Abstract

An investigation is made of the effects of cross-phase modulation and pump depletion on pulse dynamics in the stimulated Raman scattering process. It is shown that cross-phase modulation may significantly affect the frequency chirp of the pulse even to the point of reversing the sign of the chirp. As a consequence, solitonlike pulse compression using Raman amplification may become impossible with the Stokes pulse in the anomalous-dispersion regime. The chirp reversion effect is weakened by pulse walk-off, which, if strong enough, retains the frequency characteristics of the inherent self-phase modulation.

© 1989 Optical Society of America

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  1. A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142 (1973).
    [CrossRef]
  2. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
    [CrossRef]
  3. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. Tomlinson, “Extreme pulse narrowing by means of soliton effect in single-mode optical fibers,” Opt. Lett. 8, 289 (1983).
    [CrossRef] [PubMed]
  4. V. N. Lugovoi, “Stimulated Raman emission and frequency scanning in an optical waveguide,” Sov. Phys. JETP 44, 683 (1976).
  5. A. S. Gouveia-Neto, A. S. L. Gomes, and 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 (1987).
    [CrossRef] [PubMed]
  6. A. Höök, D. Anderson, and M. Lisak, “Soliton-like Stokes pulses in stimulated Raman scattering,” Opt. Lett. 13, 1114 (1988).
    [CrossRef]
  7. M. N. Islam, L. F. Mollenauer, R. H. Stolen, J. R. Simpson, and H. T. Shang, “Cross-phase modulation in optical fibers,” Opt. Lett. 12, 625 (1987).
    [CrossRef] [PubMed]
  8. A. S. L. Gomes, V. L. da Silva, and J. R. Taylor, “Direct measurement of nonlinear frequency chirp of Raman radiation in single-mode optical fibers using a spectral window method,” J. Opt.Soc. Am. B 5, 373 (1988).
    [CrossRef]
  9. D. Schadt and 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 (1987).
    [CrossRef]
  10. M. Kuckartz, R. Schultz, and H. Harde, “Operation of a fiber-grating compressor in the Raman regime,” J. Opt. Soc. Am. B 5, 1353 (1988).
    [CrossRef]
  11. A. S. Gouveia-Neto, A. S. L. Gomes, J. R. Taylor, B. J. Ainslie, and S. P. Craig, “Femtosecond single-pass cascade Raman soliton generation at 1.5 μ m,” Electron. Lett. 23, 1034 (1987).
    [CrossRef]
  12. A. Hasegawa, “Amplification and reshaping of optical solitons in a glass fiber—IV: Use of the stimulated Raman process,” Opt. Lett. 8, 650 (1983).
    [CrossRef] [PubMed]
  13. D. Cotter, “Fibre nonlinearities in optical communications, ”Opt. Quantum Electron. 19, 1 (1987).
    [CrossRef]
  14. V. A. Vysloukh and V. N. Serkin, “Generation of high-energy solitons of stimulated Raman radiation in fiber light guides,” JETP Lett. 38, 199 (1983).
  15. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871 (1988).
    [CrossRef] [PubMed]
  16. R. Nakach, “Some contributions to the study of nonlinear dispersive wave phenomena in plasmas,” Tech. Rep. 72 (Chalmers University of Technology, Göteborg, Sweden, 1977).
  17. A. R. Chraplyvy and J. Stone, “Single-pass mode-locked or Q-switched pump operation of D2 gas-in-glass fiber Raman lasers operating at 1.56-μ m wavelength,” Opt. Lett. 10, 344 (1985).
    [CrossRef] [PubMed]
  18. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659 (1986).
    [CrossRef] [PubMed]
  19. P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, “Induced frequency shift of copropagating ultrafast optical pulses, ”Appl. Phys. Lett. 52, 1939 (1988).
    [CrossRef]
  20. G. P. Agrawal, “Modulational instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880 (1987).
    [CrossRef] [PubMed]

1988 (5)

A. Höök, D. Anderson, and M. Lisak, “Soliton-like Stokes pulses in stimulated Raman scattering,” Opt. Lett. 13, 1114 (1988).
[CrossRef]

A. S. L. Gomes, V. L. da Silva, and J. R. Taylor, “Direct measurement of nonlinear frequency chirp of Raman radiation in single-mode optical fibers using a spectral window method,” J. Opt.Soc. Am. B 5, 373 (1988).
[CrossRef]

M. Kuckartz, R. Schultz, and H. Harde, “Operation of a fiber-grating compressor in the Raman regime,” J. Opt. Soc. Am. B 5, 1353 (1988).
[CrossRef]

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871 (1988).
[CrossRef] [PubMed]

P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, “Induced frequency shift of copropagating ultrafast optical pulses, ”Appl. Phys. Lett. 52, 1939 (1988).
[CrossRef]

1987 (6)

1986 (1)

1985 (1)

1983 (3)

1980 (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

1976 (1)

V. N. Lugovoi, “Stimulated Raman emission and frequency scanning in an optical waveguide,” Sov. Phys. JETP 44, 683 (1976).

