Abstract

The characteristic function of soliton phase jitter is found analytically when the soliton is perturbed by amplifier noise. In addition to that from amplitude jitter, the nonlinear phase noise due to frequency and timing jitter is also analyzed. With nonlinear phase noise, the overall phase jitter is non-Gaussian distributed. For a fixed mean nonlinear phase shift, the contribution of nonlinear phase noise from frequency and timing jitter decreases with distance and signal-to-noise ratio.

© 2004 Optical Society of America

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    [CrossRef]
  32. R. Holzlohner, V. S. Grigoryan, C. R. Menyuk, and W. L. Kath, “Accurate calculation of eye diagrams and bit error rates in optical transmission systems using linearization,” J. Lightwave Technol. 20, 389–400 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  35. K.-P. Ho, “Non-Gaussian statistics of the soliton timing jitter due to amplifier noise,” Opt. Lett. 28, 2165–2167 (2003).
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    [CrossRef]

2003 (8)

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]

H. Bissessur, G. Charlet, E. Gohin, C. Simonneau, L. Pierre, and W. Idler, “1.6 Tbit/s (40×40 Gbit/s) DPSK transmission over 3×100 km of TeraLight fibre with direct detection,” Electron. Lett. 39, 192–193 (2003).
[CrossRef]

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, and E. Burrows, “25 40-Gb/s copolarized DPSK transmission over 12 100-km NZDF with 50-GHz channel spacing,” IEEE Photon. Technol. Lett. 15, 467–469 (2003).
[CrossRef]

P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, “Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber,” IEEE Photon. Technol. Lett. 15, 473–475 (2003).
[CrossRef]

R. O. Moore, G. Biondini, and W. L. Kath, “Importance sampling for noise-induced amplitude and timing jitter in soliton transmission systems,” Opt. Lett. 28, 105–107 (2003).
[CrossRef] [PubMed]

K.-P. Ho, “Asymptotic probability density of nonlinear phase noise,” Opt. Lett. 28, 1350–1352 (2003).
[CrossRef] [PubMed]

K.-P. Ho, “Probability density of nonlinear phase noise,” J. Opt. Soc. Am. B 20, 1875–1879 (2003).
[CrossRef]

K.-P. Ho, “Non-Gaussian statistics of the soliton timing jitter due to amplifier noise,” Opt. Lett. 28, 2165–2167 (2003).
[CrossRef] [PubMed]

2002 (2)

Y. Miyamoto, H. Masuda, A. Hirano, S. Kuwahara, Y. Kisaka, H. Kawakami, M. Tomizawa, Y. Tada, and S. Aozasa, “S-band WDM coherent transmission of 40× 43-Gbit/s CS-RZ DPSK signals over 400 km DSF using hybrid GS-TDFAs/Raman amplifiers,” Electron. Lett. 38, 1569–1570 (2002).
[CrossRef]

R. Holzlohner, V. S. Grigoryan, C. R. Menyuk, and W. L. Kath, “Accurate calculation of eye diagrams and bit error rates in optical transmission systems using linearization,” J. Lightwave Technol. 20, 389–400 (2002).
[CrossRef]

2001 (1)

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Performance assessment of DPSK soliton transmission system,” Electron. Lett. 37, 644–646 (2001).
[CrossRef]

2000 (1)

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Experimental investigation of soliton optical phase jitter,” IEEE J. Quantum Electron. 36, 1333–1338 (2000).
[CrossRef]

1999 (1)

1998 (1)

1997 (2)

H. A. Haus, W. S. Wong, and F. I. Khatri, “Continuum generation by perturbation of soliton,” J. Opt. Soc. Am. B 14, 304–313 (1997).
[CrossRef]

P. Shum, H. Ghafouri-Shiraz, and S. F. Yu, “Analysis of a DPSK soliton transmission system,” Opt. Laser Technol. 29, 411–414 (1997).
[CrossRef]

1996 (1)

P. Shum and H. Ghafouri-Shiraz, “Analysis of bit error rate in an optical soliton communication system,” Opt. Laser Technol. 28, 535–547 (1996).
[CrossRef]

1995 (1)

T. Georges, “Perturbation theory for the assessment of soliton transmission control,” Opt. Laser Technol. 1, 97–116 (1995).

