Abstract

Coherent optical orthogonal frequency-division multiplexed (OFDM) systems must be carefully designed to minimize the detrimental impact of fiber nonlinearity manifested through four-wave mixing (FWM). Because of the small subcarrier spacing associated with OFDM, a significant fraction of FWM processes is well matched, resulting in a rapid buildup of FWM light with propagation distance. In this paper, we consider optical phase conjugation (OPC) as an approach to suppress such well-matched FWM processes. An analytical formula accurately predicting the degree of suppression is derived and discussed. It is shown that when combined with the methods previously proposed in the literature, the application of OPC can dramatically reduce the overall FWM power accumulated within the link for a wide range of crucial design parameters.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. J. Lowery, S. Wang, M. Premaratne, “Calculation of power limit due to fiber nonlinearity in optical OFDM systems,” Opt. Express, vol. 15, no. 20, pp. 13282–13287, Oct. 2007.
    [CrossRef] [PubMed]
  2. M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, I. Shpantzer, V. Karagodsky, “Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links,” Opt. Express, vol. 16, no. 20, pp. 15777–15810, Sept. 2008.
    [CrossRef] [PubMed]
  3. W. Qiu, S. Yu, J. Zhang, J. Shen, W. Li, H. Guo, W. Gu, “The nonlinear impairments due to the data correlation among sub-carriers in coherent optical OFDM systems,” J. Lightwave Technol., vol. 27, no. 23, pp. 5321–5326, Dec. 2009.
    [CrossRef]
  4. B. Goebel, B. Fesl, L. D. Coelho, N. Hanik, “On the effect of FWM in coherent optical OFDM systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf., San Diego, CA, 2008, paper JWA58.
  5. V. Pechenkin, I. J. Fair, “Correlation between peak-to-average power ratio and four-wave mixing in optical OFDM systems,” J. Opt. Commun. Netw., vol. 1, no. 7, pp. 636–644, Dec. 2009.
    [CrossRef]
  6. A. J. Lowery, “Fiber nonlinearity pre- and post-compensation for long-haul optical links using OFDM,” Opt. Express, vol. 15, no. 20, pp. 12965–12970, Oct. 2007.
    [CrossRef] [PubMed]
  7. A. J. Lowery, “Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation,” IEEE Photon. Technol. Lett., vol. 19, no. 19, pp. 1556–1558, Oct. 2007.
    [CrossRef]
  8. R. Weidenfeld, M. Nazarathy, R. Noe, I. Shpantzer, “Volterra nonlinear compensation of 112 Gb∕s ultra-long-haul coherent optical OFDM based on frequency-shaped decision feedback,” in 35th European Conf. on Optical Communication, Vienna, Austria, 2009.
  9. L. Du, A. Lowery, “Compensating XPM for 100 Gbit∕s coherent channels with 10 Gbit∕s direct-detection NRZ neighbors,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf., San Diego, CA, 2010, paper OTuE7.
  10. L. B. Du, A. J. Lowery, “Improved nonlinearity precompensation for long-haul high-data-rate transmission using coherent optical OFDM,” Opt. Express, vol. 16, no. 24, pp. 19920–19925, Nov. 2008.
    [CrossRef] [PubMed]
  11. G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed.Wiley, 2002.
    [CrossRef]
  12. A. Yariv, D. Fekete, D. M. Pepper, “Compensation for channel dispersion by nonlinear optical phase conjugation,” Opt. Lett., vol. 4, no. 2, pp. 52–54, Feb. 1979.
    [CrossRef] [PubMed]
  13. K. Inoue, “Phase-mismatching characteristic of four-wave mixing in fiber lines with multistage optical amplifiers,” Opt. Lett., vol. 17, no. 11, pp. 801–803, June 1992.
    [CrossRef] [PubMed]
  14. D. G. Schadt, “Effect of amplifier spacing on four-wave mixing in multichannel coherent communications,” Electron. Lett., vol. 27, no. 20, pp. 1805–1807, Sept. 1991.
    [CrossRef]
  15. S. Watanabe, “Cancellation of four-wave mixing in a single-mode fiber by midway optical phase conjugation,” Opt. Lett., vol. 19, no. 17, pp. 1308–1310, Sept. 1994.
    [CrossRef] [PubMed]
  16. A. Pizzinat, A. Schiffini, F. Alberti, A. N. Pinto, P. Almeida, “40-Gb∕s systems on G.652 fibers: comparison between periodic and all-at-the-end dispersion compensation,” J. Lightwave Technol., vol. 20, no. 9, pp. 1673–1679, Sept. 2002.
    [CrossRef]
  17. K. Inoue, H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol., vol. 13, no. 1, pp. 88–93, Jan. 1995.
    [CrossRef]

