Abstract

We predict that parametric sum-frequency generation of an ultra-short pulse may result from the mixing of an ultra-short optical pulse with a quasi-continuous wave control. We analytically show that the intensity, time duration and group velocity of the generated idler pulse may be controlled in a stable manner by adjusting the intensity level of the background pump.

© 2007 Optical Society of America

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References

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  1. G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum. 74, 1-18 (2003).
    [CrossRef]
  2. J. A. Armstrong, S. S. Jha, and N. S. Shiren, "Some effects of group-velocity dispersion on parametric interactions," IEEE J. Quantum Electron. QE-6, 123-129 (1970).
    [CrossRef]
  3. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Pulses (AIP, New York, 1992).
  4. Y. Wang and R. Dragila, "Efficient conversion of picosecond laser pulses into second-harmonic frequency using group-velocity dispersion," Phys. Rev. A 41, 5645-5649 (1990)
    [CrossRef] [PubMed]
  5. A. Stabinis, G. Valiulis and E. A. Ibragimov, "Effective sum frequency pulse compression in nonlinear crystals," Opt. Commun. 86, 301-306 (1991).
    [CrossRef]
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    [CrossRef]
  11. E. Ibragimov, A. Struthers, and D. J. Kaup, "Soliton pulse compression in the theory of optical parametric amplification," Opt. Commun. 152, 101-107 (1998).
    [CrossRef]
  12. S. Fournier, R. L. Lopez-Martens, C. Le Blanc, E. Baubeau, and F. Salin, "Solitonlike pulse shortening in a femtosecond parametric amplifier," Opt. Lett. 23, 627-629 (1998).
    [CrossRef]
  13. V. E. Zakharov and S. V. Manakov, "Resonant interaction of wave packets in nonlinear media," Sov. Phys. JETP Lett. 18, 243-245 (1973).
  14. D. J. Kaup, "The three-wave interaction - a nondispersive phenomenon," Stud. Appl. Math. 55, 9-44 (1976).
  15. K. Nozaki and T. Taniuti, "Propagation of solitary pulses in interactions of plasma waves," J. Phys. Soc. Japan 34, 796-800 (1973).
    [CrossRef]
  16. Y. Ohsawa and K. Nozaki, "Propagation of solitary pulses in interactions of plasma waves. II," J. Phys. Soc. Japan 36, 591-595 (1974).
    [CrossRef]
  17. F. Calogero and A. Degasperis, "Novel solution of the system describing the resonant interaction of three waves," Physica D 200, 242-256 (2005).
    [CrossRef]
  18. A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, "Stable control of pulse speed in parametric three-wave solitons," Phys. Rev. Lett. 97, 093901 (2006).
    [CrossRef] [PubMed]
  19. M. Conforti, F. Baronio, A. Degasperis, and S. Wabnitz, "Inelastic scattering and interactions of three-wave parametric solitons," Phys. Rev. E 74, 065602(R) (2006).
    [CrossRef]
  20. A. Picozzi and M. Haelterman, "Spontaneous formation of symbiotic solitary waves in a backward quasi-phasematched parametric oscillator," Opt. Lett. 23, 1808-1810 (1998).
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2006 (1)

A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, "Stable control of pulse speed in parametric three-wave solitons," Phys. Rev. Lett. 97, 093901 (2006).
[CrossRef] [PubMed]

2005 (1)

F. Calogero and A. Degasperis, "Novel solution of the system describing the resonant interaction of three waves," Physica D 200, 242-256 (2005).
[CrossRef]

2003 (1)

G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum. 74, 1-18 (2003).
[CrossRef]

1999 (1)

E. Ibragimov, A. Struthers, D. J. Kaup, J. D. Khaydarov, and K. D. Singer, "Three-wave interaction solitons in optical parametric amplification," Phys. Rev. E 59, 6122-6137 (1999).
[CrossRef]

1998 (3)

1997 (1)

1996 (1)

1995 (2)

1992 (1)

1991 (1)

A. Stabinis, G. Valiulis and E. A. Ibragimov, "Effective sum frequency pulse compression in nonlinear crystals," Opt. Commun. 86, 301-306 (1991).
[CrossRef]

1990 (1)

Y. Wang and R. Dragila, "Efficient conversion of picosecond laser pulses into second-harmonic frequency using group-velocity dispersion," Phys. Rev. A 41, 5645-5649 (1990)
[CrossRef] [PubMed]

1976 (1)

D. J. Kaup, "The three-wave interaction - a nondispersive phenomenon," Stud. Appl. Math. 55, 9-44 (1976).

1974 (1)

Y. Ohsawa and K. Nozaki, "Propagation of solitary pulses in interactions of plasma waves. II," J. Phys. Soc. Japan 36, 591-595 (1974).
[CrossRef]

1973 (2)

K. Nozaki and T. Taniuti, "Propagation of solitary pulses in interactions of plasma waves," J. Phys. Soc. Japan 34, 796-800 (1973).
[CrossRef]

V. E. Zakharov and S. V. Manakov, "Resonant interaction of wave packets in nonlinear media," Sov. Phys. JETP Lett. 18, 243-245 (1973).