1994 (2)

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]

A. Mecozzi, “Long-distance transmission at zero dispersion: combined effect of Kerr nonlinearity and the noise of the in-line amplifiers,” J. Opt. Soc. Am. B 11, 462–469 (1994).
[CrossRef]

1992 (1)

K. Blow, N. Doran, and S. Phoenix, “The soliton phase,” Opt. Commun. 88, 137–140 (1992).
[CrossRef]

1991 (3)

D. J. Kaup, “Second-order perturbation for solitons in optical fibers,” Phys. Rev. A 44, 4582–4590 (1991).
[CrossRef] [PubMed]

E. M. Stein and J. C. Stein, “Stock price distribution with stochastic volatility: an analytical approach,” Rev. Financ. Stud. 4, 727–752 (1991).
[CrossRef]

P. A. Humblet and M. Azizog̃lu, “On the bit error rate of lightwave systems with optical amplifiers,” J. Lightwave Technol. 9, 1576–1582 (1991).
[CrossRef]

1990 (2)

1989 (1)

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763–915 (1989).
[CrossRef]

1986 (1)

J. P. Gordon and H. A. Haus, “Random walk of coherently amplified solitons in optical fiber transmission,” Opt. Lett. 11, 865–867 (1986).
[CrossRef]

1984 (1)

G. Nicholson, “Probability of error for optical heterodyne DPSK system with quantum phase noise,” Electron. Lett. 20, 1005–1007 (1984).
[CrossRef]

1945 (1)

R. H. Cameron and W. T. Martin, “Evaluation of various Wiener integrals by use of certain Sturm-Liouville differential equations,” Bull. Am. Math. Soc. 51, 73–90 (1945).
[CrossRef]

Achiam, Y.

P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, “Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber,” IEEE Photon. Technol. Lett. 15, 473–475 (2003).
[CrossRef]

Aozasa, S.

Y. Miyamoto, H. Masuda, A. Hirano, S. Kuwahara, Y. Kisaka, H. Kawakami, M. Tomizawa, Y. Tada, and S. Aozasa, “S-band WDM coherent transmission of 40× 43-Gbit/s CS-RZ DPSK signals over 400 km DSF using hybrid GS-TDFAs/Raman amplifiers,” Electron. Lett. 38, 1569–1570 (2002).
[CrossRef]

Azizog~lu, M.

P. A. Humblet and M. Azizog̃lu, “On the bit error rate of lightwave systems with optical amplifiers,” J. Lightwave Technol. 9, 1576–1582 (1991).
[CrossRef]

Biondini, G.

Bissessur, H.

H. Bissessur, G. Charlet, E. Gohin, C. Simonneau, L. Pierre, and W. Idler, “1.6 Tbit/s (40×40 Gbit/s) DPSK transmission over 3×100 km of TeraLight fibre with direct detection,” Electron. Lett. 39, 192–193 (2003).
[CrossRef]

Blow, K.

K. Blow, N. Doran, and S. Phoenix, “The soliton phase,” Opt. Commun. 88, 137–140 (1992).
[CrossRef]

Burrows, E.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, and E. Burrows, “25 40-Gb/s copolarized DPSK transmission over 12 100-km NZDF with 50-GHz channel spacing,” IEEE Photon. Technol. Lett. 15, 467–469 (2003).
[CrossRef]

Cameron, R. H.

R. H. Cameron and W. T. Martin, “Evaluation of various Wiener integrals by use of certain Sturm-Liouville differential equations,” Bull. Am. Math. Soc. 51, 73–90 (1945).
[CrossRef]

Chandrasekhar, S.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, and E. Burrows, “25 40-Gb/s copolarized DPSK transmission over 12 100-km NZDF with 50-GHz channel spacing,” IEEE Photon. Technol. Lett. 15, 467–469 (2003).
[CrossRef]

Charlet, G.

H. Bissessur, G. Charlet, E. Gohin, C. Simonneau, L. Pierre, and W. Idler, “1.6 Tbit/s (40×40 Gbit/s) DPSK transmission over 3×100 km of TeraLight fibre with direct detection,” Electron. Lett. 39, 192–193 (2003).
[CrossRef]

Cho, P. S.

