Abstract

An analytical expression for the variance of nonlinear phase noise for a quasi-linear system using the midpoint optical phase conjugation (OPC) is obtained. It is shown that the the system with OPC and dispersion inversion (DI) can exactly cancel the nonlinear phase noise up to the first order in nonlinear coefficient if the amplifier and the end point of the system are equidistant from the OPC. It is found that the nonlinear phase noise variance of the midpoint phase-conjugated optical transmission system with DI is smaller than that of the system without DI.

© 2007 Optical Society of America

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    [CrossRef]

2006 (5)

X. Zhu, S. Kumar and X. Li, "Comparison between DPSK and OOK modulation schemes in nonlinear optical transmission systems," App. Opt. 45, 6812-6822 (2006).
[CrossRef]

S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P.M. Krummrich, W. Sohler, G.-D. Khoe, and H. de Waardt, "Optical phase conjugation for ultra long haul phase- shift-keyed transmission," IEEE J. of Lightwave Technol. 24, 54-64 (2006).
[CrossRef]

F. Zhang, C.-A. Bunge, and K. Petermann, "Analysis of nonlinear phase noise in single-channel return-to-zero differential phase-shift keying transmission systems," Opt. Lett. 31, 1038-1040 (2006).
[CrossRef] [PubMed]

K.-P. Ho and H.-C. Wang, "Effect of dispersion on nonlinear phase noise," Opt. Lett. 31, 2109-2111 (2006).
[CrossRef] [PubMed]

D. Boivin, G. -K. Chang, J. R. Barry, and M. Hanna, "Reduction of Gordon-Mollenauer phase noise in dispersionmanaged systems using in-line spectral inversion," J. Opt. Soc. Am. B 23, 2019-2023 (2006).
[CrossRef]

2005 (5)

S. Kumar and D. Yang, "Second order theory for self-phase modulation and cross-phase modulation in optical fibers," J. Lightwave Technol. 23, 2073 (2005).
[CrossRef]

K.-P. Ho and H.-C. Wang, "Comparison of nonlinear phase noise and intrachannel four wave mixing for RZ-DPSK signals in dispersive transmission systems," IEEE Photon. Technol. Lett. 17, 1426-1428 (2005).
[CrossRef]

K.-P. Ho, "Mid-Span Compensation of Nonlinear Phase Noise," Optics Comm. 245, 391-398 (2005).
[CrossRef]

S. Kumar, "Effect of dispersion on nonlinear phase noise in optical transmission systems," Opt.Lett. 30, 3278- 3280 (2005).
[CrossRef]

X. Tang and Z. Wu, "Reduction of intrachannel nonlinearity using optical phase conjugation," IEEE Photon. Technol. Lett. 17, 1863-1865 (2005).
[CrossRef]

2004 (6)

A. G. Striegler and B. Schmauss, "Compensation of intrachannel effects in symmetric dispersion-managed transmission systems," J. of Lightwave Technol. 22, 1877-1882 (2004).
[CrossRef]

A. Chowdhury, and R. J. Essiambre, "Optical phase conjugation and psuedo linear transmission," Opt.Lett. 29, 1105-1107 (2004).
[CrossRef] [PubMed]

P. Minzioni, F. Alberti, and A. Schiffini, "Experimental demonstration of nonlinearity and dispersion compensation in an embedded link by optical phase conjugation," IEEE Photon. Technol. Lett. 16, 813-815 (2004).
[CrossRef]

M. Hanna, D. Boivin, P.-A. Lacourt, and J.-P. Goedgebuer, "Calculation of optical phase jitter in dispersionmanaged systems by the use of the moment method," J. Opt. Soc. Am. B 21, 24-28 (2004).
[CrossRef]

H. Wei and D. V. Plant, "Simultaneous nonlinearity suppression and wide-band dispersion compensation using optical phase conjugation," Opt. Express 12, 1938-1958 (2004).
[CrossRef] [PubMed]