2009 (2)

2008 (2)

2007 (3)

2002 (1)

1995 (1)

K. Inoue, H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol., vol. 13, no. 1, pp. 88–93, Jan. 1995.
[CrossRef]

1994 (1)

1992 (1)

1991 (1)

D. G. Schadt, “Effect of amplifier spacing on four-wave mixing in multichannel coherent communications,” Electron. Lett., vol. 27, no. 20, pp. 1805–1807, Sept. 1991.
[CrossRef]

1979 (1)

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed.Wiley, 2002.
[CrossRef]

Alberti, F.

Almeida, P.

Cho, P.

Coelho, L. D.

B. Goebel, B. Fesl, L. D. Coelho, N. Hanik, “On the effect of FWM in coherent optical OFDM systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf., San Diego, CA, 2008, paper JWA58.

Du, L.

L. Du, A. Lowery, “Compensating XPM for 100 Gbit∕s coherent channels with 10 Gbit∕s direct-detection NRZ neighbors,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf., San Diego, CA, 2010, paper OTuE7.

Du, L. B.

Fair, I. J.

Fekete, D.

Fesl, B.

B. Goebel, B. Fesl, L. D. Coelho, N. Hanik, “On the effect of FWM in coherent optical OFDM systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf., San Diego, CA, 2008, paper JWA58.

Goebel, B.

B. Goebel, B. Fesl, L. D. Coelho, N. Hanik, “On the effect of FWM in coherent optical OFDM systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf., San Diego, CA, 2008, paper JWA58.

Gu, W.

Guo, H.

Hanik, N.

B. Goebel, B. Fesl, L. D. Coelho, N. Hanik, “On the effect of FWM in coherent optical OFDM systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf., San Diego, CA, 2008, paper JWA58.

Inoue, K.

K. Inoue, H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol., vol. 13, no. 1, pp. 88–93, Jan. 1995.
[CrossRef]

K. Inoue, “Phase-mismatching characteristic of four-wave mixing in fiber lines with multistage optical amplifiers,” Opt. Lett., vol. 17, no. 11, pp. 801–803, June 1992.
[CrossRef] [PubMed]

Karagodsky, V.

Khurgin, J.

Li, W.

Lowery, A.

L. Du, A. Lowery, “Compensating XPM for 100 Gbit∕s coherent channels with 10 Gbit∕s direct-detection NRZ neighbors,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf., San Diego, CA, 2010, paper OTuE7.

Lowery, A. J.

Meiman, Y.

Nazarathy, M.

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, I. Shpantzer, V. Karagodsky, “Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links,” Opt. Express, vol. 16, no. 20, pp. 15777–15810, Sept. 2008.
[CrossRef] [PubMed]

R. Weidenfeld, M. Nazarathy, R. Noe, I. Shpantzer, “Volterra nonlinear compensation of 112 Gb∕s ultra-long-haul coherent optical OFDM based on frequency-shaped decision feedback,” in 35th European Conf. on Optical Communication, Vienna, Austria, 2009.

Noe, R.

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, I. Shpantzer, V. Karagodsky, “Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links,” Opt. Express, vol. 16, no. 20, pp. 15777–15810, Sept. 2008.
[CrossRef] [PubMed]

R. Weidenfeld, M. Nazarathy, R. Noe, I. Shpantzer, “Volterra nonlinear compensation of 112 Gb∕s ultra-long-haul coherent optical OFDM based on frequency-shaped decision feedback,” in 35th European Conf. on Optical Communication, Vienna, Austria, 2009.

Pechenkin, V.

Pepper, D. M.

Pinto, A. N.

Pizzinat, A.

Premaratne, M.

Qiu, W.

Schadt, D. G.

D. G. Schadt, “Effect of amplifier spacing on four-wave mixing in multichannel coherent communications,” Electron. Lett., vol. 27, no. 20, pp. 1805–1807, Sept. 1991.
[CrossRef]

Schiffini, A.

Shen, J.

Shpantzer, I.

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, I. Shpantzer, V. Karagodsky, “Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links,” Opt. Express, vol. 16, no. 20, pp. 15777–15810, Sept. 2008.
[CrossRef] [PubMed]

R. Weidenfeld, M. Nazarathy, R. Noe, I. Shpantzer, “Volterra nonlinear compensation of 112 Gb∕s ultra-long-haul coherent optical OFDM based on frequency-shaped decision feedback,” in 35th European Conf. on Optical Communication, Vienna, Austria, 2009.

