Abstract

Spectral blue- and red-shifts in a range of 100 nm are achieved by propagating 40 fs pulses with a 70 nm spectrum centered at 1450 nm in a 25-mm-long periodically poled stoichiometric lithium tantalate crystal. We show experimentally that these shifts, originating from a phase-mismatched second harmonic generation process under conditions of strong group-velocity mismatch, can be efficiently controlled by acting on pulse intensity and phase-mismatch.

© 2006 Optical Society of America

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References

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  1. Y. S. Kivshar and G. P. Agrawal, Optical solitons (Academic press, San Diego, 2003).
  2. G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum 74, 1-18 (2003).
    [CrossRef]
  3. J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, "High-power air-clad large-mode-area photonic crystal fiber laser," Opt. Express 11, 818-823 (2003).
    [CrossRef] [PubMed]
  4. F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, "Self-steepening of Light Pulses," Phys. Rev. 164, 312-323 (1967).
    [CrossRef]
  5. T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, "Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments," Phys. Rev. 177, 306-313 (1969).
    [CrossRef]
  6. D. Grischkowsky, M. Loy, and P. Liao, "Adiabatic following model for two-photon transitions: Nonlinear mixing and pulse propagation," Phys. Rev. A 12, 2514-2533 (1975).
    [CrossRef]
  7. D. Anderson and M. Lisak, "Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides," Phys. Rev. A 27, 1393-1398 (1983).
    [CrossRef]
  8. A.S. Rodrigues, M. Santagiustina, and E.M. Wright, "Nonlinear pulse propagation in the vicinity of a two-photon resonance," Phys. Rev. A 52, 3231-3238 (1995).
    [CrossRef] [PubMed]
  9. P. Guerreiro, S. Lee, A. Rodrigues, Y. Hu, E. Wright, S. Najafi, J. Mackenzie, and N. Peyghambarian, "Femtosecond pulse propagation near a two-photon transition in a semiconductor quantum-dot waveguide," Opt. Lett. 21, 659-661 (1996).
    [CrossRef] [PubMed]
  10. R. DeSalvo, D. Hagan, M. Sheik-Bahae, G. Stegeman, E. Van Stryland, and H. Vanherzeele, "Self-focusing and self-defocusing by cascaded second-order effects in KTP," Opt. Lett. 17, 28-30 (1992)
    [CrossRef] [PubMed]
  11. C. Menyuk, R. Schiek, and L. Torner, "Solitary waves due to χ(2): χ(2) cascading," J. Opt. Soc. Am. B 11, 2434-2443 (1994).
    [CrossRef]
  12. J.P. Torres and L. Torner, "Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media," Opt. Quantum Electron. 29, 757-776 (1997).
    [CrossRef]
  13. P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, "Spatial trapping of short pulses in Ti-indiffused LiNbO3 waveguides, " Opt. Lett. 27, 2182-2184 (2002).
    [CrossRef]
  14. F. Ilday, K. Beckwitt, Y. Chen, H. Lim, and F. Wise, "Controllable Raman-like nonlinearities from nonstationary, cascaded quadratic processes, " J. Opt. Soc. Am. B 21, 376-383 (2004).
    [CrossRef]
  15. C. Balslev Clausen, O. Bang, and Yu. S. Kivshar, "Spatial solitons and induced Kerr effects in quasi-phase-matched Quadratic Media," Phys. Rev. Lett. 78, 4749-4752 (1997).
    [CrossRef]
  16. In literature, the fourth term in Eq. (2) is usually referred as the self-steepening term (see for example Ref. [4-9]).
    [CrossRef]
  17. M. Marangoni, C. Manzoni, R. Ramponi, G. Cerullo, F. Baronio, C. De Angelis, and K. Kitamura, "Group-velocity control by quadratic nonlinear interactions, " Opt. Lett. 31, 534-536 (2006).
  18. K. Beckwitt, F. Ilday, and F. Wise, "Frequency shifting with local nonlinearity management in nonuniformly poled quadratic nonlinear materials," Opt. Lett. 29, 763-765 (2004).
    [CrossRef] [PubMed]

2006 (1)

2004 (2)

2003 (2)

2002 (1)

1997 (1)

