Abstract

We study soliton pulse compression in materials with cascaded quadratic nonlinearities and show that the group-velocity mismatch creates two different temporally nonlocal regimes. They correspond to what is known as the stationary and nonstationary regimes. The theory accurately predicts the transition to the stationary regime, where highly efficient pulse compression is possible.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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2006 (4)

J. Moses and F. W. Wise, Opt. Lett. 31, 1881 (2006).
[CrossRef] [PubMed]

P. V. Larsen, M. P. Sørensen, O. Bang, W. Z. Krolikowski, and S. Trillo, Phys. Rev. E 73, 036614 (2006).
[CrossRef]

J. Moses and F. W. Wise, Phys. Rev. Lett. 97, 073903 (2006).
[CrossRef] [PubMed]

M. Bache, H. Nielsen, J. Lægsgaard, and O. Bang, Opt. Lett. 31, 1612 (2006).
[CrossRef] [PubMed]

2004 (2)

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, s288 (2004).
[CrossRef]

F. Ö. Ilday, K. Beckwitt, Y.-F. Chen, H. Lim, and F. W. Wise, J. Opt. Soc. Am. B 21, 376 (2004).
[CrossRef]

2003 (1)

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, Phys. Rev. E 68, 036614 (2003).
[CrossRef]

2002 (1)

1999 (1)

J. Opt. B: Quantum Semiclassical Opt. (1)

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, s288 (2004).
[CrossRef]

J. Opt. Soc. Am. B (3)

S. Ashihara, J. Nishina, T. Shimura, and K. Kuroda, J. Opt. Soc. Am. B 19, 2505 (2002).
[CrossRef]

M. Bache, J. Moses, and F. W. Wise, "Scaling laws for soliton pulse compression in cascaded quadratic nonlinearities" J. Opt. Soc. Am. B (to be published), ArXiv:0706.1507.

F. Ö. Ilday, K. Beckwitt, Y.-F. Chen, H. Lim, and F. W. Wise, J. Opt. Soc. Am. B 21, 376 (2004).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. E (2)

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, Phys. Rev. E 68, 036614 (2003).
[CrossRef]

P. V. Larsen, M. P. Sørensen, O. Bang, W. Z. Krolikowski, and S. Trillo, Phys. Rev. E 73, 036614 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

J. Moses and F. W. Wise, Phys. Rev. Lett. 97, 073903 (2006).
[CrossRef] [PubMed]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

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Figures (2)

Fig. 1
Fig. 1

(a) Compression window Eq. (14) versus λ 1 in a BBO. Also Δ k sr = 4 π d 12 T 0 of [1] for a 100 fs pulse is shown. (b) t 1 , 2 and T R , SHG versus Δ k for λ 1 = 1064 nm .

Fig. 2
Fig. 2

Numerical simulations of soliton compression of a 100 fs sech pulse in BBO for λ 1 = 1064 nm and N eff = 5.3 . The normalized FW intensity at z opt is shown for (a) Δ k = 50 mm 1 (stationary regime) and (b) Δ k = 30 mm 1 (nonstationary regime). The response functions R ± T 0 and δ ω NL T 0 induced by cascaded SPM for (a) and (b) are shown in (c), (e) and (d), (f), respectively.

Equations (14)

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( i z 1 2 k 1 ( 2 ) t t ) E 1 + κ 1 E 1 * E 2 e i Δ k z + ρ 1 E 1 ( E 1 2 + η E 2 2 ) = 0 ,
( i z i d 12 t 1 2 k 2 ( 2 ) t t ) E 2 + κ 2 E 1 2 e i Δ k z + ρ 2 E 2 ( E 2 2 + η E 1 2 ) = 0 ,
( i ξ D 1 τ τ ) U 1 + Δ β N SHG U 1 * U 2 e i Δ β ξ + N Kerr 2 U 1 ( U 1 2 + η n ¯ U 2 2 ) = 0 ,
( i ξ i δ τ D 2 τ τ ) U 2 + Δ β N SHG U 1 2 e i Δ β ξ + 2 n ¯ 2 N Kerr 2 U 2 ( U 2 2 + η n ¯ 1 U 1 2 ) = 0 ,
ϕ 2 ( τ ) = N SHG Δ β d τ R ± ( τ ) U 1 2 ( τ τ ) .
R + ( τ ) = τ 2 2 + τ 1 2 2 τ 1 τ 2 2 e i s 2 τ τ 2 e τ τ 1 ,
R ( τ ) = τ 2 2 τ 1 2 2 τ 1 τ 2 2 e i s 2 τ τ 2 sin ( τ τ 1 ) ,
τ 1 = Δ β D 2 τ 2 2 1 2 , τ 2 = 2 D 2 δ .
d 12 2 < 2 Δ k k 2 ( 2 ) , stationary regime , R + ,
d 12 2 > 2 Δ k k 2 ( 2 ) , nonstationary regime , R ,
[ i ξ D 1 τ τ ] U 1 + N Kerr 2 U 1 U 1 2 N SHG 2 U 1 * d τ R ± ( τ ) U 1 2 ( τ τ ) = 0 .
[ i ξ D 1 τ τ ] U 1 ( N SHG 2 N Kerr 2 ) U 1 U 1 2 = i N SHG 2 τ R , SHG U 1 2 τ U 1 ,
τ R , SHG T R , SHG T 0 = 4 τ 1 2 τ 2 τ 1 2 + τ 2 2 = 2 d 12 Δ k T 0 .
Δ k sr < Δ k < Δ k c , max .

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