1970 (1)

J. A. Armstrong, S. S. Jha, and N. S. Shiren, "Some effects of group-velocity dispersion on parametric interactions," IEEE J. Quantum Electron. QE-6, 123-129 (1970).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. A. Armstrong, S. S. Jha, and N. S. Shiren, "Some effects of group-velocity dispersion on parametric interactions," IEEE J. Quantum Electron. QE-6, 123-129 (1970).
[CrossRef]

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

J. Phys. Soc. Japan (2)

K. Nozaki and T. Taniuti, "Propagation of solitary pulses in interactions of plasma waves," J. Phys. Soc. Japan 34, 796-800 (1973).
[CrossRef]

Y. Ohsawa and K. Nozaki, "Propagation of solitary pulses in interactions of plasma waves. II," J. Phys. Soc. Japan 36, 591-595 (1974).
[CrossRef]

Opt. Commun. (2)

E. Ibragimov, A. Struthers, and D. J. Kaup, "Soliton pulse compression in the theory of optical parametric amplification," Opt. Commun. 152, 101-107 (1998).
[CrossRef]

A. Stabinis, G. Valiulis and E. A. Ibragimov, "Effective sum frequency pulse compression in nonlinear crystals," Opt. Commun. 86, 301-306 (1991).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. A (1)

Y. Wang and R. Dragila, "Efficient conversion of picosecond laser pulses into second-harmonic frequency using group-velocity dispersion," Phys. Rev. A 41, 5645-5649 (1990)
[CrossRef] [PubMed]

Phys. Rev. E (1)

E. Ibragimov, A. Struthers, D. J. Kaup, J. D. Khaydarov, and K. D. Singer, "Three-wave interaction solitons in optical parametric amplification," Phys. Rev. E 59, 6122-6137 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, "Stable control of pulse speed in parametric three-wave solitons," Phys. Rev. Lett. 97, 093901 (2006).
[CrossRef] [PubMed]

Physica D (1)

F. Calogero and A. Degasperis, "Novel solution of the system describing the resonant interaction of three waves," Physica D 200, 242-256 (2005).
[CrossRef]

Rev. Sci. Instrum. (1)

G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum. 74, 1-18 (2003).
[CrossRef]

Sov. Phys. JETP Lett. (1)

V. E. Zakharov and S. V. Manakov, "Resonant interaction of wave packets in nonlinear media," Sov. Phys. JETP Lett. 18, 243-245 (1973).

Stud. Appl. Math. (1)

D. J. Kaup, "The three-wave interaction - a nondispersive phenomenon," Stud. Appl. Math. 55, 9-44 (1976).

Other (2)

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Pulses (AIP, New York, 1992).

M. Conforti, F. Baronio, A. Degasperis, and S. Wabnitz, "Inelastic scattering and interactions of three-wave parametric solitons," Phys. Rev. E 74, 065602(R) (2006).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Sum-frequency parametric interaction of two short optical signals atω1 and ω2. The characteristic delays are δ1=0,δ2=2,δ3=1.

Fig. 2.
Fig. 2.

Sum-frequency parametric interaction of a short pulse atω2 and a quasi-CW control at ω1. The characteristic delays are δ1=0,δ2=2,δ3=1.

Fig. 3.
Fig. 3.

Numerical evolution (lines) and theoretical predictions (circles) of energy, pulse duration and velocity of idler (red) and signal (blue) waves reported in Fig.2.

Equations (19)

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A 1 ξ + δ 1 A 1 τ = i A 2 * A 3 ,
A 2 ξ + δ 2 A 2 τ = i A 1 * A 3 ,
A 3 ξ + δ 3 A 3 τ = i A 1 A 2 ,
A j = π χ ( 2 ) n j ω 1 ω 2 ω 3 n 1 n 2 n 3 ω j E j .
U 13 = U 1 + U 3 = 1 2 + ( A 1 2 + A 3 2 ) d τ ,
U 23 = U 2 + U 3 = 1 2 + ( A 2 2 + A 3 2 ) d τ ,
U = U 1 + U 2 + 2 U 3 = 1 2 + ( A 1 2 + A 2 2 + 2 A 3 2 ) d τ .
A 1 = { 1 + 2 p b * b 2 + a 2 [ 1 tanh [ B ( τ + δ ξ ) ] ] } i a g 1 exp ( i q 1 τ 1 ) g ( δ 2 δ 3 )
A 2 = 2 p a b 2 + a 2 g 2 g ( δ 2 δ 3 ) exp [ i ( q 2 τ 2 + χ τ + ω ξ ) ] cosh [ B ( τ + δ ξ ) ] ,
A 3 = 2 p b * b 2 + a 2 g 3 g ( δ 2 δ 3 ) exp [ i ( q 3 τ 3 χ τ ω ξ ) ] cosh [ B ( τ + δ ξ ) ] ,
b = ( Q 1 ) ( p + i k Q ) , r = p 2 k 2 a 2 ,
Q = 1 p 1 2 [ r + r 2 + 4 k 2 p 2 ] ,
B = p [ δ 2 + δ 3 Q ( δ 2 δ 3 ) ] ( δ 2 δ 3 ) ,
δ = 2 δ 2 δ 3 [ δ 2 + δ 3 Q ( δ 2 δ 3 ) ] ,
χ = k [ δ 2 + δ 3 ( δ 2 δ 3 ) Q ] ( δ 2 δ 3 ) ,
ω = 2 k δ 2 δ 3 ( δ 2 δ 3 ) , τ n = τ + δ n ξ
q n = q ( δ n + 1 δ n + 2 ) , g n = ( δ n δ n + 1 ) ( δ n δ n + 2 ) 1 2
g = g 1 g 2 g 3 , n = 1 , 2 , 3 mod ( 3 ) .
p ¯ = p , a ¯ = C δ 2 δ 3 , q ¯ = γ , k ¯ = k + ( q ¯ q ) ( δ 2 δ 3 ) 2 .

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