Abstract

We discuss the possibility of exploiting spectral broadening resulting from fiber nonlinearity for the transmission of information. The spectral broadening induced by nonlinearity combined with the appropriate waveform can turn quadrature amplitude modulation-like constellations into frequency-shift-keying constellations over a much larger dimension. Thus, the Kerr effect can be thought of as a large dimensional mapper/modulator. A simple single-span fiber-optic link implemented over dispersion shifted fiber is assumed for the demonstration of the principle. It is shown that for a particular constellation the achievable data rates in the presence of nonlinearity can be significantly higher than the capacity characterizing a linear channel with the same input bandwidth.

© 2012 Optical Society of America

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References

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  1. P. V. Mamyshev, “All-optical data regeneration based on self-phase modulation effect,” in 24th European Conference on Optical Communications (ECOC ’98), Madrid, Spain, September 20, 1998 (1998).
  2. J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
    [CrossRef]
  3. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001), p. 98.
  4. A. Bhattacharya, Digital Communication, 3rd ed. (Tata McGraw-Hill Education, 2005), p. 391.
  5. J. Conway, N. Sloane, and E. Bannai, Sphere Packings, Lattices, and Groups, Grundlehren Der Mathematischen Wissenschaften (Springer, 1999), p. 10.
  6. R. E. Blahut, IEEE Trans. Inf. Theory 18, 460 (1972).
    [CrossRef]
  7. C. E. Shannon, Proc. IRE 37, 10 (1949).
    [CrossRef]
  8. K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, Phys. Rev. Lett. 91, 203901 (2003).
    [CrossRef]
  9. R. J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, Phys. Rev. Lett. 101, 163901 (2008).
    [CrossRef]
  10. E. Meron, M. Feder, and M. Shtaif, “On the achievable communication rates of generalized soliton transmission systems,” arxiv.org/abs/1207.0297 (2012).
  11. M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part I: mathematical tools,” arxiv.org/abs/1202.3653 (2012).

2008 (1)

R. J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef]

2003 (1)

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef]

2002 (1)

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

1972 (1)

R. E. Blahut, IEEE Trans. Inf. Theory 18, 460 (1972).
[CrossRef]

1949 (1)

C. E. Shannon, Proc. IRE 37, 10 (1949).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001), p. 98.

Andrekson, P.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Bannai, E.

J. Conway, N. Sloane, and E. Bannai, Sphere Packings, Lattices, and Groups, Grundlehren Der Mathematischen Wissenschaften (Springer, 1999), p. 10.

Bhattacharya, A.

A. Bhattacharya, Digital Communication, 3rd ed. (Tata McGraw-Hill Education, 2005), p. 391.

Blahut, R. E.

R. E. Blahut, IEEE Trans. Inf. Theory 18, 460 (1972).
[CrossRef]

Conway, J.

J. Conway, N. Sloane, and E. Bannai, Sphere Packings, Lattices, and Groups, Grundlehren Der Mathematischen Wissenschaften (Springer, 1999), p. 10.

Derevyanko, S. A.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef]

Essiambre, R. J.

R. J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef]

Feder, M.

E. Meron, M. Feder, and M. Shtaif, “On the achievable communication rates of generalized soliton transmission systems,” arxiv.org/abs/1207.0297 (2012).

Foschini, G. J.

R. J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef]

Hansryd, J.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Hedekvist, P. O.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Kramer, G.

R. J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef]

Kschischang, F. R.

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part I: mathematical tools,” arxiv.org/abs/1202.3653 (2012).

Li, J.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Mamyshev, P. V.

P. V. Mamyshev, “All-optical data regeneration based on self-phase modulation effect,” in 24th European Conference on Optical Communications (ECOC ’98), Madrid, Spain, September 20, 1998 (1998).

Meron, E.

E. Meron, M. Feder, and M. Shtaif, “On the achievable communication rates of generalized soliton transmission systems,” arxiv.org/abs/1207.0297 (2012).

Shannon, C. E.

C. E. Shannon, Proc. IRE 37, 10 (1949).
[CrossRef]

Shtaif, M.

E. Meron, M. Feder, and M. Shtaif, “On the achievable communication rates of generalized soliton transmission systems,” arxiv.org/abs/1207.0297 (2012).

Sloane, N.

J. Conway, N. Sloane, and E. Bannai, Sphere Packings, Lattices, and Groups, Grundlehren Der Mathematischen Wissenschaften (Springer, 1999), p. 10.

Turitsyn, K. S.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef]

Turitsyn, S. K.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef]

Westlund, M.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Winzer, P. J.

R. J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef]

Yousefi, M. I.

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part I: mathematical tools,” arxiv.org/abs/1202.3653 (2012).

Yurkevich, I. V.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef]

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

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

IEEE Trans. Inf. Theory (1)

R. E. Blahut, IEEE Trans. Inf. Theory 18, 460 (1972).
[CrossRef]

Phys. Rev. Lett. (2)

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef]

R. J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef]

Proc. IRE (1)

C. E. Shannon, Proc. IRE 37, 10 (1949).
[CrossRef]

Other (6)

P. V. Mamyshev, “All-optical data regeneration based on self-phase modulation effect,” in 24th European Conference on Optical Communications (ECOC ’98), Madrid, Spain, September 20, 1998 (1998).

E. Meron, M. Feder, and M. Shtaif, “On the achievable communication rates of generalized soliton transmission systems,” arxiv.org/abs/1207.0297 (2012).

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part I: mathematical tools,” arxiv.org/abs/1202.3653 (2012).

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001), p. 98.

A. Bhattacharya, Digital Communication, 3rd ed. (Tata McGraw-Hill Education, 2005), p. 391.

J. Conway, N. Sloane, and E. Bannai, Sphere Packings, Lattices, and Groups, Grundlehren Der Mathematischen Wissenschaften (Springer, 1999), p. 10.

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Figures (5)

Fig. 1.
Fig. 1.

Values of cn,k used in the signal constellation with n in the range of 1–8. Minimal distance pair for κ=0 is circled. The arrow marks the minimal distance pair for large κ.

Fig. 2.
Fig. 2.

Real part of the output electric field for pulses with different amplitudes. The curves are plotted for κ=5 and for different values of n.

Fig. 3.
Fig. 3.

Power spectrum (decibel units) of the signal for pulses with different amplitudes. The curves are plotted for κ=5 and for different values of n.

Fig. 4.
Fig. 4.

Minimal distance normalized to the average symbol energy Es for the 32-point constellation shown in Fig. 1 (k=1, 2, 3, 4 and n in the range of 1–8). The dashed horizontal line is an upper bound for the minimum distance that can be achieved with 32 points in the absence of spectral broadening [5]. The graph saturates at 0.44=2Egnmin/Es=2/4.5=0.44.

Fig. 5.
Fig. 5.

Solid curve is the achievable data rate with the constellation shown in Fig. 1. The dashed curve shows the Shannon capacity in the original bandwidth, i.e., without nonlinear broadening. The output bandwidth is approximately 10 times larger than that at the input.

Equations (4)

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

y(t)=x(t)ejγL|x(t)|2+n(t),
g(t)=2EgTs{tt[0,Ts/2]T/2tt[Ts/2,Ts]0t0ortTs,
cn,k=n·exp(kjπ/4),
dmin2=min0T|Q[cn,kg(t)]Q[cm,lg(t)]|2dt,

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