Abstract

We examine the effects of optical nonlinearities that are due to the intensity-dependent index of refraction in optical fibers. The broadening of the frequency spectrum of an optical pulse will combine with the group-velocity dispersion, increasing the temporal pulse spreading, thereby limiting the information transmission rate. We derive an exact formula for the rms frequency width of a Gaussian input pulse after it undergoes self-phase modulation. This new formula gives good agreement with experimental results.

© 1985 Optical Society of America

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References

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  1. R. H. Stolen, “Nonlinearity in fiber transmission,” Proc. IEEE 68, 1232–1236 (1980).
    [Crossref]
  2. R. H. Stolen and C. Lin, “Self phase modulation in silica optical fibers,” Phy. Rev. A 17, 1448–1453 (1978).
    [Crossref]
  3. A. Hasegawa and Y. Kodama, “Signal transmission by optical solitons in monomode fiber,” Proc. IEEE 69, 1145–1150 (1981).
    [Crossref]
  4. C. H. Lin and T. K. Gustafson, “Optical pulsewidth measurement using self phase modulation,” IEEE J. Quantum Electron. QE-8, 429–430 (1972).
    [Crossref]
  5. R. A. Fisher and W. K. Bischel, “Numerical studies of the interplay between self phase modulation and dispersion for intense plane wave laser pulses,” J. Appl. Phys. 46, 4921–4934 (1975).
    [Crossref]
  6. N. Tzoar and M. Jain, “Self phase modulation in long-geometry optical waveguides,” Phy. Rev. A 23, 1266–1269 (1981).
    [Crossref]
  7. D. Anderson and M. Lisak, “Nonlinear asymmetric self phase modulation and self steepening of pulses in long optical waveguides,” Phy. Rev. A 27, 1393–1398 (1983).
    [Crossref]

1983 (1)

D. Anderson and M. Lisak, “Nonlinear asymmetric self phase modulation and self steepening of pulses in long optical waveguides,” Phy. Rev. A 27, 1393–1398 (1983).
[Crossref]

1981 (2)

N. Tzoar and M. Jain, “Self phase modulation in long-geometry optical waveguides,” Phy. Rev. A 23, 1266–1269 (1981).
[Crossref]

A. Hasegawa and Y. Kodama, “Signal transmission by optical solitons in monomode fiber,” Proc. IEEE 69, 1145–1150 (1981).
[Crossref]

1980 (1)

R. H. Stolen, “Nonlinearity in fiber transmission,” Proc. IEEE 68, 1232–1236 (1980).
[Crossref]

1978 (1)

R. H. Stolen and C. Lin, “Self phase modulation in silica optical fibers,” Phy. Rev. A 17, 1448–1453 (1978).
[Crossref]

1975 (1)

R. A. Fisher and W. K. Bischel, “Numerical studies of the interplay between self phase modulation and dispersion for intense plane wave laser pulses,” J. Appl. Phys. 46, 4921–4934 (1975).
[Crossref]

1972 (1)

C. H. Lin and T. K. Gustafson, “Optical pulsewidth measurement using self phase modulation,” IEEE J. Quantum Electron. QE-8, 429–430 (1972).
[Crossref]

Anderson, D.

D. Anderson and M. Lisak, “Nonlinear asymmetric self phase modulation and self steepening of pulses in long optical waveguides,” Phy. Rev. A 27, 1393–1398 (1983).
[Crossref]

Bischel, W. K.

R. A. Fisher and W. K. Bischel, “Numerical studies of the interplay between self phase modulation and dispersion for intense plane wave laser pulses,” J. Appl. Phys. 46, 4921–4934 (1975).
[Crossref]

Fisher, R. A.

R. A. Fisher and W. K. Bischel, “Numerical studies of the interplay between self phase modulation and dispersion for intense plane wave laser pulses,” J. Appl. Phys. 46, 4921–4934 (1975).
[Crossref]

Gustafson, T. K.

C. H. Lin and T. K. Gustafson, “Optical pulsewidth measurement using self phase modulation,” IEEE J. Quantum Electron. QE-8, 429–430 (1972).
[Crossref]

Hasegawa, A.

A. Hasegawa and Y. Kodama, “Signal transmission by optical solitons in monomode fiber,” Proc. IEEE 69, 1145–1150 (1981).
[Crossref]

Jain, M.

N. Tzoar and M. Jain, “Self phase modulation in long-geometry optical waveguides,” Phy. Rev. A 23, 1266–1269 (1981).
[Crossref]

Kodama, Y.

