevick, D.

D. Yevick, W. Bardyszewski, “A random walk procedure for evaluating probability distribution functions in communication systems,” IEEE Photon. Technol. Lett. 16, 108–110 (2004).
[CrossRef]

D. Yevick, “The accuracy of multicanonical system models,” IEEE Photon. Technol. Lett. 15, 224–226 (2003).
[CrossRef]

D. Yevick, “Multicanonical evaluation of joint probability density functions in communication system modeling,” IEEE Photon. Technol. Lett. 15, 1540–1542 (2003).
[CrossRef]

D. Yevick, “Multicanonical communication system modeling—application to PMD statistics,” IEEE Photon. Technol. Lett. 14, 1512–1514 (2002).
[CrossRef]

Yevick, D. O.

T. Lu, D. O. Yevick, “Efficient multicanonical algorithms,” IEEE Photon. Technol. Lett. 17, 861–863 (2005).
[CrossRef]

D. O. Yevick, M. Chanachowicz, M. Reimer, M. O’Sullivan, W. Huang, T. Lu, “Chebyshev and Taylor approximations of polarization mode dispersion for improved compensation bandwidth,” J. Opt. Soc. Am. A 22, 1662–1667 (2005).
[CrossRef]

T. Lu, D. O. Yevick, L. Yan, B. Zhang, A. E. Willner, “An experimental approach to multicanonical sampling,” IEEE Photon. Technol. Lett. 16, 1978–1980 (2004).
[CrossRef]

Yu, Q.

Q. Yu, L.-S. Yan, Y. Xie, M. Hauer, A. E. Willner, “Higher order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay,” IEEE Photon. Technol. Lett. 13, 863–865 (2001).
[CrossRef]

Zhang, B.

T. Lu, D. O. Yevick, L. Yan, B. Zhang, A. E. Willner, “An experimental approach to multicanonical sampling,” IEEE Photon. Technol. Lett. 16, 1978–1980 (2004).
[CrossRef]

Electron. Lett.

A. Eyal, W. K. Marshall, M. Tur, A. Yariv, “Representation of second-order polarization mode dispersion,” Electron. Lett. 35, 1658–1659 (1999).
[CrossRef]

Fields Inst. Commun.

B. A. Berg, “Introduction to multicanonical Monte Carlo simulations,” Fields Inst. Commun. 26, 1–24 (2000).

IEEE Photon. Technol. Lett.

T. Lu, D. O. Yevick, “Efficient multicanonical algorithms,” IEEE Photon. Technol. Lett. 17, 861–863 (2005).
[CrossRef]

J. N. Damask, G. Gray, P. Leo, G. Simer, K. Rochford, D. Veasey, “Method to measure and estimate total outage probability for PMD-impaired systems,” IEEE Photon. Technol. Lett. 15, 48–50 (2003).
[CrossRef]

Q. Yu, L.-S. Yan, Y. Xie, M. Hauer, A. E. Willner, “Higher order polarization mode dispersion compensation using a fixed time delay followed by a variable time delay,” IEEE Photon. Technol. Lett. 13, 863–865 (2001).
[CrossRef]

D. Yevick, “Multicanonical communication system modeling—application to PMD statistics,” IEEE Photon. Technol. Lett. 14, 1512–1514 (2002).
[CrossRef]

D. Yevick, “The accuracy of multicanonical system models,” IEEE Photon. Technol. Lett. 15, 224–226 (2003).
[CrossRef]

D. Yevick, “Multicanonical evaluation of joint probability density functions in communication system modeling,” IEEE Photon. Technol. Lett. 15, 1540–1542 (2003).
[CrossRef]

D. Yevick, W. Bardyszewski, “A random walk procedure for evaluating probability distribution functions in communication systems,” IEEE Photon. Technol. Lett. 16, 108–110 (2004).
[CrossRef]

T. Lu, D. O. Yevick, L. Yan, B. Zhang, A. E. Willner, “An experimental approach to multicanonical sampling,” IEEE Photon. Technol. Lett. 16, 1978–1980 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Other

I. Kaminow and T. Li, eds., Systems and Impairments, Vol. IVB of Optical Fiber Telecommunications (Academic, 2002).

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Figures (8)

Fig. 1
Fig. 1

pdf of the eye opening penalty calculated with the Monte Carlo (solid curve), standard multicanonical (dashed–dotted curve), and modified multicanonical (dashed curve) procedures in the absence of PMD compensation.

