Abstract

Through numerical modeling, we illustrate the possibility of a new approach to digital signal processing in coherent optical communications based on the application of the so-called inverse scattering transform. Considering without loss of generality a fiber link with normal dispersion and quadrature phase shift keying signal modulation, we demonstrate how an initial information pattern can be recovered (without direct backward propagation) through the calculation of nonlinear spectral data of the received optical signal.

© 2013 Optical Society of America

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References

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  1. P. J. Winzer and R.-J. Essiambre, Proc. IEEE 94, 952 (2006).
    [CrossRef]
  2. S. J. Savory, Opt. Express 16, 804 (2008).
    [CrossRef]
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    [CrossRef]
  4. D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, IEEE J. Sel. Top. Quantum Electron. 16, 1217 (2010).
    [CrossRef]
  5. V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  6. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford University, 1995).
  7. S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons (Consultants Bureau, 1984).
  8. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM, 1981).
  9. A. Hasegawa and T. Nyu, J. Lightwave Technol. 11, 395 (1993).
    [CrossRef]
  10. E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, 1998).
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    [CrossRef]
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    [CrossRef]
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2012 (1)

2011 (3)

2010 (3)

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, IEEE J. Sel. Top. Quantum Electron. 16, 1217 (2010).
[CrossRef]

E. M. Ip and J. M. Kahn, J. Lightwave Technol. 28, 502 (2010).
[CrossRef]

L. B. Du and A. J. Lowery, Opt. Express 18, 17075 (2010).
[CrossRef]

2008 (2)

S. J. Savory, Opt. Express 16, 804 (2008).
[CrossRef]

J. D. Ania-Castanon, V. Karalekas, P. Harper, and S. K. Turitsyn, Phys. Rev. Lett. 101, 123903 (2008).
[CrossRef]

2006 (3)

P. J. Winzer and R.-J. Essiambre, Proc. IEEE 94, 952 (2006).
[CrossRef]

J. D. Ania-Castanon, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, Phys. Rev. Lett. 96, 023902 (2006).
[CrossRef]

T. J. Ellingham, J. D. Ania-Castanon, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, IEEE Photon. Technol. Lett. 18, 268 (2006).

2003 (2)

1993 (1)

A. Hasegawa and T. Nyu, J. Lightwave Technol. 11, 395 (1993).
[CrossRef]

1972 (1)

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Ablowitz, M. J.

M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM, 1981).

Ania-Castanon, J. D.

J. D. Ania-Castanon, V. Karalekas, P. Harper, and S. K. Turitsyn, Phys. Rev. Lett. 101, 123903 (2008).
[CrossRef]

J. D. Ania-Castanon, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, Phys. Rev. Lett. 96, 023902 (2006).
[CrossRef]

T. J. Ellingham, J. D. Ania-Castanon, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, IEEE Photon. Technol. Lett. 18, 268 (2006).

Bayvel, P.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, IEEE J. Sel. Top. Quantum Electron. 16, 1217 (2010).
[CrossRef]

Behrens, C.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, IEEE J. Sel. Top. Quantum Electron. 16, 1217 (2010).
[CrossRef]

Chen, X.

J. D. Ania-Castanon, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, Phys. Rev. Lett. 96, 023902 (2006).
[CrossRef]

T. J. Ellingham, J. D. Ania-Castanon, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, IEEE Photon. Technol. Lett. 18, 268 (2006).

Chugtai, M. N.

Du, L. B.

Ellingham, T. J.

T. J. Ellingham, J. D. Ania-Castanon, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, IEEE Photon. Technol. Lett. 18, 268 (2006).

J. D. Ania-Castanon, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, Phys. Rev. Lett. 96, 023902 (2006).
[CrossRef]

Ellis, A. D.

Essiambre, R.-J.

P. J. Winzer and R.-J. Essiambre, Proc. IEEE 94, 952 (2006).
[CrossRef]

Forzati, M.

Harper, P.

J. D. Ania-Castanon, V. Karalekas, P. Harper, and S. K. Turitsyn, Phys. Rev. Lett. 101, 123903 (2008).
[CrossRef]

Hasegawa, A.

A. Hasegawa and T. Nyu, J. Lightwave Technol. 11, 395 (1993).
[CrossRef]

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford University, 1995).

Hellerbrand, S.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, IEEE J. Sel. Top. Quantum Electron. 16, 1217 (2010).
[CrossRef]

Holzlohner, R.

Iannone, E.

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

Ibbotson, R.

J. D. Ania-Castanon, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, Phys. Rev. Lett. 96, 023902 (2006).
[CrossRef]

T. J. Ellingham, J. D. Ania-Castanon, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, IEEE Photon. Technol. Lett. 18, 268 (2006).

Ip, E. M.

Kahn, J. M.

Karalekas, V.

J. D. Ania-Castanon, V. Karalekas, P. Harper, and S. K. Turitsyn, Phys. Rev. Lett. 101, 123903 (2008).
[CrossRef]

Kikuchi, K.

