Abstract

The Raman self-frequency shift of ultrashort pulses in dispersive optical fibers can be suppressed by cross-phase modulation from a copropagating pump pulse. In both analytical and numerical analyses, we show that the interaction of group-velocity dispersion, cross-phase modulation, and intrapulse stimulated Raman scattering results in a periodic rather than a progressive self-frequency shift.

© 1988 Optical Society of America

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References

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  1. E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, A. A. Fomichev, “Stimulated Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).
  2. F. M. Mitschke, L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986).
    [CrossRef] [PubMed]
  3. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662–664 (1986).
    [CrossRef] [PubMed]
  4. A. S. Gouveia-Neto, A. S. L. Gomes, J. R. Taylor, “High-efficiency single-pass solitonlike compression of Raman radiation in an optical fiber around 1.4 μ m,” Opt. Lett. 12, 1035–1037 (1987).
    [CrossRef] [PubMed]
  5. K. J. Blow, N. J. Doran, D. Wood, “Suppression of self-frequency shift by bandwidth-limited amplification,” J. Opt. Soc. Am. B 5, 1301–1304 (1988).
    [CrossRef]
  6. D. Schadt, B. Jaskorzynska, U. Osterberg, “Numerical study on stimulated Raman scattering and self-phase modulation in optical fibers influenced by walk-off between pump and Stokes pulses,” J. Opt. Soc. Am. B 3, 1257–1262 (1986).
    [CrossRef]
  7. R. H. Stolen, A. M. Johnson, “The effect of pulse walk-off on stimulated Raman scattering in fibers,” IEEE J. Quantum Electron. QE-22, 2154–2160 (1986).
    [CrossRef]
  8. W. Hodel, H. P. Weber, “Decay of higher-order solitons in an optical fiber induced by Raman self-pumping,” Opt. Lett. 12, 924–926 (1987).
    [CrossRef] [PubMed]
  9. B. Jaskorzynska, D. Schadt, “All-fiber distributed compression of weak pulses in the regime of negative group velocity dispersion,” IEEE J. Quantum Electron. (to be published).
  10. P. Beaud, W. Hodel, B. Zysset, H. P. Weber, “Ultrashort pulse propagation, pulse breakup and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. QE-23, 1938–1946 (1987).
    [CrossRef]
  11. D. Schadt, B. Jaskorzynska, “Frequency chirp and spectra due to self-phase modulation and stimulated Raman scattering influenced by pulse walk-off in optical fibers,” J. Opt. Soc. Am. B 4, 856–862 (1987).
    [CrossRef]

1988 (1)

1987 (4)

1986 (4)

1985 (1)

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, A. A. Fomichev, “Stimulated Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Beaud, P.

P. Beaud, W. Hodel, B. Zysset, H. P. Weber, “Ultrashort pulse propagation, pulse breakup and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. QE-23, 1938–1946 (1987).
[CrossRef]

Blow, K. J.

Dianov, E. M.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, A. A. Fomichev, “Stimulated Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Doran, N. J.

Fomichev, A. A.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, A. A. Fomichev, “Stimulated Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Gomes, A. S. L.

Gordon, J. P.

Gouveia-Neto, A. S.

Hodel, W.

P. Beaud, W. Hodel, B. Zysset, H. P. Weber, “Ultrashort pulse propagation, pulse breakup and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. QE-23, 1938–1946 (1987).
[CrossRef]

W. Hodel, H. P. Weber, “Decay of higher-order solitons in an optical fiber induced by Raman self-pumping,” Opt. Lett. 12, 924–926 (1987).
[CrossRef] [PubMed]

Jaskorzynska, B.

Johnson, A. M.

R. H. Stolen, A. M. Johnson, “The effect of pulse walk-off on stimulated Raman scattering in fibers,” IEEE J. Quantum Electron. QE-22, 2154–2160 (1986).
[CrossRef]

Karasik, A. Ya.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, A. A. Fomichev, “Stimulated Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Mamyshev, P. V.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, A. A. Fomichev, “Stimulated Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Mitschke, F. M.

