Abstract

We compute in the femtosecond regime the coherence time compression ratio and the corresponding spectral broadening owing to self-phase modulation of an incoherent signal propagating in an optical fiber. We incorporate in our differential equation the terms responsible for group-velocity dispersion, higher-order dispersion terms self-steepening, and induced Raman scattering. Using typical fiber parameters, we show that it is possible to compress the coherence time of an incoherent signal to few femtoseconds.

© 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. S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, Phys. Rev. A 29, 2286 (1984).
    [CrossRef]
  3. N. Morita, T. Yajima, Phys. Rev. A 30, 2525 (1984).
    [CrossRef]
  4. J. T. Manassah, Opt. Lett. 15, 329 (1990).
    [CrossRef] [PubMed]
  5. M. T. de Araujo, H. R. da Cruz, A. S. Gouveia-Neto, J. Opt. Soc. Am. B 8, 2094 (1991).
    [CrossRef]
  6. F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
    [CrossRef]
  7. R. H. Stolen, E. P. Ippen, Appl. Phys. Lett. 22, 276 (1973); R. H. Stolen, J. P. Gordon, W. J. Tomlinson, H. A. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
    [CrossRef]
  8. R. L. Fork, C. H. Brito-Cruz, P. C. Becker, C. V. Shank, Opt. Lett. 12, 483 (1987).
    [CrossRef] [PubMed]
  9. N. Wax, ed., Noise and Stochastic Processes (Dover, New York, 1954).
  10. For a recent review see, for example, The Laser Supercontinuum Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989).
  11. See, for example, A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1984).
  12. J. T. Manassah, Opt. Lett. 16, 1638 (1991).
    [CrossRef] [PubMed]

1991 (2)

1990 (1)

1987 (1)

1984 (3)

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

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, Phys. Rev. A 29, 2286 (1984).
[CrossRef]

N. Morita, T. Yajima, Phys. Rev. A 30, 2525 (1984).
[CrossRef]

1973 (1)

R. H. Stolen, E. P. Ippen, Appl. Phys. Lett. 22, 276 (1973); R. H. Stolen, J. P. Gordon, W. J. Tomlinson, H. A. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
[CrossRef]

1967 (1)

F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Asaka, S.

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, Phys. Rev. A 29, 2286 (1984).
[CrossRef]

Beach, R.

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

Becker, P. C.

Brito-Cruz, C. H.

da Cruz, H. R.

de Araujo, M. T.

De Martini, F.

F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Fork, R. L.

Fujiwara, M.

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, Phys. Rev. A 29, 2286 (1984).
[CrossRef]

Gouveia-Neto, A. S.

Gustafson, T. K.

F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Hartmann, S. R.

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

Ippen, E. P.

R. H. Stolen, E. P. Ippen, Appl. Phys. Lett. 22, 276 (1973); R. H. Stolen, J. P. Gordon, W. J. Tomlinson, H. A. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
[CrossRef]

Kelley, P. L.

F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Manassah, J. T.

Matsuoka, M.

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, Phys. Rev. A 29, 2286 (1984).
[CrossRef]

Morita, N.

N. Morita, T. Yajima, Phys. Rev. A 30, 2525 (1984).
[CrossRef]

Nakatsuka, H.

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, Phys. Rev. A 29, 2286 (1984).
[CrossRef]

Papoulis, A.

See, for example, A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1984).

Shank, C. V.

Stolen, R. H.

R. H. Stolen, E. P. Ippen, Appl. Phys. Lett. 22, 276 (1973); R. H. Stolen, J. P. Gordon, W. J. Tomlinson, H. A. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
[CrossRef]

Townes, C. H.

F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Yajima, T.