P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, “Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber,” IEEE Photon. Technol. Lett. 15, 473–475 (2003).
[CrossRef]

Desurvire, E.

Doerr, C.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, and E. Burrows, “25 40-Gb/s copolarized DPSK transmission over 12 100-km NZDF with 50-GHz channel spacing,” IEEE Photon. Technol. Lett. 15, 467–469 (2003).
[CrossRef]

Doran, N.

K. Blow, N. Doran, and S. Phoenix, “The soliton phase,” Opt. Commun. 88, 137–140 (1992).
[CrossRef]

Georges, T.

T. Georges, “Perturbation theory for the assessment of soliton transmission control,” Opt. Laser Technol. 1, 97–116 (1995).

Ghafouri-Shiraz, H.

P. Shum, H. Ghafouri-Shiraz, and S. F. Yu, “Analysis of a DPSK soliton transmission system,” Opt. Laser Technol. 29, 411–414 (1997).
[CrossRef]

P. Shum and H. Ghafouri-Shiraz, “Analysis of bit error rate in an optical soliton communication system,” Opt. Laser Technol. 28, 535–547 (1996).
[CrossRef]

Gnauck, A. H.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, and E. Burrows, “25 40-Gb/s copolarized DPSK transmission over 12 100-km NZDF with 50-GHz channel spacing,” IEEE Photon. Technol. Lett. 15, 467–469 (2003).
[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]

Godin, Y. A.

P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, “Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber,” IEEE Photon. Technol. Lett. 15, 473–475 (2003).
[CrossRef]

Goedgebuer, J.-P.

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Performance assessment of DPSK soliton transmission system,” Electron. Lett. 37, 644–646 (2001).
[CrossRef]

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Experimental investigation of soliton optical phase jitter,” IEEE J. Quantum Electron. 36, 1333–1338 (2000).
[CrossRef]

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Soliton optical phase control by use of in-line filters,” Opt. Lett. 24, 732–734 (1999).
[CrossRef]

Gohin, E.

H. Bissessur, G. Charlet, E. Gohin, C. Simonneau, L. Pierre, and W. Idler, “1.6 Tbit/s (40×40 Gbit/s) DPSK transmission over 3×100 km of TeraLight fibre with direct detection,” Electron. Lett. 39, 192–193 (2003).
[CrossRef]

Gordon, J. P.

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

J. P. Gordon and H. A. Haus, “Random walk of coherently amplified solitons in optical fiber transmission,” Opt. Lett. 11, 865–867 (1986).
[CrossRef]

Grigoryan, V. S.

P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, “Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber,” IEEE Photon. Technol. Lett. 15, 473–475 (2003).
[CrossRef]

R. Holzlohner, V. S. Grigoryan, C. R. Menyuk, and W. L. Kath, “Accurate calculation of eye diagrams and bit error rates in optical transmission systems using linearization,” J. Lightwave Technol. 20, 389–400 (2002).
[CrossRef]

Hanna, M.

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Performance assessment of DPSK soliton transmission system,” Electron. Lett. 37, 644–646 (2001).
[CrossRef]

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Experimental investigation of soliton optical phase jitter,” IEEE J. Quantum Electron. 36, 1333–1338 (2000).
[CrossRef]

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Soliton optical phase control by use of in-line filters,” Opt. Lett. 24, 732–734 (1999).
[CrossRef]

Haus, H. A.

H. A. Haus, W. S. Wong, and F. I. Khatri, “Continuum generation by perturbation of soliton,” J. Opt. Soc. Am. B 14, 304–313 (1997).
[CrossRef]

J. P. Gordon and H. A. Haus, “Random walk of coherently amplified solitons in optical fiber transmission,” Opt. Lett. 11, 865–867 (1986).
[CrossRef]

Hirano, A.

Y. Miyamoto, H. Masuda, A. Hirano, S. Kuwahara, Y. Kisaka, H. Kawakami, M. Tomizawa, Y. Tada, and S. Aozasa, “S-band WDM coherent transmission of 40× 43-Gbit/s CS-RZ DPSK signals over 400 km DSF using hybrid GS-TDFAs/Raman amplifiers,” Electron. Lett. 38, 1569–1570 (2002).
[CrossRef]

Ho, K.-P.

