Abstract

We apply an approach based on the Fokker–Planck equation to study the statistics of optical soliton parameters in the presence of additive noise. This rigorous method not only allows us to reproduce and justify the classical Gordon–Haus formula but also leads to new exact results.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. P. Gordon and H. A. Haus, Opt. Lett. 11,665 (1986).
    [CrossRef] [PubMed]
  2. J. Elgin, Phys. Lett. A 110,441 (1985).
    [CrossRef]
  3. T. Georges, Opt. Commun. 123,617 (1996).
    [CrossRef]
  4. C. R. Menyuk, Opt. Lett. 20,285 (1995).
    [CrossRef] [PubMed]
  5. F. Kh. Abdullaev, S. A. Darmanyan, and F. Lederer, Opt. Commun. 126, 89 (1996).
    [CrossRef]
  6. J. P. Gordon and L. F. Mollenauer, Opt. Lett. 15,1351 (1990).
    [CrossRef] [PubMed]
  7. C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8,616 (2002).
    [CrossRef]
  8. G. Falkovich, I. Kolokolov, V. Lebedev, and S. Turitsyn, Phys. Rev. E 63,025601(R) (2001).
    [CrossRef]
  9. G. Falkovich, M. G. Stepanov, and S. K. Turitsyn, Phys. Rev. E 64,067602 (2001).
    [CrossRef]
  10. E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).
  11. D. J. Kaup, Phys. Rev. A 42,5689 (1990).
    [CrossRef] [PubMed]
  12. H. A. Haus and Y. Lai, J. Opt. Soc. Am. B 7,386 (1990).
    [CrossRef]
  13. H. Risken, The Fokker–Planck Equation (Springer, New York, 1996).
  14. B. A. Malomed and N. Flytzanis, Phys. Rev. E 48, 5 (1993).
    [CrossRef]

2002 (1)

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8,616 (2002).
[CrossRef]

2001 (2)

G. Falkovich, I. Kolokolov, V. Lebedev, and S. Turitsyn, Phys. Rev. E 63,025601(R) (2001).
[CrossRef]

G. Falkovich, M. G. Stepanov, and S. K. Turitsyn, Phys. Rev. E 64,067602 (2001).
[CrossRef]

1996 (2)

T. Georges, Opt. Commun. 123,617 (1996).
[CrossRef]

F. Kh. Abdullaev, S. A. Darmanyan, and F. Lederer, Opt. Commun. 126, 89 (1996).
[CrossRef]

1995 (1)

1993 (1)

B. A. Malomed and N. Flytzanis, Phys. Rev. E 48, 5 (1993).
[CrossRef]

1990 (3)

1986 (1)

1985 (1)

J. Elgin, Phys. Lett. A 110,441 (1985).
[CrossRef]

Abdullaev, F. Kh.

F. Kh. Abdullaev, S. A. Darmanyan, and F. Lederer, Opt. Commun. 126, 89 (1996).
[CrossRef]

Darmanyan, S. A.

F. Kh. Abdullaev, S. A. Darmanyan, and F. Lederer, Opt. Commun. 126, 89 (1996).
[CrossRef]

Elgin, J.

J. Elgin, Phys. Lett. A 110,441 (1985).
[CrossRef]

Falkovich, G.

G. Falkovich, M. G. Stepanov, and S. K. Turitsyn, Phys. Rev. E 64,067602 (2001).
[CrossRef]

G. Falkovich, I. Kolokolov, V. Lebedev, and S. Turitsyn, Phys. Rev. E 63,025601(R) (2001).
[CrossRef]

Flytzanis, N.

B. A. Malomed and N. Flytzanis, Phys. Rev. E 48, 5 (1993).
[CrossRef]

Georges, T.

T. Georges, Opt. Commun. 123,617 (1996).
[CrossRef]

Gordon, J. P.

Haus, H. A.

Iannone, E.

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

Kaup, D. J.

D. J. Kaup, Phys. Rev. A 42,5689 (1990).
[CrossRef] [PubMed]

Kolokolov, I.

G. Falkovich, I. Kolokolov, V. Lebedev, and S. Turitsyn, Phys. Rev. E 63,025601(R) (2001).
[CrossRef]

Lai, Y.

Lebedev, V.