N. Morita, T. Yajima, Phys. Rev. A 30, 2525 (1984).
[CrossRef]

Appl. Phys. Lett. (1)

R. H. Stolen, E. P. Ippen, Appl. Phys. Lett. 22, 276 (1973); R. H. Stolen, J. P. Gordon, W. J. Tomlinson, H. A. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
[CrossRef]

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

Opt. Lett. (3)

Phys. Rev. (1)

F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Phys. Rev. A (2)

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, Phys. Rev. A 29, 2286 (1984).
[CrossRef]

N. Morita, T. Yajima, Phys. Rev. A 30, 2525 (1984).
[CrossRef]

Phys. Rev. Lett. (1)

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

Other (3)

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

For a recent review see, for example, The Laser Supercontinuum Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989).

See, for example, A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1984).

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Figures (4)

Fig. 1
Fig. 1

Magnitude of the normalized autocorrelation function plotted as function of the normalized time. The incoherent signal parameters are Tc = 50 fs, λ0 = 1 μm, and n2E02 = 10−3; the material parameters are ΩR = 4.76, ΓR = 4.85, χ0 = 0.275, β(2) = 2 × 10−26 s2/m, and β(3) = 5 × 10−41 s3/m. Curve i, ∊V = 0; curve ii, ∊V = 0.06; curve iii, ∊V = 0.1; curve iv, ∊V = 0.2; curve v, ∊V = 0.26.

Fig. 2
Fig. 2

Comparison of the magnitude of the normalized autocorrelation function between the full theory and the simple dispersionless theory. The parameters of Fig. 1 are assumed. Curve i, ∊V = 0.1, full theory; curve ii, ∊V = 0.1, dispersionless theory; curve iii, ∊V = 0.26, full theory; curve iv, ∊V = 0.26, dispersionless theory.

Fig. 3
Fig. 3

Compression ratio of the HWHM as a function of ∊V. The parameters of Fig. 1 are assumed, and τ H WHM in = 41.63 fs. Curve i, full theory; curve ii, dispersionless theory.

Fig. 4
Fig. 4

Spectral distribution plotted as a function of the frequency difference multiplied by the initial coherence time (i.e., the normalized frequency difference). The parameters of Fig. 1 are assumed. Curve i, ∊V = 0; curve ii, ∊V = 0.06; curve iii, ∊V = 0.1; curve iv, ∊V = 0.2; curve v, ∊V = 0.26.

Equations (8)

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ϕ ˜ ( Ω , V ) V = i K 2 ( 1 - Ω K ) F [ ϕ ( U , V ) 2 ϕ ( U , V ) ] + i K 2 F ( ϕ ( U , V ) F - 1 { χ R ( Ω ) F [ ϕ ( U , V ) 2 ] } ) + i ( ν g T c ) [ β ( 2 ) Ω 2 2 T c 2 - β ( 3 ) Ω 3 6 T c 3 ] ϕ ˜ ( Ω , V ) ,
E = E 0 ϕ ,             = n 2 E 0 2 n 0 , V = z ν g T c ,             U = z ν g T c - t T c ,
χ R ( Ω ) = χ 0 Ω R Γ R Ω R 2 - Ω 2 + i Γ R Ω ,
K ( T , V = 0 ) = E 0 2 ϕ * ( U + T / T c , V = 0 ) ϕ ( U , V = 0 ) = E 0 2 f = E 0 2 exp ( - T 2 / T c 2 ) ,
T i j = exp [ - ( j - i ) 2 p 2 ] ,
R i j = μ = 1 L ϕ μ i * ( V ) ϕ μ j ( V ) [ μ = 1 L ϕ μ i * ( V ) ϕ μ i ( V ) ] 1 / 2 [ μ = 1 L ϕ μ j * ( V ) ϕ μ j ( V ) ] 1 / 2 ,
K m ( V ) = E 0 2 exp ( - i ω 0 T ) i = 0 M - m - 1 R i , m + i ( V ) M - m .
K ( T , V ) = E 0 2 exp ( - i ω 0 T ) f [ 1 + α 2 ( 1 - f 2 ) ] 2 ,

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