1973 (1)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Agrawal, G. P.

P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, “Induced frequency shift of copropagating ultrafast optical pulses, ”Appl. Phys. Lett. 52, 1939 (1988).
[CrossRef]

G. P. Agrawal, “Modulational instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880 (1987).
[CrossRef] [PubMed]

Ainslie, B. J.

A. S. Gouveia-Neto, A. S. L. Gomes, J. R. Taylor, B. J. Ainslie, and S. P. Craig, “Femtosecond single-pass cascade Raman soliton generation at 1.5 μ m,” Electron. Lett. 23, 1034 (1987).
[CrossRef]

Alfano, R. R.

P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, “Induced frequency shift of copropagating ultrafast optical pulses, ”Appl. Phys. Lett. 52, 1939 (1988).
[CrossRef]

Anderson, D.

Baldeck, P. L.

P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, “Induced frequency shift of copropagating ultrafast optical pulses, ”Appl. Phys. Lett. 52, 1939 (1988).
[CrossRef]

Chraplyvy, A. R.

Cotter, D.

D. Cotter, “Fibre nonlinearities in optical communications, ”Opt. Quantum Electron. 19, 1 (1987).
[CrossRef]

Craig, S. P.

A. S. Gouveia-Neto, A. S. L. Gomes, J. R. Taylor, B. J. Ainslie, and S. P. Craig, “Femtosecond single-pass cascade Raman soliton generation at 1.5 μ m,” Electron. Lett. 23, 1034 (1987).
[CrossRef]

da Silva, V. L.

A. S. L. Gomes, V. L. da Silva, and J. R. Taylor, “Direct measurement of nonlinear frequency chirp of Raman radiation in single-mode optical fibers using a spectral window method,” J. Opt.Soc. Am. B 5, 373 (1988).
[CrossRef]

Gomes, A. S. L.

A. S. L. Gomes, V. L. da Silva, and J. R. Taylor, “Direct measurement of nonlinear frequency chirp of Raman radiation in single-mode optical fibers using a spectral window method,” J. Opt.Soc. Am. B 5, 373 (1988).
[CrossRef]

A. S. Gouveia-Neto, A. S. L. Gomes, J. R. Taylor, B. J. Ainslie, and S. P. Craig, “Femtosecond single-pass cascade Raman soliton generation at 1.5 μ m,” Electron. Lett. 23, 1034 (1987).
[CrossRef]

A. S. Gouveia-Neto, A. S. L. Gomes, and 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 (1987).
[CrossRef] [PubMed]

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. Tomlinson, “Extreme pulse narrowing by means of soliton effect in single-mode optical fibers,” Opt. Lett. 8, 289 (1983).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Gouveia-Neto, A. S.

A. S. Gouveia-Neto, A. S. L. Gomes, J. R. Taylor, B. J. Ainslie, and S. P. Craig, “Femtosecond single-pass cascade Raman soliton generation at 1.5 μ m,” Electron. Lett. 23, 1034 (1987).
[CrossRef]

A. S. Gouveia-Neto, A. S. L. Gomes, and 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 (1987).
[CrossRef] [PubMed]

Harde, H.

Hasegawa, A.

A. Hasegawa, “Amplification and reshaping of optical solitons in a glass fiber—IV: Use of the stimulated Raman process,” Opt. Lett. 8, 650 (1983).
[CrossRef] [PubMed]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Höök, A.

Islam, M. N.

Jaskorzynska, B.

Kuckartz, M.

Lisak, M.

Lugovoi, V. N.

V. N. Lugovoi, “Stimulated Raman emission and frequency scanning in an optical waveguide,” Sov. Phys. JETP 44, 683 (1976).

Mitschke, F. M.

Mollenauer, L. F.

Nakach, R.

R. Nakach, “Some contributions to the study of nonlinear dispersive wave phenomena in plasmas,” Tech. Rep. 72 (Chalmers University of Technology, Göteborg, Sweden, 1977).