H. Wei and D. V. Plant, "Intra-channel nonlinearity compensation with scaled translational symmetry," Opt. Express,  12, 4282-4296 (2004).
[CrossRef] [PubMed]

2003 (4)

2002 (5)

2001 (1)

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

2000 (1)

A. Mecozzi, C. B. Clausen, and M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392-394 (2000).
[CrossRef]

1996 (1)

1994 (1)

A. Mecozzi, "Limits to long-haul coherent transmission set by the Kerr nonlinearity and noise of the in-line amplifiers," J. Lightwave Technol. 12, 1993-2000 (1994).
[CrossRef]

1990 (1)

J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communication systems using linear amplifiers," Opt.Lett. 15, 1351-1353 (1990).
[CrossRef] [PubMed]

Alberti, F.

P. Minzioni, F. Alberti, and A. Schiffini, "Experimental demonstration of nonlinearity and dispersion compensation in an embedded link by optical phase conjugation," IEEE Photon. Technol. Lett. 16, 813-815 (2004).
[CrossRef]

Angkaew, T.

Barry, J. R.

Boivin, D.

Bononi, A.

Bunge, C.-A.

Calabro, S.

S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P.M. Krummrich, W. Sohler, G.-D. Khoe, and H. de Waardt, "Optical phase conjugation for ultra long haul phase- shift-keyed transmission," IEEE J. of Lightwave Technol. 24, 54-64 (2006).
[CrossRef]

Chang, G. -K.

Chowdhury, A.

A. Chowdhury, and R. J. Essiambre, "Optical phase conjugation and psuedo linear transmission," Opt.Lett. 29, 1105-1107 (2004).
[CrossRef] [PubMed]

Chowdhury, D.

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

Clausen, C. B.

A. Mecozzi, C. B. Clausen, and M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392-394 (2000).
[CrossRef]

Conradi, J.

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

Culverhouse, J.

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

de Waardt, H.

S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P.M. Krummrich, W. Sohler, G.-D. Khoe, and H. de Waardt, "Optical phase conjugation for ultra long haul phase- shift-keyed transmission," IEEE J. of Lightwave Technol. 24, 54-64 (2006).
[CrossRef]

Ennser, K.

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

Essiambre, R. J.

A. Chowdhury, and R. J. Essiambre, "Optical phase conjugation and psuedo linear transmission," Opt.Lett. 29, 1105-1107 (2004).
[CrossRef] [PubMed]

Gabitov, I.

Giroux, C.

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

Gnauck, A. H.

H. Kim and A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. 15, 320-322 (2003).
[CrossRef]

Goedgebuer, J.-P.

Gordon, J. P.

J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communication systems using linear amplifiers," Opt.Lett. 15, 1351-1353 (1990).
[CrossRef] [PubMed]

Green, A. G.

Grigoryan, V. S.

Hallock, B.

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

Hanna, M.

Ho, K.-P.

K.-P. Ho and H.-C. Wang, "Effect of dispersion on nonlinear phase noise," Opt. Lett. 31, 2109-2111 (2006).
[CrossRef] [PubMed]

K.-P. Ho, "Mid-Span Compensation of Nonlinear Phase Noise," Optics Comm. 245, 391-398 (2005).
[CrossRef]

K.-P. Ho and H.-C. Wang, "Comparison of nonlinear phase noise and intrachannel four wave mixing for RZ-DPSK signals in dispersive transmission systems," IEEE Photon. Technol. Lett. 17, 1426-1428 (2005).
[CrossRef]

Holzlohner, R.

Jansen, S. L.

S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P.M. Krummrich, W. Sohler, G.-D. Khoe, and H. de Waardt, "Optical phase conjugation for ultra long haul phase- shift-keyed transmission," IEEE J. of Lightwave Technol. 24, 54-64 (2006).
[CrossRef]

Kaewplung, P.

Kennedy, T.

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

Khoe, G.-D.

S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P.M. Krummrich, W. Sohler, G.-D. Khoe, and H. de Waardt, "Optical phase conjugation for ultra long haul phase- shift-keyed transmission," IEEE J. of Lightwave Technol. 24, 54-64 (2006).
[CrossRef]

Kikuchi, K.

