Abstract

Self-steepening of ultrashort light pulses is shown to reduce the soliton self-frequency shift (SSFS) induced by the Raman effect in an optical fiber. We derive an analytical expression for the SSFS that conserves the number of photons and allows the SSFS to be calculated for arbitrary frequency profiles of fiber dispersion and Raman gain without a numerical solution of the pulse evolution equation. The accuracy of this analytical approach to SSFS calculation is tested by numerical simulations based on the generalized nonlinear Schrödinger equation.

© 2008 Optical Society of America

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2007 (1)

A. M. Zheltikov, Phys. Rev. E 75, 037603 (2007).
[CrossRef]

2006 (3)

2005 (2)

2004 (1)

F. Biancalana, D. V. Skryabin, and A. V. Yulin, Phys. Rev. E 70, 016615 (2004).
[CrossRef]

2003 (2)

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

P. St. J. Russell, Science 299, 358 (2003).
[CrossRef] [PubMed]

2001 (1)

1990 (1)

1989 (1)

K. J. Blow and D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

1986 (2)

1985 (1)

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, and A. A. Fomichev, JETP Lett. 41, 294 (1985).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

Andresen, E. R.

Baltuska, A.

Biancalana, F.

F. Biancalana, D. V. Skryabin, and A. V. Yulin, Phys. Rev. E 70, 016615 (2004).
[CrossRef]

Birkedal, V.

Blow, K. J.

K. J. Blow and D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

Chandalia, J. K.

Chernikov, S. V.

Coen, S.

B. Kibler, J. M. Dudley, and S. Coen, Appl. Phys. B 81, 337 (2005).
[CrossRef]

de Sterke, C. M.

Dianov, E. M.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, and A. A. Fomichev, JETP Lett. 41, 294 (1985).

Dudley, J. M.

B. Kibler, J. M. Dudley, and S. Coen, Appl. Phys. B 81, 337 (2005).
[CrossRef]

Eggleton, B. J.

Fomichev, A. A.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, and A. A. Fomichev, JETP Lett. 41, 294 (1985).

Fuji, T.

Gordon, J. P.

Holzwarth, R.

Ishii, N.

Karasik, A. Y.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, and A. A. Fomichev, JETP Lett. 41, 294 (1985).

Keiding, S. R.

Kibler, B.

B. Kibler, J. M. Dudley, and S. Coen, Appl. Phys. B 81, 337 (2005).
[CrossRef]

Knight, J. C.

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

Knox, W. H.

Köhler, S.

Kosinski, S. G.

Krausz, F.

Liu, X.

Luan, F.

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

Mamyshev, P. V.

P. V. Mamyshev and S. V. Chernikov, Opt. Lett. 15, 1076 (1990).
[CrossRef] [PubMed]

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, and A. A. Fomichev, JETP Lett. 41, 294 (1985).

Metzger, T.

Mitschke, F. M.

Mollenauer, L. F.

Prokhorov, A. M.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, and A. A. Fomichev, JETP Lett. 41, 294 (1985).

Russell, P. St. J.

P. St. J. Russell, Science 299, 358 (2003).
[CrossRef] [PubMed]

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

Serebryannikov, E. E.

Serkin, V. N.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, and A. A. Fomichev, JETP Lett. 41, 294 (1985).

Sidorov-Biryukov, D. A.

Skryabin, D. V.

F. Biancalana, D. V. Skryabin, and A. V. Yulin, Phys. Rev. E 70, 016615 (2004).
[CrossRef]

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

Stel'makh, M. F.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, and A. A. Fomichev, JETP Lett. 41, 294 (1985).

Teisset, C. Y.

Thøgersen, J.

Tsoy, E. N.

Windeler, R. S.

Wood, D.

K. J. Blow and D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

Xu, C.

Yulin, A. V.

F. Biancalana, D. V. Skryabin, and A. V. Yulin, Phys. Rev. E 70, 016615 (2004).
[CrossRef]

Zheltikov, A. M.

Appl. Phys. B (1)

B. Kibler, J. M. Dudley, and S. Coen, Appl. Phys. B 81, 337 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. J. Blow and D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

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

JETP Lett. (1)

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, and A. A. Fomichev, JETP Lett. 41, 294 (1985).

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. E (2)

A. M. Zheltikov, Phys. Rev. E 75, 037603 (2007).
[CrossRef]

F. Biancalana, D. V. Skryabin, and A. V. Yulin, Phys. Rev. E 70, 016615 (2004).
[CrossRef]

Science (2)

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

P. St. J. Russell, Science 299, 358 (2003).
[CrossRef] [PubMed]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

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Figures (2)

Fig. 1
Fig. 1

Spectral profiles of dispersion β 2 and nonlinearity γ of the fiber used in calculations of the SSFS. The inset shows the parameter h calculated with the use of Eq. (5) as a function of the soliton pulse width τ.

Fig. 2
Fig. 2

(a) SSFS calculated as a function of the propagation coordinate z (a) using (solid curves) the GNSE [Eq. (9)] and (dashed curves) NSE [Eq. (2)] with the nonlinear term modified in accordance with Eq. (3) for soliton pulses with an initial energy of 100 pJ , an initial pulse width of 10 fs , and an initial central wavelength of 800 nm ; (b) using (solid curves) the GNSE and (dashed curves) Eqs. (7, 8) for soliton pulses with (1) W 0 = 35 pJ , τ = 28 fs ; (2) W 0 = 50 pJ , τ = 21 fs ; (3) W 0 = 71 pJ , τ = 15 fs ; (4) W 0 = 100 pJ , τ = 10 fs ; (5) W 0 = 141 pJ , τ = 7 fs .

Equations (9)

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A ( η , 0 ) = A 0 sech ( η τ ) ,
A z = i β 2 ( ν 0 ) 2 2 A η 2 + i γ 0 A A 2 ,
A 2 A A ( η , z ) R ( θ ) A ( η θ , z ) 2 d θ ,
d ν s d z = 2 π c σ h ( τ ) β 2 ( ν s ) ( 1.763 τ ) 4 .
h ( τ ) = 993 τ 0 g ( ν ) Ω 3 ( sinh π Ω 2 ) 2 d Ω ,
ν 1 A ( ν , z ) 2 d ν = const ,
z z 0 = 8 ( 1.763 ) 4 ν 0 8 π c σ W 0 4 γ 0 4 ν 0 ν β 2 ( ν s ) 3 ν s 8 h ( τ ) d ν s ,
A z = i k = 2 7 i k k ! β k k A η k + i γ 0 ( 1 + i 2 π ν 0 η ) ( A R ( θ ) A ( η θ ) 2 d θ ) ,
R ( θ ) = ( 1 f R ) δ ( θ ) + f R ϴ ( θ ) τ 1 2 + τ 2 2 τ 1 τ 2 2 e ( θ τ 2 ) sin ( θ τ 1 ) ,

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