J.P. Torres and L. Torner, "Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media," Opt. Quantum Electron. 29, 757-776 (1997).
[CrossRef]

1996 (1)

1995 (1)

A.S. Rodrigues, M. Santagiustina, and E.M. Wright, "Nonlinear pulse propagation in the vicinity of a two-photon resonance," Phys. Rev. A 52, 3231-3238 (1995).
[CrossRef] [PubMed]

1994 (1)

1992 (1)

1983 (1)

D. Anderson and M. Lisak, "Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides," Phys. Rev. A 27, 1393-1398 (1983).
[CrossRef]

1975 (1)

D. Grischkowsky, M. Loy, and P. Liao, "Adiabatic following model for two-photon transitions: Nonlinear mixing and pulse propagation," Phys. Rev. A 12, 2514-2533 (1975).
[CrossRef]

1969 (1)

T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, "Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments," Phys. Rev. 177, 306-313 (1969).
[CrossRef]

1967 (1)

F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, "Self-steepening of Light Pulses," Phys. Rev. 164, 312-323 (1967).
[CrossRef]

Anderson, D.

D. Anderson and M. Lisak, "Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides," Phys. Rev. A 27, 1393-1398 (1983).
[CrossRef]

Baronio, F.

Barthelemy, A.

Beckwitt, K.

Broeng, J.

Cerullo, G.

Chen, Y.

Couderc, V.

De Angelis, C.

De Martini, F.

F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, "Self-steepening of Light Pulses," Phys. Rev. 164, 312-323 (1967).
[CrossRef]

De Silvestri, S.

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

DeSalvo, R.

Grischkowsky, D.

D. Grischkowsky, M. Loy, and P. Liao, "Adiabatic following model for two-photon transitions: Nonlinear mixing and pulse propagation," Phys. Rev. A 12, 2514-2533 (1975).
[CrossRef]

Guerreiro, P.

Gustafson, T.K.

T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, "Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments," Phys. Rev. 177, 306-313 (1969).
[CrossRef]

F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, "Self-steepening of Light Pulses," Phys. Rev. 164, 312-323 (1967).
[CrossRef]

Hagan, D.

Haus, H.A.

T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, "Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments," Phys. Rev. 177, 306-313 (1969).
[CrossRef]

Hu, Y.

Ilday, F.

Iliew, R.

Jakobsen, C.

Kelley, P.L.

T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, "Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments," Phys. Rev. 177, 306-313 (1969).
[CrossRef]

F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, "Self-steepening of Light Pulses," Phys. Rev. 164, 312-323 (1967).
[CrossRef]

Kitamura, K.

Lederer, F.

Lee, S.

Lefort, L.

Liao, P.

D. Grischkowsky, M. Loy, and P. Liao, "Adiabatic following model for two-photon transitions: Nonlinear mixing and pulse propagation," Phys. Rev. A 12, 2514-2533 (1975).
[CrossRef]

Lifsitz, J.R.

T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, "Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments," Phys. Rev. 177, 306-313 (1969).
[CrossRef]

Lim, H.

Limpert, J.

Lisak, M.

D. Anderson and M. Lisak, "Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides," Phys. Rev. A 27, 1393-1398 (1983).
[CrossRef]

Loy, M.

D. Grischkowsky, M. Loy, and P. Liao, "Adiabatic following model for two-photon transitions: Nonlinear mixing and pulse propagation," Phys. Rev. A 12, 2514-2533 (1975).
[CrossRef]

Mackenzie, J.

Manzoni, C.

Marangoni, M.

Menyuk, C.

Min, Y.

Najafi, S.

Nolte, S.

Petersson, A.

Peyghambarian, N.

Pioger, P.

Quiring, V.

Ramponi, R.

Rodrigues, A.

Rodrigues, A.S.

A.S. Rodrigues, M. Santagiustina, and E.M. Wright, "Nonlinear pulse propagation in the vicinity of a two-photon resonance," Phys. Rev. A 52, 3231-3238 (1995).
[CrossRef] [PubMed]

Santagiustina, M.

A.S. Rodrigues, M. Santagiustina, and E.M. Wright, "Nonlinear pulse propagation in the vicinity of a two-photon resonance," Phys. Rev. A 52, 3231-3238 (1995).
[CrossRef] [PubMed]

Schiek, R.