Kim, H.

H. Kim and A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. 15, 320-322 (2003).
[CrossRef]

Krummrich, P. M.

S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P.M. Krummrich, W. Sohler, G.-D. Khoe, and H. de Waardt, "Optical phase conjugation for ultra long haul phase- shift-keyed transmission," IEEE J. of Lightwave Technol. 24, 54-64 (2006).
[CrossRef]

Kruse, A.

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

Kumar, S.

X. Zhu, S. Kumar and X. Li, "Comparison between DPSK and OOK modulation schemes in nonlinear optical transmission systems," App. Opt. 45, 6812-6822 (2006).
[CrossRef]

S. Kumar, "Effect of dispersion on nonlinear phase noise in optical transmission systems," Opt.Lett. 30, 3278- 3280 (2005).
[CrossRef]

S. Kumar and D. Yang, "Second order theory for self-phase modulation and cross-phase modulation in optical fibers," J. Lightwave Technol. 23, 2073 (2005).
[CrossRef]

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

Lacourt, P.-A.

Lakoba, T.

Lascar, N.

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

Li, X.

X. Zhu, S. Kumar and X. Li, "Comparison between DPSK and OOK modulation schemes in nonlinear optical transmission systems," App. Opt. 45, 6812-6822 (2006).
[CrossRef]

McKinstrie, C.

McKinstrie, C. J.

C. J. McKinstrie and C. Xie, "Phase jitter in single-channel soliton systems with constant dispersion," IEEE J. Sel. Top. Quantum Electron. 8, 616-625 (2002).
[CrossRef]

McKinstrie, C.J.

Mecozzi, A.

A. Mecozzi, C. B. Clausen, and M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392-394 (2000).
[CrossRef]

A. Mecozzi, "Limits to long-haul coherent transmission set by the Kerr nonlinearity and noise of the in-line amplifiers," J. Lightwave Technol. 12, 1993-2000 (1994).
[CrossRef]

Menyuk, C. R.

Minzioni, P.

P. Minzioni, F. Alberti, and A. Schiffini, "Experimental demonstration of nonlinearity and dispersion compensation in an embedded link by optical phase conjugation," IEEE Photon. Technol. Lett. 16, 813-815 (2004).
[CrossRef]

Mitra, P.

Mitra, P. P.

Mollenauer, L. F.

J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communication systems using linear amplifiers," Opt.Lett. 15, 1351-1353 (1990).
[CrossRef] [PubMed]

Narimanov, E. E.

Petermann, K.

Plant, D. V.

Radic, S.

Roudas, I.

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

Schiffini, A.

P. Minzioni, F. Alberti, and A. Schiffini, "Experimental demonstration of nonlinearity and dispersion compensation in an embedded link by optical phase conjugation," IEEE Photon. Technol. Lett. 16, 813-815 (2004).
[CrossRef]

Schmauss, B.

A. G. Striegler and B. Schmauss, "Compensation of intrachannel effects in symmetric dispersion-managed transmission systems," J. of Lightwave Technol. 22, 1877-1882 (2004).
[CrossRef]

Serena, P.

Shtaif, M.

A. Mecozzi, C. B. Clausen, and M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392-394 (2000).
[CrossRef]

Sohler, W.

S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P.M. Krummrich, W. Sohler, G.-D. Khoe, and H. de Waardt, "Optical phase conjugation for ultra long haul phase- shift-keyed transmission," IEEE J. of Lightwave Technol. 24, 54-64 (2006).
[CrossRef]

Spinnler, B.

S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P.M. Krummrich, W. Sohler, G.-D. Khoe, and H. de Waardt, "Optical phase conjugation for ultra long haul phase- shift-keyed transmission," IEEE J. of Lightwave Technol. 24, 54-64 (2006).
[CrossRef]

Striegler, A.G.