G. Falkovich, I. Kolokolov, V. Lebedev, and S. Turitsyn, Phys. Rev. E 63,025601(R) (2001).
[CrossRef]

Lederer, F.

F. Kh. Abdullaev, S. A. Darmanyan, and F. Lederer, Opt. Commun. 126, 89 (1996).
[CrossRef]

Malomed, B. A.

B. A. Malomed and N. Flytzanis, Phys. Rev. E 48, 5 (1993).
[CrossRef]

Matera, F.

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

McKinstrie, C. J.

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8,616 (2002).
[CrossRef]

Mecozzi, A.

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

Menyuk, C. R.

Mollenauer, L. F.

Risken, H.

H. Risken, The Fokker–Planck Equation (Springer, New York, 1996).

Settembre, M.

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

Stepanov, M. G.

G. Falkovich, M. G. Stepanov, and S. K. Turitsyn, Phys. Rev. E 64,067602 (2001).
[CrossRef]

Turitsyn, S.

G. Falkovich, I. Kolokolov, V. Lebedev, and S. Turitsyn, Phys. Rev. E 63,025601(R) (2001).
[CrossRef]

Turitsyn, S. K.

G. Falkovich, M. G. Stepanov, and S. K. Turitsyn, Phys. Rev. E 64,067602 (2001).
[CrossRef]

Xie, C.

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8,616 (2002).
[CrossRef]

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

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8,616 (2002).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

T. Georges, Opt. Commun. 123,617 (1996).
[CrossRef]

F. Kh. Abdullaev, S. A. Darmanyan, and F. Lederer, Opt. Commun. 126, 89 (1996).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. A (1)

J. Elgin, Phys. Lett. A 110,441 (1985).
[CrossRef]

Phys. Rev. A (1)

D. J. Kaup, Phys. Rev. A 42,5689 (1990).
[CrossRef] [PubMed]

Phys. Rev. E (3)

G. Falkovich, I. Kolokolov, V. Lebedev, and S. Turitsyn, Phys. Rev. E 63,025601(R) (2001).
[CrossRef]

G. Falkovich, M. G. Stepanov, and S. K. Turitsyn, Phys. Rev. E 64,067602 (2001).
[CrossRef]

B. A. Malomed and N. Flytzanis, Phys. Rev. E 48, 5 (1993).
[CrossRef]

Other (2)

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

H. Risken, The Fokker–Planck Equation (Springer, New York, 1996).

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.


Equations (24)

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

qz=i22qτ2+iq2q+nτ,z.
nτ,z=nτ,znτ,z=0,
nτ,zn*τ,z=Dδz-zδτ-τ.
q0τ,z=AzsechAzτ-Tzexp-iΩzτ+iϕz,
Az=A0,
Ωz=Ω0,
ϕz=ϕ0+12A02-Ω02z,
Tz=T0-Ω0z,
dAdz=RedτgA*τnτ,z,
dϕdz=12A2-Ω2+TdΩzdz+Redτgϕ*τ,znτ,z,
dΩdz=RedτgΩ*τ,znτ,z,
dTdz=-Ω+RedτgT*τ,znτ,z,
gAτ,z=q0τ,z,A,ϕ,Ω,T,
gϕτ,z=iA1-Aτ-TtanhAτ-T×q0τ,z,A,ϕ,Ω,T,
gΩτ,z=-i tanhAτ-Tq0τ,z,A,ϕ,Ω,T,
gTτ,z=τ-TAq0τ,z,A,ϕ,Ω,T.
Pz=-12A2-Ω2Pϕ+ΩPT+D16AT2+112A2+π262Pϕ2+D3AT2PϕΩ+D2A2PA2+D6A2PΩ2+Dπ224A32PT2.
Pz=-QiDiQP+2QiQjDijQP,
PΩ,Tz=-T-ΩP+2Ω2D6A0P+2T2Dπ224A03P.
Pz=D2A2PA2+D6A2PΩ2.
P(Ω,A|z)=12π-PkA,zexp-ikΩdk,
Pk(A|z)=AA01/2αksinhαkzexp-αkA+A0×cothαkzI12αkAA0sinhαkz,
P(A|z)=1zAA01/2exp-A+A0zI12AA0z.
PAAA01/2exp-A-A02z, A.

Metrics