Toba, H.

K. Inoue, H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol., vol. 13, no. 1, pp. 88–93, Jan. 1995.
[CrossRef]

Wang, S.

Watanabe, S.

Weidenfeld, R.

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, I. Shpantzer, V. Karagodsky, “Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links,” Opt. Express, vol. 16, no. 20, pp. 15777–15810, Sept. 2008.
[CrossRef] [PubMed]

R. Weidenfeld, M. Nazarathy, R. Noe, I. Shpantzer, “Volterra nonlinear compensation of 112 Gb∕s ultra-long-haul coherent optical OFDM based on frequency-shaped decision feedback,” in 35th European Conf. on Optical Communication, Vienna, Austria, 2009.

Yariv, A.

Yu, S.

Zhang, J.

Electron. Lett. (1)

D. G. Schadt, “Effect of amplifier spacing on four-wave mixing in multichannel coherent communications,” Electron. Lett., vol. 27, no. 20, pp. 1805–1807, Sept. 1991.
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. J. Lowery, “Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation,” IEEE Photon. Technol. Lett., vol. 19, no. 19, pp. 1556–1558, Oct. 2007.
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Commun. Netw. (1)

Opt. Express (4)

Opt. Lett. (3)

Other (4)

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed.Wiley, 2002.
[CrossRef]

B. Goebel, B. Fesl, L. D. Coelho, N. Hanik, “On the effect of FWM in coherent optical OFDM systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf., San Diego, CA, 2008, paper JWA58.

R. Weidenfeld, M. Nazarathy, R. Noe, I. Shpantzer, “Volterra nonlinear compensation of 112 Gb∕s ultra-long-haul coherent optical OFDM based on frequency-shaped decision feedback,” in 35th European Conf. on Optical Communication, Vienna, Austria, 2009.

L. Du, A. Lowery, “Compensating XPM for 100 Gbit∕s coherent channels with 10 Gbit∕s direct-detection NRZ neighbors,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf., San Diego, CA, 2010, paper OTuE7.

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 (17)

Fig. 1
Fig. 1

Two-span NEL | C klm | 2 normalized with respect to L eff as a function of the phase mismatch coefficient Δ β klm . The quantity | 2 L klm | 2 L eff 2 characterizing the pure PA setup is also displayed.

Fig. 2
Fig. 2

FWM suppression factor comparison. D klm is sampled at the major and minor maxima of F klm in Eq. (7).

Fig. 3
Fig. 3

Zoomed-in version of Fig. 2 showing the ripples of the array factor F klm in the vicinity of Δ β klm = 0 .

Fig. 4
Fig. 4

Suppression factor when Δ β klm is very close to 0.

Fig. 5
Fig. 5

Distribution of the phase mismatch coefficient Δ β klm .

Fig. 6
Fig. 6

Theoretical FWM power distribution across the OFDM spectrum.

Fig. 7
Fig. 7

Simulated FWM power distribution across the OFDM spectrum (averaged over 6000 simulated OFDM symbols).

Fig. 8
Fig. 8

Two-span NEL | C klm | 2 normalized with respect to L eff as a function of the phase mismatch coefficient Δ β klm . Normalized two-span NEL for the OPC-based system is also shown for comparison.

Fig. 9
Fig. 9

FWM suppression factor comparison. D klm is sampled at the major and minor maxima of F klm in Eq. (7).

Fig. 10
Fig. 10

Theoretical FWM power distribution across the OFDM spectrum.

Fig. 11
Fig. 11

Simulated FWM power distribution across the OFDM spectrum (averaged over 6000 simulated OFDM symbols).

Fig. 12
Fig. 12

FWM power as a function of Δ f sc for different dispersion compensation approaches.

Fig. 13
Fig. 13

Difference in FWM power between the OPC-based system and the other approaches in Fig. 12.

Fig. 14
Fig. 14

FWM power as a function of the span length L s for different dispersion compensation approaches.

Fig. 15
Fig. 15

Difference in FWM power between the OPC-based system and the other approaches in Fig. 14.

Fig. 16
Fig. 16

Average FWM power per subcarrier as a function of the transmission distance. The OPC module is located after the 43rd span, and the total number of spans is 86.

Fig. 17
Fig. 17

Average FWM power per subcarrier as a function of the transmission distance. The OPC module is located after the 43rd span, and the total number of spans is 129.