A. G. Striegler and B. Schmauss, "Compensation of intrachannel effects in symmetric dispersion-managed transmission systems," J. of Lightwave Technol. 22, 1877-1882 (2004).
[CrossRef]

Suche, H.

S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P.M. Krummrich, W. Sohler, G.-D. Khoe, and H. de Waardt, "Optical phase conjugation for ultra long haul phase- shift-keyed transmission," IEEE J. of Lightwave Technol. 24, 54-64 (2006).
[CrossRef]

Tang, X.

X. Tang and Z. Wu, "Reduction of intrachannel nonlinearity using optical phase conjugation," IEEE Photon. Technol. Lett. 17, 1863-1865 (2005).
[CrossRef]

Tomkos, I.

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

Turitsyn, S.

van den Borne, D.

S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P.M. Krummrich, W. Sohler, G.-D. Khoe, and H. de Waardt, "Optical phase conjugation for ultra long haul phase- shift-keyed transmission," IEEE J. of Lightwave Technol. 24, 54-64 (2006).
[CrossRef]

Vanucci, A.

Vodhanel, R. S.

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

Wang, C.-C.

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

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K.-P. Ho and H.-C. Wang, "Effect of dispersion on nonlinear phase noise," Opt. Lett. 31, 2109-2111 (2006).
[CrossRef] [PubMed]

K.-P. Ho and H.-C. Wang, "Comparison of nonlinear phase noise and intrachannel four wave mixing for RZ-DPSK signals in dispersive transmission systems," IEEE Photon. Technol. Lett. 17, 1426-1428 (2005).
[CrossRef]

Wegener, L. G. L.

Wei, H.

Wu, Z.

X. Tang and Z. Wu, "Reduction of intrachannel nonlinearity using optical phase conjugation," IEEE Photon. Technol. Lett. 17, 1863-1865 (2005).
[CrossRef]

Xie, C.

Yang, D.

Zhang, F.

Zhu, X.

X. Zhu, S. Kumar and X. Li, "Comparison between DPSK and OOK modulation schemes in nonlinear optical transmission systems," App. Opt. 45, 6812-6822 (2006).
[CrossRef]

App. Opt. (1)

X. Zhu, S. Kumar and X. Li, "Comparison between DPSK and OOK modulation schemes in nonlinear optical transmission systems," App. Opt. 45, 6812-6822 (2006).
[CrossRef]

IEEE J. of Lightwave Technol. (1)

S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P.M. Krummrich, W. Sohler, G.-D. Khoe, and H. de Waardt, "Optical phase conjugation for ultra long haul phase- shift-keyed transmission," IEEE J. of Lightwave Technol. 24, 54-64 (2006).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

C. J. McKinstrie and C. Xie, "Phase jitter in single-channel soliton systems with constant dispersion," IEEE J. Sel. Top. Quantum Electron. 8, 616-625 (2002).
[CrossRef]

I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R. S. Vodhanel, and C.-C. Wang, "Demonstration of negative dispersion fibers for DWDM metropolitan area networks," IEEE J. Sel. Top. Quantum Electron. 7, 439-460 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (5)

A. Mecozzi, C. B. Clausen, and M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392-394 (2000).
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P. Minzioni, F. Alberti, and A. Schiffini, "Experimental demonstration of nonlinearity and dispersion compensation in an embedded link by optical phase conjugation," IEEE Photon. Technol. Lett. 16, 813-815 (2004).
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X. Tang and Z. Wu, "Reduction of intrachannel nonlinearity using optical phase conjugation," IEEE Photon. Technol. Lett. 17, 1863-1865 (2005).
[CrossRef]

H. Kim and A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. 15, 320-322 (2003).
[CrossRef]

K.-P. Ho and H.-C. Wang, "Comparison of nonlinear phase noise and intrachannel four wave mixing for RZ-DPSK signals in dispersive transmission systems," IEEE Photon. Technol. Lett. 17, 1426-1428 (2005).
[CrossRef]

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A. G. Striegler and B. Schmauss, "Compensation of intrachannel effects in symmetric dispersion-managed transmission systems," J. of Lightwave Technol. 22, 1877-1882 (2004).
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Figures (4)

Fig. 1.
Fig. 1.