A. Hasegawa and Y. Kodama, “Signal transmission by optical solitons in monomode fiber,” Proc. IEEE 69, 1145–1150 (1981).
[Crossref]

Lin, C.

R. H. Stolen and C. Lin, “Self phase modulation in silica optical fibers,” Phy. Rev. A 17, 1448–1453 (1978).
[Crossref]

Lin, C. H.

C. H. Lin and T. K. Gustafson, “Optical pulsewidth measurement using self phase modulation,” IEEE J. Quantum Electron. QE-8, 429–430 (1972).
[Crossref]

Lisak, M.

D. Anderson and M. Lisak, “Nonlinear asymmetric self phase modulation and self steepening of pulses in long optical waveguides,” Phy. Rev. A 27, 1393–1398 (1983).
[Crossref]

Stolen, R. H.

R. H. Stolen, “Nonlinearity in fiber transmission,” Proc. IEEE 68, 1232–1236 (1980).
[Crossref]

R. H. Stolen and C. Lin, “Self phase modulation in silica optical fibers,” Phy. Rev. A 17, 1448–1453 (1978).
[Crossref]

Tzoar, N.

N. Tzoar and M. Jain, “Self phase modulation in long-geometry optical waveguides,” Phy. Rev. A 23, 1266–1269 (1981).
[Crossref]

IEEE J. Quantum Electron. (1)

C. H. Lin and T. K. Gustafson, “Optical pulsewidth measurement using self phase modulation,” IEEE J. Quantum Electron. QE-8, 429–430 (1972).
[Crossref]

J. Appl. Phys. (1)

R. A. Fisher and W. K. Bischel, “Numerical studies of the interplay between self phase modulation and dispersion for intense plane wave laser pulses,” J. Appl. Phys. 46, 4921–4934 (1975).
[Crossref]

Phy. Rev. A (3)

N. Tzoar and M. Jain, “Self phase modulation in long-geometry optical waveguides,” Phy. Rev. A 23, 1266–1269 (1981).
[Crossref]

D. Anderson and M. Lisak, “Nonlinear asymmetric self phase modulation and self steepening of pulses in long optical waveguides,” Phy. Rev. A 27, 1393–1398 (1983).
[Crossref]

R. H. Stolen and C. Lin, “Self phase modulation in silica optical fibers,” Phy. Rev. A 17, 1448–1453 (1978).
[Crossref]

Proc. IEEE (2)

A. Hasegawa and Y. Kodama, “Signal transmission by optical solitons in monomode fiber,” Proc. IEEE 69, 1145–1150 (1981).
[Crossref]

R. H. Stolen, “Nonlinearity in fiber transmission,” Proc. IEEE 68, 1232–1236 (1980).
[Crossref]

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Equations (14)

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i A z + i γ A + n 2 ω 0 c A 2 A = 0.
r ( z , τ ) = r 0 ( τ ) exp ( - γ z ) ,
θ ( z , τ ) = θ 0 ( τ ) + [ n 2 ω 0 r 0 ( τ ) 2 c ] ( 1 - e - 2 γ z 2 γ )
r 0 ( τ ) = A 0 exp ( - τ 2 2 σ 2 ) ,
Δ θ = A 0 2 n 2 ω 0 L c exp ( - τ 2 σ 2 )
= ϕ m exp ( - τ 2 σ 2 ) ,
Δ ω max = max d d t [ ϕ m exp ( - τ 2 σ 2 ) ] .
Δ ω = ( Δ ω ) 0 + Δ ω max = ( 1 + 0.86 ϕ m ) ( Δ ω ) 0 ,
( Δ ω ) 2 = ω 2 - ω 2 = ω 2 g ( ω ) 2 d ω g ( ω ) 2 d ω - [ ω g ( ω ) 2 d ω g ( ω ) 2 d ω ] 2 ,
A ( τ ) = A 0 exp ( - γ z ) exp ( - τ 2 2 σ 2 ) exp ( i ϕ m e - τ 2 / σ 2 ) .
f ( n ) ( 0 ) = ( - 1 ) n ω n F [ f ] ( ω ) d ω
F [ f ] F [ g ] = F [ f * g ] .
( Δ ω ) 2 = A ( τ ) 2 d τ A ( τ ) 2 d τ + [ A ( τ ) A * ( τ ) d τ A ( τ ) 2 d τ ] 2 .
Δ ω ( Δ ω ) 0 = ( 1 + 4 3 3 ϕ m 2 ) 1 / 2 = [ 1 + ( 0.88 ϕ m ) 2 ] 1 / 2 .

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