Holzlohner, R.

Humblet, P. A.

P. A. Humblet and M. Azizog̃lu, “On the bit error rate of lightwave systems with optical amplifiers,” J. Lightwave Technol. 9, 1576–1582 (1991).
[CrossRef]

Idler, W.

H. Bissessur, G. Charlet, E. Gohin, C. Simonneau, L. Pierre, and W. Idler, “1.6 Tbit/s (40×40 Gbit/s) DPSK transmission over 3×100 km of TeraLight fibre with direct detection,” Electron. Lett. 39, 192–193 (2003).
[CrossRef]

Kath, W. L.

Kaup, D. J.

D. J. Kaup, “Second-order perturbation for solitons in optical fibers,” Phys. Rev. A 44, 4582–4590 (1991).
[CrossRef] [PubMed]

D. J. Kaup, “Perturbation theory for solitons in optical fibers,” Phys. Rev. A 42, 5689–5694 (1990).
[CrossRef] [PubMed]

Kawakami, H.

Y. Miyamoto, H. Masuda, A. Hirano, S. Kuwahara, Y. Kisaka, H. Kawakami, M. Tomizawa, Y. Tada, and S. Aozasa, “S-band WDM coherent transmission of 40× 43-Gbit/s CS-RZ DPSK signals over 400 km DSF using hybrid GS-TDFAs/Raman amplifiers,” Electron. Lett. 38, 1569–1570 (2002).
[CrossRef]

Khatri, F. I.

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]

Kisaka, Y.

Y. Miyamoto, H. Masuda, A. Hirano, S. Kuwahara, Y. Kisaka, H. Kawakami, M. Tomizawa, Y. Tada, and S. Aozasa, “S-band WDM coherent transmission of 40× 43-Gbit/s CS-RZ DPSK signals over 400 km DSF using hybrid GS-TDFAs/Raman amplifiers,” Electron. Lett. 38, 1569–1570 (2002).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763–915 (1989).
[CrossRef]

Kuwahara, S.

Y. Miyamoto, H. Masuda, A. Hirano, S. Kuwahara, Y. Kisaka, H. Kawakami, M. Tomizawa, Y. Tada, and S. Aozasa, “S-band WDM coherent transmission of 40× 43-Gbit/s CS-RZ DPSK signals over 400 km DSF using hybrid GS-TDFAs/Raman amplifiers,” Electron. Lett. 38, 1569–1570 (2002).
[CrossRef]

Leclerc, O.

Leuthold, J.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, and E. Burrows, “25 40-Gb/s copolarized DPSK transmission over 12 100-km NZDF with 50-GHz channel spacing,” IEEE Photon. Technol. Lett. 15, 467–469 (2003).
[CrossRef]

Malomed, B. A.

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763–915 (1989).
[CrossRef]

Martin, W. T.

R. H. Cameron and W. T. Martin, “Evaluation of various Wiener integrals by use of certain Sturm-Liouville differential equations,” Bull. Am. Math. Soc. 51, 73–90 (1945).
[CrossRef]

Masuda, H.

Y. Miyamoto, H. Masuda, A. Hirano, S. Kuwahara, Y. Kisaka, H. Kawakami, M. Tomizawa, Y. Tada, and S. Aozasa, “S-band WDM coherent transmission of 40× 43-Gbit/s CS-RZ DPSK signals over 400 km DSF using hybrid GS-TDFAs/Raman amplifiers,” Electron. Lett. 38, 1569–1570 (2002).
[CrossRef]

Mecozzi, A.

A. Mecozzi, “Long-distance transmission at zero dispersion: combined effect of Kerr nonlinearity and the noise of the in-line amplifiers,” J. Opt. Soc. Am. B 11, 462–469 (1994).
[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.

Miyamoto, Y.