Fig. 2
Fig. 2

Eye diagram of the output signals generated by a 50 section PMD emulator for (A) no, (B) asymmetric Taylor,[10] (C) Chebyshev, and (D) symmetric Taylor compensation.

Fig. 3
Fig. 3

Average eye opening penalty as a joint function of the uncompensated first- and second-order normalized PMD for the output signals generated by a 50 section PMD emulator with (A) no, (B) Chebyshev, (C) symmetric Taylor, and (D) asymmetric Taylor[10] compensation.

Fig. 4
Fig. 4

Same as Fig. 3 but for the conditional 1 dB outage probability.

Fig. 5
Fig. 5

As in Fig. 3 but for the 1 dB outage probability density.

Fig. 6
Fig. 6

pdf of the eye opening penalty predicted by the modified multicanonical method for no (solid curve), second-order asymmetric Taylor[10] (dashed–dotted curve), Chebyshev (dashed curve), and modified Taylor (dotted curve) compensation.

Fig. 7
Fig. 7

As in Fig. 6 but for the system outage probability as a function of system penalty in dBQ computed with the modified multicanonical method.

Fig. 8
Fig. 8

System outage probability as a function of eye opening penalty in decibels for a 10 Gbits s RZ signal with no (solid curve) and Chebyshev (dashed curve) compensation.

Equations (15)

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q I ¯ 1 I ¯ 0 σ 1 + σ 0 ,
BER ( q ) = 1 2 [ 1 erf ( q 2 ) ] .
Δ q = 10 log 10 ( q out q b 2 b ) ,
p outage ( Δ q th ) = Δ q th p ( Δ q ) d Δ q
T ( ω 0 + Δ ω ) = T ( ω 0 ) exp ( N 1 Δ ω ) exp [ N 2 ( Δ ω ) 2 2 ! ] exp [ N 3 ( Δ ω ) 3 3 ! ] exp [ N 4 ( Δ ω ) 4 4 ! ]
N 1 = T 1 ( ω 0 ) T ( 1 ) ( ω 0 ) ,
N 2 = T 1 ( ω 0 ) T ( 2 ) ( ω 0 ) N 1 2 ,
N 3 = T 1 ( ω 0 ) T ( 3 ) ( ω 0 ) N 1 3 3 N 1 N 2 ,
N 4 = T 1 ( ω 0 ) T ( 4 ) ( ω 0 ) N 1 4 3 N 2 2 4 N 1 N 3 6 N 1 2 N 2 ,
T ( ω 0 + Δ ω ) = exp ( S 0 Δ ω 2 ) exp [ S 1 ( Δ ω ) 2 2 ] exp ( S 0 Δ ω 2 ) T ( ω 0 ) + O ( Δ ω 3 ) ,
S 0 = T ( 1 ) ( ω 0 ) T 1 ( ω 0 ) ,
S 1 = T ( 2 ) ( ω 0 ) T 1 ( ω 0 ) S 0 2 ,
S 2 = T ( 3 ) ( ω 0 ) T 1 ( ω 0 ) 1.5 ( S 1 S 0 + S 0 S 1 ) S 0 3 .
T 1 ( ω ) = 1 2 C 0 P 0 ( Δ ω ) + C 1 P 1 ( Δ ω ) + C 2 P 2 ( Δ ω ) + + C M 1 P M 1 ( Δ ω ) ,
y ¯ n α = σ n , 0 2 y ¯ n 1 α + σ n 1 2 y ¯ n , 0 α σ n 1 2 + σ n , 0 2

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