Tables (1)

Tables Icon

Table 1 OFDM System Parameters

Equations (28)

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

V n ( 1 ) ( 1 ) = i γ U k ( 0 ) U l ( 0 ) U m * ( 0 ) e i β n L s L klm .
L klm = 1 e ( α + i Δ β klm ) L s α + i Δ β klm
Δ β klm = β m + β n β k β l .
Δ β klm = β 2 ( 2 π Δ f sc ) 2 ( k m ) ( l m ) .
U k ( 1 ) = U k ( 0 ) e i β k L s .
V n ( 2 ) ( 2 ) = i γ U k ( 1 ) U l ( 1 ) U m * ( 1 ) e i β n L s L klm = i γ U k ( 0 ) U l ( 0 ) U m * ( 0 ) e i ( β k + β l β m ) L s e i β n L s L klm .
V n ( 2 ) ( 2 ) = i γ U k ( 0 ) U l ( 0 ) U m * ( 0 ) e i 2 β n L s e i Δ β klm L s L klm .
V n ( r ) ( r ) = i γ U k ( r 1 ) U l ( r 1 ) U m * ( r 1 ) e i β n L s L klm = i γ U k ( 0 ) U l ( 0 ) U m * ( 0 ) e i β n r L s e i Δ β klm ( r 1 ) L s L klm .
V n ( r ) ( N ) = i γ U k ( 0 ) U l ( 0 ) U m * ( 0 ) e i β n L e i Δ β klm ( r 1 ) L s L klm .
W n ( + ) ( N ) = r = 1 N V n ( r ) ( N ) = i γ U k ( 0 ) U l ( 0 ) U m * ( 0 ) e i β n L L klm r = 0 N 1 e i Δ β klm r L s .
F klm = r = 0 N 1 e i Δ β klm r L s = 1 e i Δ β klm N L s 1 e i Δ β klm L s = e i Δ β klm ( L L s ) 2 sin ( Δ β klm L 2 ) sin ( Δ β klm L s 2 ) .
W n ( + ) ( N ) = i γ U k ( 0 ) U l ( 0 ) U m * ( 0 ) e i β n L F klm L klm .
D klm = F klm L klm .
D 0 = N 1 e α L s α = N L eff .
U j ( N ) = U j ( 0 ) e i β j L .
U j ( N + ) = U j * ( N ) = U j * ( 0 ) e i β j L .
W n ( + ) ( N + ) = W n ( + ) * ( N ) = i γ U k * ( 0 ) U l * ( 0 ) U m ( 0 ) e i β n L F klm * L klm * .
W n ( + ) ( 2 N ) = i γ U k * ( 0 ) U l * ( 0 ) U m ( 0 ) F klm * L klm * .
W n ( ) ( 2 N ) = i γ U k ( N + ) U l ( N + ) U m * ( N + ) e i β n L F klm L klm = i γ U k * ( 0 ) U l * ( 0 ) U m ( 0 ) e i ( β k + β l β m ) L e i β n L F klm L klm = i γ U k * ( 0 ) U l * ( 0 ) U m ( 0 ) e i Δ β klm L F klm L klm .
W n ( 2 N ) = W n ( + ) ( 2 N ) + W n ( ) ( 2 N ) = i γ U k * ( 0 ) U l * ( 0 ) U m ( 0 ) D klm ,
D klm = e i Δ β klm L F klm L klm F klm * L klm * .
D klm = e i Δ β klm L 2 sin ( Δ β klm L 2 ) sin ( Δ β klm L s 2 ) C klm .
C klm = 2 i α 2 + ( Δ β klm ) 2 [ α ( 1 + e α L s ) sin ( Δ β klm L s 2 ) Δ β klm ( 1 e α L s ) cos ( Δ β klm L s 2 ) ] .
W n ( ) ( 2 N ) = i γ U k ( N ) U l ( N ) U m * ( N ) e i β n L F klm * L klm * = i γ U k ( 0 ) U l ( 0 ) U m * ( 0 ) e i ( β k + β l β m ) L e i β n L F klm * L klm * = i γ U k ( 0 ) U l ( 0 ) U m * ( 0 ) e i Δ β klm L F klm * L klm * .
W n ( 2 N ) = W n ( + ) ( 2 N ) + W n ( ) ( 2 N ) = i γ U k ( 0 ) U l ( 0 ) U m * ( 0 ) D klm ,
D klm = F klm L klm + e i Δ β klm L F klm * L klm * .
D klm = e i Δ β klm L 2 sin ( Δ β klm L 2 ) sin ( Δ β klm L s 2 ) C klm .
C klm = 2 α 2 + ( Δ β klm ) 2 [ α ( 1 e α L s ) cos ( Δ β klm L s 2 ) + Δ β klm ( 1 + e α L s ) sin ( Δ β klm L s 2 ) ] .