Y. Miyamoto, H. Masuda, A. Hirano, S. Kuwahara, Y. Kisaka, H. Kawakami, M. Tomizawa, Y. Tada, and S. Aozasa, “S-band WDM coherent transmission of 40× 43-Gbit/s CS-RZ DPSK signals over 400 km DSF using hybrid GS-TDFAs/Raman amplifiers,” Electron. Lett. 38, 1569–1570 (2002).
[CrossRef]

Mollenauer, L. F.

Moore, R. O.

Nicholson, G.

G. Nicholson, “Probability of error for optical heterodyne DPSK system with quantum phase noise,” Electron. Lett. 20, 1005–1007 (1984).
[CrossRef]

Phoenix, S.

K. Blow, N. Doran, and S. Phoenix, “The soliton phase,” Opt. Commun. 88, 137–140 (1992).
[CrossRef]

Pierre, L.

H. Bissessur, G. Charlet, E. Gohin, C. Simonneau, L. Pierre, and W. Idler, “1.6 Tbit/s (40×40 Gbit/s) DPSK transmission over 3×100 km of TeraLight fibre with direct detection,” Electron. Lett. 39, 192–193 (2003).
[CrossRef]

Porte, H.

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Performance assessment of DPSK soliton transmission system,” Electron. Lett. 37, 644–646 (2001).
[CrossRef]

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Experimental investigation of soliton optical phase jitter,” IEEE J. Quantum Electron. 36, 1333–1338 (2000).
[CrossRef]

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Soliton optical phase control by use of in-line filters,” Opt. Lett. 24, 732–734 (1999).
[CrossRef]

Raybon, G.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, and E. Burrows, “25 40-Gb/s copolarized DPSK transmission over 12 100-km NZDF with 50-GHz channel spacing,” IEEE Photon. Technol. Lett. 15, 467–469 (2003).
[CrossRef]

Rhodes, W. T.

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Performance assessment of DPSK soliton transmission system,” Electron. Lett. 37, 644–646 (2001).
[CrossRef]

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Experimental investigation of soliton optical phase jitter,” IEEE J. Quantum Electron. 36, 1333–1338 (2000).
[CrossRef]

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Soliton optical phase control by use of in-line filters,” Opt. Lett. 24, 732–734 (1999).
[CrossRef]

Salamon, A.

P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, “Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber,” IEEE Photon. Technol. Lett. 15, 473–475 (2003).
[CrossRef]

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P. Shum, H. Ghafouri-Shiraz, and S. F. Yu, “Analysis of a DPSK soliton transmission system,” Opt. Laser Technol. 29, 411–414 (1997).
[CrossRef]

P. Shum and H. Ghafouri-Shiraz, “Analysis of bit error rate in an optical soliton communication system,” Opt. Laser Technol. 28, 535–547 (1996).
[CrossRef]

Simonneau, C.

H. Bissessur, G. Charlet, E. Gohin, C. Simonneau, L. Pierre, and W. Idler, “1.6 Tbit/s (40×40 Gbit/s) DPSK transmission over 3×100 km of TeraLight fibre with direct detection,” Electron. Lett. 39, 192–193 (2003).
[CrossRef]

Stein, E. M.

E. M. Stein and J. C. Stein, “Stock price distribution with stochastic volatility: an analytical approach,” Rev. Financ. Stud. 4, 727–752 (1991).
[CrossRef]

Stein, J. C.

E. M. Stein and J. C. Stein, “Stock price distribution with stochastic volatility: an analytical approach,” Rev. Financ. Stud. 4, 727–752 (1991).
[CrossRef]

Stulz, L.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, and E. Burrows, “25 40-Gb/s copolarized DPSK transmission over 12 100-km NZDF with 50-GHz channel spacing,” IEEE Photon. Technol. Lett. 15, 467–469 (2003).
[CrossRef]

Tada, Y.

Y. Miyamoto, H. Masuda, A. Hirano, S. Kuwahara, Y. Kisaka, H. Kawakami, M. Tomizawa, Y. Tada, and S. Aozasa, “S-band WDM coherent transmission of 40× 43-Gbit/s CS-RZ DPSK signals over 400 km DSF using hybrid GS-TDFAs/Raman amplifiers,” Electron. Lett. 38, 1569–1570 (2002).
[CrossRef]

Tomizawa, M.