Schadt, D.

Schultz, R.

Serkin, V. N.

V. A. Vysloukh and V. N. Serkin, “Generation of high-energy solitons of stimulated Raman radiation in fiber light guides,” JETP Lett. 38, 199 (1983).

Shang, H. T.

Simpson, J. R.

Stegeman, G. I.

Stolen, R. H.

Stone, J.

Tappert, F.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Taylor, J. R.

A. S. L. Gomes, V. L. da Silva, and J. R. Taylor, “Direct measurement of nonlinear frequency chirp of Raman radiation in single-mode optical fibers using a spectral window method,” J. Opt.Soc. Am. B 5, 373 (1988).
[CrossRef]

A. S. Gouveia-Neto, A. S. L. Gomes, J. R. Taylor, B. J. Ainslie, and S. P. Craig, “Femtosecond single-pass cascade Raman soliton generation at 1.5 μ m,” Electron. Lett. 23, 1034 (1987).
[CrossRef]

A. S. Gouveia-Neto, A. S. L. Gomes, and 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 (1987).
[CrossRef] [PubMed]

Tomlinson, W.

Trillo, S.

Vysloukh, V. A.

V. A. Vysloukh and V. N. Serkin, “Generation of high-energy solitons of stimulated Raman radiation in fiber light guides,” JETP Lett. 38, 199 (1983).

Wabnitz, S.

Wright, E. M.

Appl. Phys. Lett. (2)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, “Induced frequency shift of copropagating ultrafast optical pulses, ”Appl. Phys. Lett. 52, 1939 (1988).
[CrossRef]

Electron. Lett. (1)

A. S. Gouveia-Neto, A. S. L. Gomes, J. R. Taylor, B. J. Ainslie, and S. P. Craig, “Femtosecond single-pass cascade Raman soliton generation at 1.5 μ m,” Electron. Lett. 23, 1034 (1987).
[CrossRef]

J. Opt. Soc. Am. B (2)

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

A. S. L. Gomes, V. L. da Silva, and J. R. Taylor, “Direct measurement of nonlinear frequency chirp of Raman radiation in single-mode optical fibers using a spectral window method,” J. Opt.Soc. Am. B 5, 373 (1988).
[CrossRef]

JETP Lett. (1)

V. A. Vysloukh and V. N. Serkin, “Generation of high-energy solitons of stimulated Raman radiation in fiber light guides,” JETP Lett. 38, 199 (1983).

Opt. Lett. (8)

Opt. Quantum Electron. (1)

D. Cotter, “Fibre nonlinearities in optical communications, ”Opt. Quantum Electron. 19, 1 (1987).
[CrossRef]

Phys. Rev. Lett. (2)

G. P. Agrawal, “Modulational instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880 (1987).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Sov. Phys. JETP (1)

V. N. Lugovoi, “Stimulated Raman emission and frequency scanning in an optical waveguide,” Sov. Phys. JETP 44, 683 (1976).

Other (1)

R. Nakach, “Some contributions to the study of nonlinear dispersive wave phenomena in plasmas,” Tech. Rep. 72 (Chalmers University of Technology, Göteborg, Sweden, 1977).

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Figures (8)

Fig. 1
Fig. 1

Sign of chirp-determining function F(z). Is(0, τ)/Ip(0, τ) = 0.1.

Fig. 2
Fig. 2

Chirp-reversing distance as a function of [Is(0, τ)/Ip0].

Fig. 3
Fig. 3

Evolution of Stokes chirp.

Fig. 4
Fig. 4

Evolution of Is and Ip (solid) and ωcs (dashed) for zA/zW = 0.1 and Is0/Ip0 = 0.05: (a) z=0; (b) z = 1.0; (c) z = 1.5; (d) z = 2.5;

Fig. 5
Fig. 5

Evolution of Is and Ip (solid) and ωcs (dashed) for zA/zw = 0.1 and Is0/Ip0 = 0.6: (a) z = 0; (b) z = 1.0; (c) z = 1.5; (d) z = 2.5.

Fig. 6
Fig. 6

Evolution of Is, and Ip (solid) and ωcs (dashed) for zA/zW=5.0 and Is0/Ip0=0.05: (a) z = 0; (b) z = 1.0; (c) z = 2.0; (d) z = 2.5.

Fig. 7
Fig. 7

Evolution of Is and Ip (solid) and ωcs (dashed) for zA/zw = 5.0 and Is0/Ip0 = 0.6: (a) z = 0; (b) z = 1.0; (c) z = 2.0; (d) z = 2.5.

