Abstract

Dispersive waves (DW) are generated owing to perturbation of solitons by higher-order dispersion (HOD) and nonlinearity during supercontinuum (SC) generation. The frequencies of these waves are governed by a phase-matching condition in the form of a polynomial whose coefficients depend on the numerical values of the properly normalized third- and HOD parameters. Our extensive numerical solutions show that all odd HOD terms generate a single peak on the blue or the red side of the carrier frequency, depending on the sign of the corresponding term. In contrast, positive even HOD terms create conjugate DW peaks, in both the blue and red sides. No radiation is observed for negative values of these parameters. The combination of all even and odd HOD coefficients may generate more than two DW peaks for some specific choice of parameters. The results predicted by the phase-matching condition agree well with extensive numerical simulations revealing interesting facts of SC generation.

© 2009 Optical Society of America

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References

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  1. J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. A. Hasegawa and M. Matsumoto, Optical Solitons in Fibers (Springer, 2002).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  11. E. Tsoy and C. De Sterke, Phys. Rev. A 76, 043804 (2007).
    [CrossRef]
  12. S. Roy, S. K. Bhadra, and G. P. Agrawal, Phys. Rev. A 79, 023824 (2009).
    [CrossRef]

2009 (1)

S. Roy, S. K. Bhadra, and G. P. Agrawal, Phys. Rev. A 79, 023824 (2009).
[CrossRef]

2008 (1)

2007 (1)

E. Tsoy and C. De Sterke, Phys. Rev. A 76, 043804 (2007).
[CrossRef]

2006 (2)

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

Q. Lin and G. P. Agrawal, Opt. Lett. 31, 3086 (2006).
[CrossRef] [PubMed]

2004 (1)

2003 (1)

A. V. Husakou and J. Herrmann, Appl. Phys. B 77, 227 (2003).
[CrossRef]

2001 (1)

A. V. Husakou and J. Herrmann, Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

1995 (1)

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

1993 (1)

V. I. Karpman, Phys. Rev. E 47, 2073 (1993).
[CrossRef]

Agrawal, G. P.

S. Roy, S. K. Bhadra, and G. P. Agrawal, Phys. Rev. A 79, 023824 (2009).
[CrossRef]

Q. Lin and G. P. Agrawal, Opt. Lett. 31, 3086 (2006).
[CrossRef] [PubMed]

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

Akhmediev, N.

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

Andersen, T.

Benabid, F.

Bhadra, S. K.

S. Roy, S. K. Bhadra, and G. P. Agrawal, Phys. Rev. A 79, 023824 (2009).
[CrossRef]

Biancalana, F.

Coen, S.

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

Couny, F.

De Sterke, C.

E. Tsoy and C. De Sterke, Phys. Rev. A 76, 043804 (2007).
[CrossRef]

Dudley, J. M.

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

Genty, G.

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

Hansen, K.

Hasegawa, A.

A. Hasegawa and M. Matsumoto, Optical Solitons in Fibers (Springer, 2002).

Herrmann, J.

A. V. Husakou and J. Herrmann, Appl. Phys. B 77, 227 (2003).
[CrossRef]

A. V. Husakou and J. Herrmann, Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

Hilligsøe, K.

Husakou, A. V.

A. V. Husakou and J. Herrmann, Appl. Phys. B 77, 227 (2003).
[CrossRef]

A. V. Husakou and J. Herrmann, Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

Karlsson, M.

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

Karpman, V. I.

V. I. Karpman, Phys. Rev. E 47, 2073 (1993).
[CrossRef]

Keiding, S.

Kristiansen, R.

Larsen, J.

Light, P. S.

Lin, Q.

Luiten, A.

Matsumoto, M.

A. Hasegawa and M. Matsumoto, Optical Solitons in Fibers (Springer, 2002).

Mølmar, K.

Nielsen, C.

Paulsen, H.

Peng, J.

Roberts, P. J.

Roy, S.

S. Roy, S. K. Bhadra, and G. P. Agrawal, Phys. Rev. A 79, 023824 (2009).
[CrossRef]

Sokolov, A. V.

Tsoy, E.

E. Tsoy and C. De Sterke, Phys. Rev. A 76, 043804 (2007).
[CrossRef]

Appl. Phys. B (1)

A. V. Husakou and J. Herrmann, Appl. Phys. B 77, 227 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (3)

E. Tsoy and C. De Sterke, Phys. Rev. A 76, 043804 (2007).
[CrossRef]

S. Roy, S. K. Bhadra, and G. P. Agrawal, Phys. Rev. A 79, 023824 (2009).
[CrossRef]

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (1)

V. I. Karpman, Phys. Rev. E 47, 2073 (1993).
[CrossRef]

Phys. Rev. Lett. (1)

A. V. Husakou and J. Herrmann, Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

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

Other (2)

A. Hasegawa and M. Matsumoto, Optical Solitons in Fibers (Springer, 2002).

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

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Figures (2)

Fig. 1
Fig. 1

Contour and output spectra of a second-order soliton ( N = 2 ) at two dispersion lengths. The PM curve is plotted simultaneously. The dimensionless dispersion coefficients used in the plots are (a) δ 3 = 0.01 , δ 4 = 0.015 / 10 , δ 5 = 0 , δ 6 = 0 ; (b) δ 3 = 0.01 , δ 4 = 0.015 / 10 , δ 5 = 0.01 / 100 , δ 6 = 0 ; (c) δ 3 = 0.01 , δ 4 = 0.04 / 10 , δ 5 = 0.01 / 100 , δ 6 = 0 ; and (d) δ 3 = 0.01 , δ 4 = 0.04 / 10 , δ 5 = 0.015 / 100 , δ 6 = 0 .

Fig. 2
Fig. 2

Contour and output spectra of a second-order soliton ( N = 2 ) at two dispersion length. The PM curve is plotted simultaneously. The dimensionless dispersion coefficients used in the plots are (a) δ 3 = 0.01 , δ 4 = 0.015 / 10 , δ 5 = 0.01 / 100 , δ 6 = 0 ; (b) δ 3 = 0.01 , δ 4 = 0 , δ 5 = 0.01 / 100 , δ 6 = 0.01 / 1000 ; (c) δ 3 = 0.01 , δ 4 = 0.015 / 10 , δ 5 = 0 , δ 6 = 0 ; and (d) δ 3 = 0.01 , δ 4 = 0 , δ 5 = 0.01 / 100 , δ 6 = 0.01 / 1000 .

Equations (6)

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m = 2 δ m x m = 1 2 ( 2 N 1 ) 2 ,
U ξ = i 2 2 U τ 2 + m 3 i m + 1 δ m m U τ m + i N 2 ( 1 + i s τ ) ( U ( ξ , τ ) τ R ( τ τ ) | U ( ξ , τ ) | 2 d τ ) ,
ξ = z / L D ,     τ = ( t z / v g ) / T 0 ,     N = γ P 0 L D .
R ( τ ) = ( 1 f R ) δ ( τ ) + f R h R ( τ ) ,
h R ( τ ) = ( f a + f c ) h a ( τ ) + f b h b ( τ ) ,
h a ( τ ) = τ 1 2 + τ 2 2 τ 1 τ 2 2 exp ( τ τ 2 ) sin ( τ τ 1 ) , h b ( τ ) = ( 2 τ b τ τ b 2 ) exp ( τ τ b ) ,

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