Y. Miyamoto, H. Masuda, A. Hirano, S. Kuwahara, Y. Kisaka, H. Kawakami, M. Tomizawa, Y. Tada, and S. Aozasa, “S-band WDM coherent transmission of 40× 43-Gbit/s CS-RZ DPSK signals over 400 km DSF using hybrid GS-TDFAs/Raman amplifiers,” Electron. Lett. 38, 1569–1570 (2002).
[CrossRef]

Wong, W. S.

Yu, S. F.

P. Shum, H. Ghafouri-Shiraz, and S. F. Yu, “Analysis of a DPSK soliton transmission system,” Opt. Laser Technol. 29, 411–414 (1997).
[CrossRef]

Bull. Am. Math. Soc. (1)

R. H. Cameron and W. T. Martin, “Evaluation of various Wiener integrals by use of certain Sturm-Liouville differential equations,” Bull. Am. Math. Soc. 51, 73–90 (1945).
[CrossRef]

Electron. Lett. (4)

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Performance assessment of DPSK soliton transmission system,” Electron. Lett. 37, 644–646 (2001).
[CrossRef]

Y. Miyamoto, H. Masuda, A. Hirano, S. Kuwahara, Y. Kisaka, H. Kawakami, M. Tomizawa, Y. Tada, and S. Aozasa, “S-band WDM coherent transmission of 40× 43-Gbit/s CS-RZ DPSK signals over 400 km DSF using hybrid GS-TDFAs/Raman amplifiers,” Electron. Lett. 38, 1569–1570 (2002).
[CrossRef]

H. Bissessur, G. Charlet, E. Gohin, C. Simonneau, L. Pierre, and W. Idler, “1.6 Tbit/s (40×40 Gbit/s) DPSK transmission over 3×100 km of TeraLight fibre with direct detection,” Electron. Lett. 39, 192–193 (2003).
[CrossRef]

G. Nicholson, “Probability of error for optical heterodyne DPSK system with quantum phase noise,” Electron. Lett. 20, 1005–1007 (1984).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Experimental investigation of soliton optical phase jitter,” IEEE J. Quantum Electron. 36, 1333–1338 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, and E. Burrows, “25 40-Gb/s copolarized DPSK transmission over 12 100-km NZDF with 50-GHz channel spacing,” IEEE Photon. Technol. Lett. 15, 467–469 (2003).
[CrossRef]

P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, “Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber,” IEEE Photon. Technol. Lett. 15, 473–475 (2003).
[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]

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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]

P. A. Humblet and M. Azizog̃lu, “On the bit error rate of lightwave systems with optical amplifiers,” J. Lightwave Technol. 9, 1576–1582 (1991).
[CrossRef]

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[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

K. Blow, N. Doran, and S. Phoenix, “The soliton phase,” Opt. Commun. 88, 137–140 (1992).
[CrossRef]

Opt. Laser Technol. (3)

P. Shum, H. Ghafouri-Shiraz, and S. F. Yu, “Analysis of a DPSK soliton transmission system,” Opt. Laser Technol. 29, 411–414 (1997).
[CrossRef]

P. Shum and H. Ghafouri-Shiraz, “Analysis of bit error rate in an optical soliton communication system,” Opt. Laser Technol. 28, 535–547 (1996).
[CrossRef]

T. Georges, “Perturbation theory for the assessment of soliton transmission control,” Opt. Laser Technol. 1, 97–116 (1995).

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef]

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Other (9)

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, “2.5 Tb/s (64× 42.7 Gb/s) transmission over 40×100 km NZDSF using RZ-DPSK format and all-Raman-amplified spans,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van de Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, and P. Reeves-Hall, “DWDM 40G transmission over trans-Pacific distance (10, 000 km) using CSRZ-DPSK, enhanced FEC and all-Raman amplified 100 km Ultra-Wave™ fiber spans,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2003), postdeadline paper PD18.

B. Zhu, L. E. Nelson, S. Stulz, A. H. Gnauck, C. Doerr, J. Leuthold, L. Grüner-Nielsen, M. O. Pederson, J. Kim, R. Lingle, Y. Emori, Y. Ohki, N. Tsukiji, A. Oguri, and S. Namiki, “6.4-Tb/s (160×42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32×100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2003), postdeadline paper PD19.

