Abstract

The effects of self-phase modulation on a Gaussian incoherent field propagating in a dispersionless nonlinear Kerr medium are calculated without assuming the mean-field-theory approximation. Deviations between the exact and approximate solutions for the correlation time compression ratio as a function of the pulse power and fiber length are computed.

© 1991 Optical Society of America

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References

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  1. R. Beach, S. R. Hartmann, Phys. Rev. Lett. 53, 663 (1984).
    [CrossRef]
  2. J. T. Manassah, Opt. Lett. 15, 329 (1990).
    [CrossRef] [PubMed]
  3. M. T. de Araujo, J. M. Hickmann, H. R. da Cruz, A. S. Gouveia-Neto, in Conference on Lasers and Electro-Optics, Vol. 10 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CWG1.
  4. N. Wax, ed., Noise and Stochastic Processes (Dover, New York, 1954).
  5. M. C. Wang, G. E. Uhlenbeck, Rev. Mod. Phys. 17, 323 (1945).
    [CrossRef]
  6. J. T. Manassah, Opt. Lett. 16, 1379 (1991).
    [CrossRef] [PubMed]

1991 (1)

1990 (1)

1984 (1)

R. Beach, S. R. Hartmann, Phys. Rev. Lett. 53, 663 (1984).
[CrossRef]

1945 (1)

M. C. Wang, G. E. Uhlenbeck, Rev. Mod. Phys. 17, 323 (1945).
[CrossRef]

Beach, R.

R. Beach, S. R. Hartmann, Phys. Rev. Lett. 53, 663 (1984).
[CrossRef]

da Cruz, H. R.

M. T. de Araujo, J. M. Hickmann, H. R. da Cruz, A. S. Gouveia-Neto, in Conference on Lasers and Electro-Optics, Vol. 10 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CWG1.

de Araujo, M. T.

M. T. de Araujo, J. M. Hickmann, H. R. da Cruz, A. S. Gouveia-Neto, in Conference on Lasers and Electro-Optics, Vol. 10 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CWG1.

Gouveia-Neto, A. S.

M. T. de Araujo, J. M. Hickmann, H. R. da Cruz, A. S. Gouveia-Neto, in Conference on Lasers and Electro-Optics, Vol. 10 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CWG1.

Hartmann, S. R.

R. Beach, S. R. Hartmann, Phys. Rev. Lett. 53, 663 (1984).
[CrossRef]

Hickmann, J. M.

M. T. de Araujo, J. M. Hickmann, H. R. da Cruz, A. S. Gouveia-Neto, in Conference on Lasers and Electro-Optics, Vol. 10 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CWG1.

Manassah, J. T.

Uhlenbeck, G. E.

M. C. Wang, G. E. Uhlenbeck, Rev. Mod. Phys. 17, 323 (1945).
[CrossRef]

Wang, M. C.

M. C. Wang, G. E. Uhlenbeck, Rev. Mod. Phys. 17, 323 (1945).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

R. Beach, S. R. Hartmann, Phys. Rev. Lett. 53, 663 (1984).
[CrossRef]

Rev. Mod. Phys. (1)

M. C. Wang, G. E. Uhlenbeck, Rev. Mod. Phys. 17, 323 (1945).
[CrossRef]

Other (2)

M. T. de Araujo, J. M. Hickmann, H. R. da Cruz, A. S. Gouveia-Neto, in Conference on Lasers and Electro-Optics, Vol. 10 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CWG1.

N. Wax, ed., Noise and Stochastic Processes (Dover, New York, 1954).

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Figures (5)

Fig. 1
Fig. 1

Magnitude of the outgoing field normalized correlation function KN(T/Tc) plotted as a function of the normalized time for different values of the α parameter for an initial correlation function with Gaussian shape. Curve i, α2 = 0.1; curve ii, α2 = 1; curve iii, α2 = 10.

Fig. 2
Fig. 2

Comparison of the magnitude of the normalized correlation function for the exact (curve i) and mean-field theory (curve ii) solutions. α = 10.

Fig. 3
Fig. 3

Ratio of the outgoing to the incoming coherence times plotted as a function of the parameter α for an initial correlation function with Gaussian shape. Curve i, exact theory; curve ii, mean-field theory.

Fig. 4
Fig. 4

Ratio of the outgoing to the incoming coherence times plotted as a function of the parameter α for an initial correlation function shape that is Gaussian (curve i) or Lorentzian (curve ii).

Fig. 5
Fig. 5

Spectral distribution S(Ω) in arbitrary units plotted as a function of the normalized frequency difference for different values of the α parameter for an incoherent signal whose initial spectral distribution is Lorentzian. Curve i, α2 = 0.1; curve ii, α2 = 1; curve iii, α2 = 5.

Equations (8)

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A ( u , z ) = A ( u , 0 ) exp [ i ω 0 n 2 c A ( u , 0 ) 2 z ] ,
K ( T , z ) = E * ( u + T , z ) E ( u , z ) = exp ( - i ω 0 T ) A * ( u + T , z ) A ( u , z ) = A 0 2 exp ( - i ω 0 T ) ψ * ( T , 0 ) ψ ( 0 , 0 ) × exp [ - i α ψ * ( T , 0 ) ψ ( T , 0 ) + i α ψ * ( 0 , 0 ) ψ ( 0 , 0 ) ] ,
A * ( u + T , 0 ) A ( u , 0 ) A 0 2 f ( T ) .
K ( T , z ) = A 0 2 exp ( - i ω 0 T ) f [ 1 + α 2 ( 1 - f 2 ) ] 2 .
S ( Ω , z ) = 1 2 π - - K ( T , z ) exp ( i ω T ) d T ,
S ( Ω , z ) T c = A 0 2 π ( 1 + α 2 ) 2 Re [ 1 ( 1 + i Ω T c ) × F 2 1 ( 2 , 1 + i Ω T c 2 , 3 + i Ω T c 2 , α 2 1 + α 2 ) ] ,
- S ( Ω , z ) d Ω = K ( 0 , z ) = A 0 2 .
K 2 ( T , z ) = A 2 2 exp ( - i ω 2 T ) f 2 [ 1 + α 2 2 ( 1 - f 2 2 ) ] 2 × 1 [ 1 + 4 α 1 2 ( 1 - f 1 2 ) ] ,

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