Mollenauer, L. F.

Osterberg, U.

Prokhorov, A. M.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, A. A. Fomichev, “Stimulated Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Schadt, D.

Serkin, V. N.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, A. A. Fomichev, “Stimulated Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Stel’makh, M. F.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, A. A. Fomichev, “Stimulated Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Stolen, R. H.

R. H. Stolen, A. M. Johnson, “The effect of pulse walk-off on stimulated Raman scattering in fibers,” IEEE J. Quantum Electron. QE-22, 2154–2160 (1986).
[CrossRef]

Taylor, J. R.

Weber, H. P.

W. Hodel, H. P. Weber, “Decay of higher-order solitons in an optical fiber induced by Raman self-pumping,” Opt. Lett. 12, 924–926 (1987).
[CrossRef] [PubMed]

P. Beaud, W. Hodel, B. Zysset, H. P. Weber, “Ultrashort pulse propagation, pulse breakup and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. QE-23, 1938–1946 (1987).
[CrossRef]

Wood, D.

Zysset, B.

P. Beaud, W. Hodel, B. Zysset, H. P. Weber, “Ultrashort pulse propagation, pulse breakup and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. QE-23, 1938–1946 (1987).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. H. Stolen, A. M. Johnson, “The effect of pulse walk-off on stimulated Raman scattering in fibers,” IEEE J. Quantum Electron. QE-22, 2154–2160 (1986).
[CrossRef]

P. Beaud, W. Hodel, B. Zysset, H. P. Weber, “Ultrashort pulse propagation, pulse breakup and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. QE-23, 1938–1946 (1987).
[CrossRef]

J. Opt. Soc. Am. B (3)

JETP Lett. (1)

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, A. A. Fomichev, “Stimulated Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Opt. Lett. (4)

Other (1)

B. Jaskorzynska, D. Schadt, “All-fiber distributed compression of weak pulses in the regime of negative group velocity dispersion,” IEEE J. Quantum Electron. (to be published).

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Figures (4)

Fig. 1
Fig. 1

Normalized power spectrum of the signal pulse as a function of normalized frequency: a, at Z = 0; b, at maximum downshift after a quarter period; c, at maximum upshift after three quarters of the period; d, after a complete frequency shift period.

Fig. 2
Fig. 2

Evolution of the self-frequency shift over one period. The solid curve represents the analytic approximation of Eq. (10), and the dashed curve is the result of a numerical simulation with the help of Eqs. (1) and (12).

Fig. 3
Fig. 3

Normalized signal intensity versus retarded time after Z ~ 0.8Z0.

Fig. 4
Fig. 4

Comparison between the temporal form of the initial signal and the signal after the period Z0.

Equations (25)