G. Vareille, L. Becouarn, P. Pecci, P. Tran, and J. F. Marcerou, “8370 km with 22 dB spans ULH transmission of 185*10.709 Gbit/s RZ-DPSK channels,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2003), postdeadline paper PD20.

T. Tsuritani, K. Ishida, A. Agata, K. Shimomura, I. Morita, T. Tokura, H. Taga, T. Mizuochi, and N. Edagawa, “70 GHz-spaced 40×42.7 Gbit/s transmission over 8700 km using CS-RZ DPSK signal, all-Raman repeaters and symmetrically dispersion-managed fiber span,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2003), postdeadline paper PD23.

J.-X. Cai, D. G. Foursa, C. R. Davidson, Y. Cai, G. Domagala, H. Li, L. Liu, W. W. Patterson, A. N. Pilipetskii, M. Nissov, and N. S. Bergano, “A DWDM demonstration of 3.73 Tb/s over 11, 000 km using 373 RZ-DPSK channels at 10 Gb/s,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2003), postdeadline paper PD22.

K.-P. Ho, “Statistical properties of nonlinear phase noise,” in Advances in Optics and Laser Research, W. T. Arkin, ed. (Nova Science, Hauppauge, N.Y., 2003), Vol. 3.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998), Chap. 5.

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); erratum 8, 956 (2002).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Distributions of soliton phase jitter for different distances for A=1 and σn2=0.05. (a) φGM(ζ), (b) φΩ,T(ζ), (c) φLN(ζ), (d) φ(ζ). The distributions are normalized for a unity peak. The x axes are not in the same scale. The distribution is plotted in linear units.

Fig. 2
Fig. 2

Distributions of soliton phase jitter for two distances of (a) ζ=1 and (b) ζ=2. Solid curves, exact overall phase jitter; dashed–dotted curves, Gaussian approximation of the overall phase jitter; dashed curves, components of phase jitter. The distribution is plotted in algorithmic units.

Fig. 3
Fig. 3

Distributions of soliton phase jitter for SNR of (a) 10 and (b) 20, including the pdf of the overall phase jitter and the contribution from the frequency and timing effect. The distribution is plotted in algorithmic units.

Equations (50)

