Abstract

In this Letter we give theoretical explanations for the recent observations of the excitation of Raman-shifting pulse pairs in solid-core photonic crystal fibers. The formation of these pairs is surprisingly common in the deep anomalous dispersion regime of a large variety of highly nonlinear optical fibers, away from zero group-velocity dispersion points. We have developed two different theoretical models, which agree very well in their conclusions. A qualitative and a quantitative explanation of pair formation is provided, and the existence of multipeak states is predicted.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2009 (1)

A. Hause and F. Mitschke, Phys. Rev. A 80, 063824 (2009).
[CrossRef]

2008 (2)

A. Hause, H. Hartwig, M. Böhm, and F. Mitschke, Phys. Rev. A 78, 063817 (2008).
[CrossRef]

A. Podlipensky, P. Szarniak, N. Y. Joly, and P. St. J. Russell, J. Opt. Soc. Am. B 25, 2049 (2008).
[CrossRef]

2007 (4)

A. Podlipensky, P. Szarniak, N. Y. Joly, C. G. Poulton, and P. St.J. Russell, Opt. Express 15, 1653 (2007).
[CrossRef] [PubMed]

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

A. V. Gorbach and D. V. Skryabin, Phys. Rev. A 76, 053803 (2007).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef] [PubMed]

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

2003 (1)

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

1996 (1)

N. Akhmediev, W. Krolikowski, and A. J. Lowery, Opt. Commun. 131, 260 (1996).
[CrossRef]

1990 (1)

1988 (1)

1987 (1)

Y. Kodama and A. Hasegawa, IEEE J. Quantum Electron. 23, 510 (1987).
[CrossRef]

1986 (2)

1985 (1)

D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1985).
[CrossRef] [PubMed]

1981 (1)

V. I. Karpman and V. V. Solov'ev, Physica 3D, 487 (1981).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

Akhmediev, N.

N. Akhmediev, W. Krolikowski, and A. J. Lowery, Opt. Commun. 131, 260 (1996).
[CrossRef]

Anderson, D.

D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1985).
[CrossRef] [PubMed]

Bekki, N.

Bélanger, P. A.

Böhm, M.

A. Hause, H. Hartwig, M. Böhm, and F. Mitschke, Phys. Rev. A 78, 063817 (2008).
[CrossRef]

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Gagnon, L.

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Gorbach, A. V.

A. V. Gorbach and D. V. Skryabin, Phys. Rev. A 76, 053803 (2007).
[CrossRef]

Gordon, J. P.

Hartwig, H.

A. Hause, H. Hartwig, M. Böhm, and F. Mitschke, Phys. Rev. A 78, 063817 (2008).
[CrossRef]

Hasegawa, A.

K. Tai, A. Hasegawa, and N. Bekki, Opt. Lett. 13, 392(1988).
[CrossRef] [PubMed]

Y. Kodama and A. Hasegawa, IEEE J. Quantum Electron. 23, 510 (1987).
[CrossRef]

Hause, A.

A. Hause and F. Mitschke, Phys. Rev. A 80, 063824 (2009).
[CrossRef]

A. Hause, H. Hartwig, M. Böhm, and F. Mitschke, Phys. Rev. A 78, 063817 (2008).
[CrossRef]

Jalali, B.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef] [PubMed]

Joly, N. Y.

Karpman, V. I.

V. I. Karpman and V. V. Solov'ev, Physica 3D, 487 (1981).

Kodama, Y.

Y. Kodama and A. Hasegawa, IEEE J. Quantum Electron. 23, 510 (1987).
[CrossRef]

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef] [PubMed]

Krolikowski, W.

N. Akhmediev, W. Krolikowski, and A. J. Lowery, Opt. Commun. 131, 260 (1996).
[CrossRef]

Lisak, M.

D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1985).
[CrossRef] [PubMed]

Lowery, A. J.

N. Akhmediev, W. Krolikowski, and A. J. Lowery, Opt. Commun. 131, 260 (1996).
[CrossRef]

Mitschke, F.

A. Hause and F. Mitschke, Phys. Rev. A 80, 063824 (2009).
[CrossRef]

A. Hause, H. Hartwig, M. Böhm, and F. Mitschke, Phys. Rev. A 78, 063817 (2008).
[CrossRef]

Mitschke, F. M.

Mollenauer, L. F.

Podlipensky, A.

Poulton, C. G.

Ropers, C.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef] [PubMed]

Russell, P. St. J.

Russell, P. St.J.

Skryabin, D. V.

A. V. Gorbach and D. V. Skryabin, Phys. Rev. A 76, 053803 (2007).
[CrossRef]

Solli, D. R.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef] [PubMed]

Solov'ev, V. V.

V. I. Karpman and V. V. Solov'ev, Physica 3D, 487 (1981).

Szarniak, P.

Tai, K.

IEEE J. Quantum Electron. (1)

Y. Kodama and A. Hasegawa, IEEE J. Quantum Electron. 23, 510 (1987).
[CrossRef]

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

Nature (1)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef] [PubMed]

Opt. Commun. (1)

N. Akhmediev, W. Krolikowski, and A. J. Lowery, Opt. Commun. 131, 260 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (4)

A. Hause, H. Hartwig, M. Böhm, and F. Mitschke, Phys. Rev. A 78, 063817 (2008).
[CrossRef]

A. Hause and F. Mitschke, Phys. Rev. A 80, 063824 (2009).
[CrossRef]

A. V. Gorbach and D. V. Skryabin, Phys. Rev. A 76, 053803 (2007).
[CrossRef]

D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1985).
[CrossRef] [PubMed]

Physica (1)

V. I. Karpman and V. V. Solov'ev, Physica 3D, 487 (1981).

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Science (1)

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

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

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Figures (2)

Fig. 1
Fig. 1

(a) Profile of the two-peak soliton solution (solid curve, see [6]), for τ R = 0.1 . Dashed line shows the gravitylike potential U ( ξ ) induced by the most intense soliton. (b) Same as (a) except for the four-peak soliton solution. (c) Frequency detuning versus input soliton order N, as calculated by the GNLSE with a constant GVD and τ R = 0.0146 . Raman states for j = 1 and j = 2 are observed around some magic input power N mag . (d) Propagation of the soliton given in (b), exhibiting metastability and eventual collapse.

Fig. 2
Fig. 2

Comparison between model and simulation: (a) predicted values of the relative force d / d z Δ Ω and the relative phase change d / d z Δ φ . (b) Corresponding simulation (see text). Arrows identify parameters used for panels (c), (d). (c) Spectral evolution at the magic point and (d) spectral evolution under equal acceleration condition but away from the magic point. Parameters are τ FWHM , V = 50 fs , β 2 = 21.8 ps 2 km 1 , γ = 0.09 W 1 k m 1 , λ = 800 nm , and T R = 2 fs .

Equations (5)

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i Z ψ + 1 2 T 2 ψ + | ψ | 2 ψ τ R ψ T | ψ | 2 = 0 ,
1 2 f ξ ξ ( q + b ξ ) f + | f | 2 f τ R f ( | f | 2 ) ξ = 0 ,
( π 16 15 τ R ) 2 2 ( 1 + r ) q ( 1 + r ) 4 exp [ 15 ( 1 + r ) ( 1 r ) 32 τ R 2 q ] = 1.
d d z ω U = γ 1 W U d t | U | 2 t ( | U + V | 2 ) .
d d z Ω R , U = 8 15 ( γ P U ) 2 | β 2 | T R .

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