Fig. 8
Fig. 8

(a) Energy spectrum of Stokes pulse amplified with time-independent gain, (b) Energy spectrum of Stokes pulse in Fig. 7(d).

Tables (1)

Tables Icon

Table 1 Characteristic Values of Parameters Considered

Equations (25)

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i ( z + k p t ) u p + k p 2 2 u p t 2 + K p ( | u p | 2 + 2 | u s | 2 ) u p = i ω p ω s R ( t ) | u s | 2 u p , i ( z + k s t ) u s + k s 2 2 u s t 2 + K s ( | u s | 2 + 2 | u p | 2 ) u s = + i R ( t ) | u p | 2 u s ,
2 i υ p ζ 1 2 z A z D k p | k s | 2 υ p τ 2 + z A z K ( | υ p | 2 + 2 | υ s | 2 ) υ p = i ω p ω s | υ s | 2 υ p ,
2 i ( ζ + z A z W τ ) υ s 1 2 z A z D k s | k s | 2 υ s τ 2 + z A z K K p K s ( | υ s | 2 + 2 | υ p | 2 ) υ s = i | υ p | 2 υ s ,
υ p = u p / u p 0 , υ s = u s / u p 0 , u p 0 = u p ( z = 0 ) = const . , ζ = 2 z / z A , τ = ( t k p z ) / τ 0 ,
i u p z + K p ( | u p | 2 + 2 | u s | 2 ) u p = i ω p ω s κ | u s | 2 u p , i u s z + K s ( | u s | 2 + 2 | u p | 2 ) u s = i κ | u p | 2 u s ,
I p z = ω p ω s κ I p I s , I s z = + κ I p I s ,
I p ( z , τ ) + I s ( z , τ ) = C ( τ ) = I p ( 0 , τ ) + I s ( 0 , τ ) , I p ( z , τ ) = C 1 + I s ( 0 , τ ) I p ( 0 , τ ) exp ( κ C z ) .
ϕ p z = + K p ( I p + 2 I s ) , ϕ s z = + K s ( I s + 2 I p ) ,
ϕ s = K s κ ( κ C z ln { I p ( 0 , τ ) C [ exp ( C κ z ) + I s ( 0 , τ ) I p ( 0 , τ ) ] } ) .
ω c s ϕ s τ = K s κ I s ( 0 , τ ) τ I p 0 { I p 0 [ exp ( C κ z ) 1 ] + C } C × [ I s ( 0 , τ ) I p 0 C κ z + ( 2 C κ z + 1 ) exp ( C κ z ) 1 ] .
ω c s = K s I s ( 0 , τ ) τ z ,
ω c s = 2 K s A 2 sech 2 ( τ ) tanh ( τ ) z ,
F ( z ) I s ( 0 , τ ) I p 0 C κ z + ( 2 C κ z + 1 ) exp ( C κ z ) 1 .
( 2 I p 0 κ z + 1 ) exp ( I p 0 κ z ) 1 = 0 ,
D 0 ω cs ( τ ) d τ .
D = ϕ ( z , 0 ) ϕ ( z , ) = K s κ { a I p 0 κ z ln [ exp ( a I p 0 κ z ) + a exp ( I p 0 κ z ) 1 + a ] } ,
D K s a I p 0 z when z 0 , D K s ( a 1 ) I p 0 z when z ± .
I p ζ = I s I p , I s ζ + z A z W I s ζ = I s I p ,
η = τ z A z W ζ , Ī s = z W z A I s , ξ = τ , Ī p = z W z A I p ,
Ī p η = Ī p Ī s , Ī s ξ = Ī p Ī s .
Ī p = Φ ξ = f ( ξ ) f ( ξ ) + g ( η ) , Ī s = Φ η = g ( η ) f ( ξ ) + g ( η ) ,
Ī p ζ = 0 = P p ( τ ) , Ī s ζ = 0 = P s ( τ ) .
f ( τ ) = τ 1 τ P p ( τ ) exp { τ 1 τ [ P s ( τ ) P p ( τ ) ] d τ } d τ c , g ( τ ) = τ 1 τ P p ( τ ) exp { τ 1 τ [ P s ( τ ) P p ( τ ) ] d τ } d τ + 1 + c ,
I p ( 0 , τ ) = I p 0 = const . , I s ( 0 , τ ) = I s 0 sech 2 ( τ τ * ) ,
( ζ + z A z W τ ) ϕ s = z A z K K p K s ( I s + 2 I p ) ,

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