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dAdζ=IdτfAn(ζ, τ),
dΩdζ=RdτfΩn(ζ, τ),
dTdζ=-Ω+IdτfTn(ζ, τ),
dϕdζ=12(A2-Ω2)+T dΩdζ+Rdτfϕn(ζ, τ),
E{n(ζ1, τ1)n(ζ2, τ2)}=σn2δ(ζ1-ζ2)δ(τ1-τ2);
q0(τ, ζ)=A(ζ)sech{A(ζ)[τ-T(ζ)]}×exp[-iΩ(ζ)τ+iϕ(ζ)]
fA=q0*,
fΩ=tanh[A(τ-T)]q0*,
fT=τ-TAq0*,
fϕ=-1A{1-A(τ-T)tanh[A(τ-T)]}q0*.
A(ζ)=A+wA(ζ),
Ω(ζ)=wΩ(ζ),
E{wA(ζ1)wA(ζ2)}=σA2 min(ζ1, ζ2),
E{wΩ(ζ1)wΩ(ζ2)}=σΩ2 min(ζ1, ζ2),
A2σA2ζ=Aσn2ζ.
T(ζ)=-0ζwΩ(ζ1)dζ1+wT(ζ),
E{wT(ζ1)wT(ζ2)}=σT2 min(ζ1, ζ2),
σT2=π212 σn2A.
ϕ(ζ)=12 0ζ[A+wA(ζ1)]2dζ1-12 0ζwΩ2(ζ1)dζ1+0ζ-0ζ1wΩ(ζ2)dζ2+wT(ζ1)dwΩ(ζ1)+wϕ(ζ),
E{wϕ(ζ1)wϕ(ζ2)}=σϕ2 min(ζ1, ζ2)
σϕ2=σn23A 1+π212.
ϕGM(ζ)=12 0ζ[A+wA(ζ1)]2dζ1
ΨϕGM(ζ)(ν)=sec1/2(ζσAjν)expA22σA jν tan(ζσAjν).
ϕGM(ζ)=-j ddνΨϕGM(ζ)(ν)|ν=0=12A2ζ+14σA2ζ2,
σϕGM(ζ)2=-d2dν2ΨϕGM(ζ)(ν)|ν=0-ϕGM(ζ)2=13A2σA2ζ3+112σA4ζ4,
ϕΩ,T(ζ)=-12 0ζwΩ2(ζ1)dζ1-0ζ0ζ1wΩ(ζ2)dζ2dwΩ(ζ1)+0ζwT(ζ1)dwΩ(ζ1)
ϕΩ,T(ζ)=12 0ζwΩ2(ζ1)dζ1+0ζwT(ζ1)dwΩ(ζ1)-wΩ(ζ)0ζwΩ(ζ1)dζ1.
ΨϕΩ,T(ζ)(ν)=Ψϕ1,ϕ2,ϕ3ν2, ν,-ν.
ϕΩ,T(ζ)=-j ddνΨϕΩ,T(ζ)(ν)|ν=0=-14σΩ2ζ2,
σϕΩ,T(ζ)2=-d2dν2ΨϕΩ,T(ζ)(ν)|ν=0-ϕΩ,T(ζ)2=12σΩ2σT2ζ2+14σΩ4ζ4,
ϕLN(ζ)=wϕ(ζ)
ΨϕLN(ζ)(ν)=exp-12σϕ2ζν2.
ϕ(ζ)=ϕΩ,T(ζ)+ϕGM(ζ),
φ1=0ζwΩ2(ζ1)dζ1,
φ2=0ζwT(ζ1)dwΩ(ζ1),
φ3=wΩ(ζ)0ζwΩ(ζ1)dζ1.
φ2=0ζ0ζ1dwT(ζ2)dwΩ(ζ1)=0ζ[wΩ(ζ)-wΩ(ζ2)]dwT(ζ2).
Ψφ1,φ2,φ3(ν1, ν2, ν3)=E{exp(jν1φ1+jν2φ2+jν3φ3)},
Ψφ1,φ2,φ3(ν1, ν2, ν3)=E-σT2ν222 0ζ[wΩ(ζ)-wΩ(ζ1)]2dζ1+jν10ζwΩ2(ζ1)dζ1+jν3wΩ(ζ)0ζwΩ(ζ1)dζ1=E-σT2ν22ζ2wΩ2(ζ)+(jν3+σT2ν22)wΩ(ζ)0ζwΩ(ζ1)dζ1+jν1-σT2ν2220ζwΩ2(ζ1)dζ1.
Ejω1wΩ(ζ)+jω20ζwΩ(ζ1)dζ1+jω32 0ζwΩ2(ζ1)dζ1
=sec1/2(jω3σΩζ)exp-12 ω12σΩ2+ω22jω3 tan(jω3σΩζ)jω3σΩ+j ω1ω2ω3[sec(jω3σΩζ)-1]-j ω22ζ2ω3=sec1/2(jω3σΩζ)exp-12 ω1,2TC(jω3)ω1,2,
C(jω3)=σΩ tan(jω3σΩζ)jω31jω3[sec(jω3σΩζ)-1]1jω3[sec(jω3σΩζ)-1]1jω3 tan(jω3σΩζ)jω3σΩ-ζ.
limω30 C(jω3)=σΩ2ζ12ζ212ζ213ζ3,
wζ=wΩ(ζ), 0ζwΩ(ζ1)dζ1T
M(jν2, jν3)=-σT2ν22ζjν3+σT2ν22jν3+σT2ν220.
Ψφ1,φ2,φ3(ν1, ν2, ν3)
=sec1/2[(2jν1-σT2ν22)1/2σΩζ]det[I-C(2jν1-σT2ν22)M(jν2, jν3)]1/2,
Ψφ1(ν1)=sec1/2(2jν1σΩζ)
Ψφ2(ν2)=sech1/2(σTσΩζν2),
Ψφ3(ν3)=1-jν3σΩ2ζ2+112 ν32σΩ4ζ4-1/2.

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