System Schematic. 1a. OPC without dispersion inversion (DI) 1b. OPC with DI.

Fig. 2.
Fig. 2.

Accumulated dispersion profile. 2a. without dispersion inversion corresponding to Fig. 1(a), 2b. with dispersion inversion corresponding to Fig. 1(b). The dotted line shows the location of OPC. The dispersion coefficient β2 of the first section is -10 ps2/km.

Fig. 3.
Fig. 3.

Variance of linear and nonlinear phase noise for a single pulse as a function of the absolute dispersion.

Fig. 4.
Fig. 4.

Variance of linear and nonlinear phase noise of a bit ’0’ using a bit pattern as a function of the absolute dispersion. The parameters are same as that of Fig. 3.

Equations (56)

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i u z β 2 ( z ) 2 2 u t 2 = γ exp [ w ( z ) ] u 2 u ,
u ( t , z ) = u 0 ( t , z ) + γ u 1 ( t , z ) + γ 2 u 2 ( t , z ) + . . . ,
u ( t , 0 ) = x ( t , 0 ) + n ( t , 0 )
u ( t , L opc ) = u ( t , 0 ) iγY ( t ) ,
Y ( t ) = 0 L opc exp [ w ( z ) ] { [ u 0 ( t , z ) 2 u 0 ( t , z ) ] m ( t , z ) } dz
u 0 ( t , z ) = m ٭ ( t , z ) u 0 ( t , 0 ) ,
m ( t , z ) = exp [ it 2 2 S ( z ) ] 2 πiS ( z )
U out H = U in H i γ 0 L opc dz exp [ w ( z ) ] M ( S ) V ( S , U in H ) ,
u 0 ( t , z ) = x ( t , z ) + n ( t , z ) ,
x ( t , z ) = x ( t , 0 ) m ( t , z ) , n ( t , z ) = n ( t , 0 ) m ( t , z )
δ ϕ out H ( t ) = γ tan 1 [ Y r ( t ) x 0 ( t ) + n 0 r ( t ) + γ Y i ( t ) ] ,
γ Y r ( t ) x 0 ( t )
u 0 2 u 0 m = [ x 2 x + 2 x 2 n + x 2 n + n 2 ( 2 x + n ) + n 2 x ] m .
δ ϕ 1 H ( t ) 2 γ x 0 ( t ) 0 L opc dz exp [ w ( z ) ] { [ ( x 2 n r ) m r ] [ ( x 2 n r ) m i ] } ,
n r ( t , z ) = n 0 r ( t ) m r ( t , z ) + n 0 i ( t ) m i ( t , z ) ,
n i ( t , z ) = n 0 i ( t ) m r ( t , z ) n 0 r ( t ) m i ( t , z ) ,
δ ϕ 1 H ( t ) 2 γ x 0 ( t ) 0 L opc dz exp [ w ( z ) ] { [ x 2 ( n 0 r m r + n 0 i m i ) ] m r [ x 2 ( n 0 i m r n 0 r m i ) ] m i } ,
δ ϕ 2 H ( t ) γ x 0 ( t ) 0 L opc dz exp [ w ( z ) ] { [ ( x r 2 x i 2 ) n r + 2 x r x i n i ] m r [ 2 x r x i n r ( x r 2 x i 2 ) n i ] m i } ,
δ ϕ out H ( t ) = δ ϕ 1 H ( t ) + δ ϕ 2 H ( t ) .
( U out H ) = ( U in H ) + i γ 0 L opc dz exp [ w ( z ) ] M ( S ) V ( S , U in H ) .
U in G = ( U out H ) = ( U in H ) + O ( γ ) .