K. Kikuchi, IEICE Electron. Exp. 8, 1642 (2011).
[CrossRef]

Killey, R. I.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, IEEE J. Sel. Top. Quantum Electron. 16, 1217 (2010).
[CrossRef]

Kodama, Y.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford University, 1995).

Korotkevich, A. O.

Li, G.

Lowery, A. J.

Lushnikov, P. M.

Makovejs, S.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, IEEE J. Sel. Top. Quantum Electron. 16, 1217 (2010).
[CrossRef]

Manakov, S. V.

S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons (Consultants Bureau, 1984).

Matera, F.

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

Mecozzi, A.

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

Menyuk, C. R.

Millar, D. S.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, IEEE J. Sel. Top. Quantum Electron. 16, 1217 (2010).
[CrossRef]

Mrtensson, J.

Mussolin, M.

Novikov, S. P.

S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons (Consultants Bureau, 1984).

Nyu, T.

A. Hasegawa and T. Nyu, J. Lightwave Technol. 11, 395 (1993).
[CrossRef]

Pitaevskii, L. P.

S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons (Consultants Bureau, 1984).

Rafique, D.

Savory, S. J.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, IEEE J. Sel. Top. Quantum Electron. 16, 1217 (2010).
[CrossRef]

S. J. Savory, Opt. Express 16, 804 (2008).
[CrossRef]

Segur, H.

M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM, 1981).

Settembre, M.

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

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Sinkin, O. V.

Skaar, J.

J. Skaar and O. H. Waagaard, IEEE J. Quantum Electron. 39, 1238 (2003).
[CrossRef]

Turitsyn, S. K.

J. D. Ania-Castanon, V. Karalekas, P. Harper, and S. K. Turitsyn, Phys. Rev. Lett. 101, 123903 (2008).
[CrossRef]

T. J. Ellingham, J. D. Ania-Castanon, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, IEEE Photon. Technol. Lett. 18, 268 (2006).

J. D. Ania-Castanon, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, Phys. Rev. Lett. 96, 023902 (2006).
[CrossRef]

Waagaard, O. H.

J. Skaar and O. H. Waagaard, IEEE J. Quantum Electron. 39, 1238 (2003).
[CrossRef]

Winzer, P. J.

P. J. Winzer and R.-J. Essiambre, Proc. IEEE 94, 952 (2006).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons (Consultants Bureau, 1984).

Zhang, L.

J. D. Ania-Castanon, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, Phys. Rev. Lett. 96, 023902 (2006).
[CrossRef]

T. J. Ellingham, J. D. Ania-Castanon, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, IEEE Photon. Technol. Lett. 18, 268 (2006).

Zhu, L.

Zweck, J.

IEEE J. Quantum Electron. (1)

J. Skaar and O. H. Waagaard, IEEE J. Quantum Electron. 39, 1238 (2003).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, IEEE J. Sel. Top. Quantum Electron. 16, 1217 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. J. Ellingham, J. D. Ania-Castanon, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, IEEE Photon. Technol. Lett. 18, 268 (2006).

IEICE Electron. Exp. (1)

K. Kikuchi, IEICE Electron. Exp. 8, 1642 (2011).
[CrossRef]

J. Lightwave Technol. (3)

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. Lett. (2)

J. D. Ania-Castanon, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, Phys. Rev. Lett. 96, 023902 (2006).
[CrossRef]

J. D. Ania-Castanon, V. Karalekas, P. Harper, and S. K. Turitsyn, Phys. Rev. Lett. 101, 123903 (2008).
[CrossRef]

Proc. IEEE (1)

P. J. Winzer and R.-J. Essiambre, Proc. IEEE 94, 952 (2006).
[CrossRef]

Sov. Phys. JETP (1)

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Other (4)

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford University, 1995).

S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons (Consultants Bureau, 1984).

M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM, 1981).

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

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Figures (5)

Fig. 1.
Fig. 1.

Real (blue) and imaginary (green) parts of the input optical signal.

Fig. 2.
Fig. 2.

Input (blue line) and propagated (green line at z=50, red line at z=100) optical signals; inset, constellation diagram (for cn) of the input signal.

Fig. 3.
Fig. 3.

(a) |r(δ)z=0| and |r(δ)z=50|, (b) imaginary part of ln(r(δ)z=50/r(δ)z=0), (c) |FU(ω)z=0| and |FU(ω)z=50|, and (d) imaginary part of ln(FU(ω)z=50/(FU(ω)z=0).

Fig. 4.
Fig. 4.

Eye diagram for the signals reconstructed via FT, (a) at z=25, (b) at z=50, (c) at z=75, and (d) at z=100; and via IST, (e) at z=25, (f) at z=50, (g) at z=75, and (h) at z=100.

Fig. 5.
Fig. 5.

Constellation diagram for the signals reconstructed via FT, (a) at z=25, (b) at z=50, (c) at z=75, and (d) at z=100; and via IST, (e) at z=25, (f) at z=50, (g) at z=75, and (h) at z=100.

Equations (3)

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

iUzs2Utt+|U|2U=0,
dudt=+iδu+U(t)v,dvdt=iδv+U*(t)u.
r(δ)z=50=r(δ)z=0×e2i×L×δ2.

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