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A ¯ s Z = i 2 z K z D k s k p 2 A ¯ s T 2 + i ω s ω p A ¯ p 2 A ¯ 2 - i ω s ω p δ 2 τ p A ¯ s 2 T A ¯ s ,
δ = | X ω | / X NR ,
A ¯ p ( T ) = exp [ - 2 ln 2 ( T 2 ) ] , A ¯ s ( 0 , T ) = A ¯ 0 , s exp [ - 2 ln 2 ( T / T s ) 2 ] ,
A ¯ p ( T ) 2 ~ 1 - 4 ln 2 ( T 2 )
G ¯ s Z - i a 2 2 G ¯ s T 2 = - i 2 b T 2 G ¯ s ,
a = k s k p z K z D ,             b = ω s ω p 2 ln 2 ,
G ¯ s ( Z , T ) = G ¯ 0 s ( η ) 1 / 2 exp [ i Ψ 1 ( Z ) + i Ψ 2 ( Z , T ) ] × exp { - 2 ln 2 [ T ( T s / η ) ] 2 } ,
Ψ 1 ( Z ) = - 1 2 tan - 1 [ w tan ( B Z ) ] , Ψ 2 ( Z , T ) = - 1 2 ( 1 - w 2 ) w 2 ln 2 sin ( 2 B Z ) T 2 ( T s / η ) 2 , η 2 ( Z ) = 2 ( 1 + w 2 ) + ( 1 - w 2 ) cos ( 2 B Z ) , B = 2 ( a b ) 1 / 2 ,             w = 2 ln 2 T s 2 ( a ¯ b ) 1 / 2 .
A ¯ s 2 T ~ G ¯ s 0 2 η 3 ( - 8 ln 2 T T s 2 ) .
A ¯ s Z = i a 2 2 A ¯ s T 2 - i 2 b T 2 A ¯ s + i c η 3 T A ¯ s ,
c = ω s ω p 4 ln 2 A ¯ 0 s 2 τ p T s 2 δ ,
A s Z = - i a 2 [ Ω - c Z η ( ξ ) 3 d ξ ] 2 A s + i 2 b 2 A s Ω 2 .
A s ( Z , ω ) = G [ Z , ω + f ( Z ) ] exp [ i Φ ( Z , ω ) ] ,
f ( Z ) = c B w 2 { sin ( B Z ) - ( 1 - w 2 ) cos ( B Z ) sin ( B Z ) [ cos 2 ( B Z ) + w 2 sin 2 ( B Z ) ] 1 / 2 } .
f ˜ ( Z ) = f ( Z ) - 2 b h B sin ( B Z ) .
f N ( Z ) = - + A s ( Z , ω ) 2 ω d ω - + A s ( Z , ω ) 2 d ω .
A s ( Z , Ω ) = A ¯ 0 s ( π T s 2 2 ln 2 ) 1 / 2 exp [ Q ( Z ) Ω 2 + P ( Z ) Ω + R ( Z ) ]
R Z + i a c 2 2 y ( Z ) 2 - i 2 b ( P 2 + 2 Q ) = 0 , P Z - i a c y ( z ) - i 8 b Q P = 0 , Q Z + i a 2 - i 8 b Q 2 = 0 , y ( Z ) = Z η 3 ( ξ ) d ξ .
Q ( Z ) = Q R + i Q I = - T s 2 8 ln 2 [ w 2 sin 2 ( B Z ) + w 2 cos 2 ( B Z ) - i w ( 1 - w 2 ) sin ( B Z ) cos ( B Z ) sin 2 ( B Z ) + w 2 cos 2 ( B Z ) ] , P ( Z ) = P R + i P I = a c [ I I sin ( B Z ) - I R w cos ( B Z ) sin 2 ( B Z ) + w 2 cos 2 ( B Z ) + i I R sin ( B Z ) + I 1 w cos ( B Z ) sin 2 ( B Z ) + w 2 cos 2 ( B Z ) ] , R ( Z ) = R R + i R I = - 1 2 ( ln [ cos 2 ( B Z ) + sin 2 ( B Z ) w 2 ] 1 / 2 - 4 b 0 Z P R P I d ξ + i { tan - 1 [ tan ( B Z ) w ] + 2 b 0 Z ( P R 2 - P I 2 ) d ξ - a c 2 2 0 Z y 2 ( ξ ) d ξ } ) ,
I ( Z ) = I R - i I I = 0 Z y ( ξ ) sin ( B ξ ) d ξ - i w 0 Z y ( ξ ) cos ( B ξ ) d ξ .
A s ( Z , Ω ) = A 0 s exp [ Q R ( Ω + P R 2 Q R ) 2 - P R 2 4 Q R + R R + i Φ ( Z , Ω ) ] ,
4 b 0 Z P I P R d ξ + P R 2 4 Q R = 0
Ω = P R 2 Q R = ω + f ( Z ) ,
A S ( Z , ω ) = A 0 s [ cos 2 ( B Z ) + sin 2 ( B Z ) w 2 ] - 1 / 4 × exp { Q R [ ω + f ( Z ) ] 2 } ,
Φ ( Z , Ω ) = Q I ( Z ) Ω 2 + P I ( Z ) Ω + R I .

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