U out G = U in G i γ L opc L tot dz exp [ w ( z ) ] M ( S ) V ( S , U in G ) dz ,
U out G = ( U in H ) i γ 0 L opc dz exp [ w ( z ) ] [ M ( S ) V ( S , U in H ) ]
i γ L opc L tot dz exp [ w ( z ) ] [ M ( S ) V ( S , ( U in H ) ) + O ( γ ) ] dz.
S ( z + L opc ) = S ( z ) .
U out G = ( U in H ) + i γ 0 L opc dz exp [ w ( z ) ] [ M ( S ) V ( S , U in H ) M ( S ) V ( S , ( U in H ) ) ] dz.
δ ϕ 1 G ( t ) 4 γ x 0 ( t ) 0 L opc dz exp [ w ( z ) ] { ( x 2 n 0 i m i ) m r ( x 2 n 0 i m r ) m i } ,
S ( z + L opc ) = S ( z ) .
U out G = ( U in H ) + i γ 0 L opc dz exp [ w ( z ) ] [ M ( S ) V ( S , U in H ) M ( S ) V ( S , ( U in H ) ) ] dz.
M ( S ) = M ( S ) ,
V S U in H = V S ( U in H )
δ ϕ out G ( t ) = 0 .
x 0 ( t ) = E T eff exp [ t 2 2 T 0 2 ] ,
u s ( LN a 2 , t ) = x 0 ( t ) [ 1 + iγEg ( mL , t ) ] ,
g ( z , t ) = T 0 2 T eff z N a L 2 f ( r , t ) dr ,
f ( r , t ) = exp [ w ( r ) Δ ( r ) t 2 ] T 0 4 + 3 S 2 ( r ) + 2 i T 0 2 S ( r ) ,
Δ ( r ) = T 0 2 iS ( r ) T 0 2 [ T 0 2 + i 3 S ( r ) ] .
u s ( N a L , t ) = x 0 ( t ) [ 1 iγE g ( mL , t ) + iγEg ( 0 , t ) ] .
δ ϕ m ( N a L , t ) = γδERe [ g ( 0 , t ) g ( mL , t ) ] .
g ( mL , t ) = ( N a 2 m ) h ( t ) T eff ,
= g ( 0 , t ) mh ( t ) T eff ,
h ( t ) = T 0 2 0 L exp [ w ( r ) Δ ( r ) t 2 ] dr T 0 4 + 3 S 2 ( r ) + 2 i T 0 2 S ( r ) ,
δ ϕ m ( N a L , t ) = m γ h r ( t ) δE T eff , m < = N a 2
δ ϕ m std ( N a L , t ) = ( N a m ) γ h r ( t ) δE T eff .
δ ϕ m ( N a L , t ) = m γ h r ( t ) δE T eff , m < = N a 2
= ( N a m ) γ h r ( t ) δE T eff . m > N a 2
δ ϕ 2 = 2 γ 2 ρE h r 2 ( 0 ) T eff 2 [ m = 1 N a 2 m 2 + m = N a 2 + 1 N a 1 ( N a m ) 2 ] ,
γ 2 ρEh r 2 ( 0 ) N a 3 6 T eff 2 ,
δϕ 2 std 2 γ 2 ρE h r 2 ( 0 ) N a 3 3 T eff 2
δ ϕ m ( N a L , t ) = γδE T 0 2 T eff Re [ mL r N a L f ( r , t ) dr + ( r + 1 ) N a N a L f ( r , t ) dr ] ,
= γδE h r ( r ) [ m + ( 1 2 r ) ] T eff ,
δ ϕ 2 = 2 γ 2 ρE h r 2 ( 0 ) T eff 2 [ m = 1 r N a [ m + ( 1 2 r ) ] 2 + m = r N a + 1 N a 1 ( N a m ) 2 ] ,
2 γ 2 ρEh r 2 ( 0 ) N a 3 ( 1 + 6 r 3 6 r 2 ) 3 T eff 2 ,
r opt = 2 3 ,
δϕ 2 min = 2 γ 2 ρE h r 2 ( 0 ) N a 3 27 T eff 2 .
ρ = n sp hf ( G 1 ) ,

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