Abstract

We derive phase-matching conditions for four-wave mixing between solitons and linear waves in optical fibers with arbitrary dispersion and demonstrate resonant excitation of new spectral components via this process.

© 2004 Optical Society of America

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2004

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

Y. Kominis and K. Hizanidis, J. Opt. Soc. Am. B 21, 562 (2004).
[CrossRef]

2003

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef] [PubMed]

F. Biancalana, D. V. Skryabin, and P. St. J. Russell, Phys. Rev. E 68, 046603 (2003).
[CrossRef]

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

V. Finazzi, T. M. Monro, and D. J. Richardson, J. Opt. Soc. Am. B 20, 1427 (2003).
[CrossRef]

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 28, 2225 (2003).
[CrossRef] [PubMed]

2002

J. M. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, and S. Coen, J. Opt. Soc. Am. B 19, 765 (2002).
[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

2000

1999

Q. H. Park and H. J. Shin, Phys. Rev. Lett. 82, 4432 (1999).
[CrossRef]

1996

H. A. Hauss, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, IEEE J. Quantum Electron. 32, 917 (1996).
[CrossRef]

1995

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

1993

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

1992

1990

P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

1982

Agrawal, G. P.

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

Akhmediev, N.

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

N. Akhmediev and S. Wabnitz, J. Opt. Soc. Am. B 9, 236 (1992).
[CrossRef]

Biancalana, F.

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

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef] [PubMed]

F. Biancalana, D. V. Skryabin, and P. St. J. Russell, Phys. Rev. E 68, 046603 (2003).
[CrossRef]

Chen, H. H.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

Coen, S.

Dudley, J. M.

Efimov, A.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef] [PubMed]

Eggleton, B. J.

Finazzi, V.

Gordon, J. P.

Griebner, U.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Grossard, N.

Harvey, J. D.

Hasegawa, A.

Hauss, H. A.

H. A. Hauss, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, IEEE J. Quantum Electron. 32, 917 (1996).
[CrossRef]

Herrmann, J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Hizanidis, K.

Husakou, A.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Ippen, E. P.

H. A. Hauss, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, IEEE J. Quantum Electron. 32, 917 (1996).
[CrossRef]

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]

Khatri, F. I.

H. A. Hauss, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, IEEE J. Quantum Electron. 32, 917 (1996).
[CrossRef]

Knight, J. C.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef] [PubMed]

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

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 28, 2225 (2003).
[CrossRef] [PubMed]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Kodama, Y.

Kominis, Y.

Korn, G.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Lee, Y. C.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

Leonhardt, R.

Luan, F.

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

Maillotte, H.

Monro, T. M.

Nickel, D.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Omenetto, F. G.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef] [PubMed]

Park, Q. H.

Q. H. Park and H. J. Shin, Phys. Rev. Lett. 82, 4432 (1999).
[CrossRef]

Provino, L.

Ranka, J. K.

Reeves, W. H.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef] [PubMed]

Richardson, D. J.

Russell, P. St. J.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef] [PubMed]

F. Biancalana, D. V. Skryabin, and P. St. J. Russell, Phys. Rev. E 68, 046603 (2003).
[CrossRef]

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

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 28, 2225 (2003).
[CrossRef] [PubMed]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Shin, H. J.

Q. H. Park and H. J. Shin, Phys. Rev. Lett. 82, 4432 (1999).
[CrossRef]

Skryabin, D. V.

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

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef] [PubMed]

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

F. Biancalana, D. V. Skryabin, and P. St. J. Russell, Phys. Rev. E 68, 046603 (2003).
[CrossRef]

Stentz, A. J.

Tamura, K. R.

H. A. Hauss, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, IEEE J. Quantum Electron. 32, 917 (1996).
[CrossRef]

Taylor, A. J.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef] [PubMed]

Wabnitz, S.

Wadsworth, W. J.

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 28, 2225 (2003).
[CrossRef] [PubMed]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Wai, P. K. A.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

Windeler, R. S.

Wong, G. K. L.

Wong, W. S.

H. A. Hauss, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, IEEE J. Quantum Electron. 32, 917 (1996).
[CrossRef]

Yulin, A. V.

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

Zhavoronkov, N.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

IEEE J. Quantum Electron.

H. A. Hauss, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, IEEE J. Quantum Electron. 32, 917 (1996).
[CrossRef]

J. Opt. Soc. Am. B

Nature

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

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

P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

Phys. Rev. E

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

F. Biancalana, D. V. Skryabin, and P. St. J. Russell, Phys. Rev. E 68, 046603 (2003).
[CrossRef]

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

Phys. Rev. Lett.

Q. H. Park and H. J. Shin, Phys. Rev. Lett. 82, 4432 (1999).
[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Science

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

Other

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

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Figures (1)

Fig. 1
Fig. 1

(a), (b) Resonance frequencies calculated from Eqs. (10) and (11) and (c), (d) supporting numerical modeling. The straight (curved) lines in (a) and (b) are the left- and right-hand sides of Eqs. (10) and (11). Choosing ω0=2π×240 THz and the fiber parameters from Ref. 7, we find β2=-47 ps2/km and ωβ2=-0.7 ps3/km. (a), (c) δs=0, w=0.1, δcw=-15; (b), (d) δs=-4, w=0.3, δcw=-40. Other parameters are τ=170 fs, q=4, and N=1.5. For γ=0.05 W-1 m-1 this corresponds to a pulse peak power of 225 W and a cw power of 0.12 W for (c) and 1.2 W for (d). The solid curves in (c) and (d) correspond to θ=0, i.e., the Raman is off, and the dashed curves to θ=0.18, i.e., the Raman is on. The propagation distances are (c) 2.8 m and (d) 16 m. The top axes are marked in wavelength units.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

zA=iDitA+iA-+RtAt-t,z2dt.
Ditm=2Mτ2-mωm-2β2ω0m!β2ω0itm,
Rt=1-θΔt+θαΘtexp-t/τ2sint/τ1.
A=Fξexp-iδst+iDs+qz,Fξ=2q1/2sechξ/r
A=Fξ+gz,ξexpizDs+q-iδst,ξt-zDs.
ip=zg-iD˜iξg-i2F2g-iF2g*,
g=w expiϕ+ψ,ϕ=zD˜δcw-δs+ξδs-δcw.
ip-p*=z+iLˆψpψp*,
iF2w expiξδs-δcw2-1=z+iLˆ+iWˆψ+ψ-,
Lˆ=-D˜iξ-2F2-F2F2D˜-iξ+2F2,Wˆ=D˜δcw-δs1001.
q+Ds-δs-δDs=Dδ,
±Dcwq+Ds-δs-δcwDs+q+Ds-δs-δDs=Dδ.
±kcw-ks/cw+ks/rad=krad.

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