Schreiber, T.

Sheik-Bahae, M.

Sohler, W.

Stegeman, G.

Taran, J.P.

T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, "Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments," Phys. Rev. 177, 306-313 (1969).
[CrossRef]

Torner, L.

J.P. Torres and L. Torner, "Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media," Opt. Quantum Electron. 29, 757-776 (1997).
[CrossRef]

C. Menyuk, R. Schiek, and L. Torner, "Solitary waves due to χ(2): χ(2) cascading," J. Opt. Soc. Am. B 11, 2434-2443 (1994).
[CrossRef]

Torres, J.P.

J.P. Torres and L. Torner, "Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media," Opt. Quantum Electron. 29, 757-776 (1997).
[CrossRef]

Townes, C.H.

F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, "Self-steepening of Light Pulses," Phys. Rev. 164, 312-323 (1967).
[CrossRef]

Tunnermann, T.

Van Stryland, E.

Vanherzeele, H.

Vienne, G.

Wise, F.

Wright, E.

Wright, E.M.

A.S. Rodrigues, M. Santagiustina, and E.M. Wright, "Nonlinear pulse propagation in the vicinity of a two-photon resonance," Phys. Rev. A 52, 3231-3238 (1995).
[CrossRef] [PubMed]

Zellmer, H.

J. Opt. Soc. Am. B (2)

Opt. Express (1)

Opt. Lett. (5)

Opt. Quantum Electron. (1)

J.P. Torres and L. Torner, "Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media," Opt. Quantum Electron. 29, 757-776 (1997).
[CrossRef]

Phys. Rev. (2)

F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, "Self-steepening of Light Pulses," Phys. Rev. 164, 312-323 (1967).
[CrossRef]

T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, "Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments," Phys. Rev. 177, 306-313 (1969).
[CrossRef]

Phys. Rev. A (3)

D. Grischkowsky, M. Loy, and P. Liao, "Adiabatic following model for two-photon transitions: Nonlinear mixing and pulse propagation," Phys. Rev. A 12, 2514-2533 (1975).
[CrossRef]

D. Anderson and M. Lisak, "Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides," Phys. Rev. A 27, 1393-1398 (1983).
[CrossRef]

A.S. Rodrigues, M. Santagiustina, and E.M. Wright, "Nonlinear pulse propagation in the vicinity of a two-photon resonance," Phys. Rev. A 52, 3231-3238 (1995).
[CrossRef] [PubMed]

Rev. Sci. Instrum (1)

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

Other (3)

C. Balslev Clausen, O. Bang, and Yu. S. Kivshar, "Spatial solitons and induced Kerr effects in quasi-phase-matched Quadratic Media," Phys. Rev. Lett. 78, 4749-4752 (1997).
[CrossRef]

In literature, the fourth term in Eq. (2) is usually referred as the self-steepening term (see for example Ref. [4-9]).
[CrossRef]

Y. S. Kivshar and G. P. Agrawal, Optical solitons (Academic press, San Diego, 2003).

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Figures (3)

Fig. 1.
Fig. 1.

Experimental (a) and numerical (b) FF spectra at the output of the crystal: I=0.1 GW/cm2 (dotted line); I=7 GW/cm2 (dash-dotted line); I=20 GW/cm2 (solid line). The phase mismatch is ΔkL=-80π. The inset shows the FF spectral evolution in the λ-z plane at I=20 GW/cm2.

Fig. 2.
Fig. 2.

Experimental (a) and numerical (b) FF spectra at the output of the crystal: I=0.1GW/cm2 (dotted line); I=7 GW/cm2 (dash-dotted line); I=20 GW/cm2 (solid line). The phase mismatch is ΔkL=80π.

Fig. 3.
Fig. 3.

Experimental (symbols) and calculated (lines) FF frequency shifts as a function of injected input intensity for different phase-mismatch conditions: ΔkL=-80π (crosses and solid line), ΔkL=-400π (circles and dashed line), ΔkL=80π (stars and dotted line).

Equations (6)

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j w z β FF 2 2 w t 2 + χ FF v w * e j Δ k z = 0
j v z j δ v t β SH 2 2 v t 2 + χ SH w 2 e j Δ k z = 0
j w z β FF 2 2 w t 2 + χ FF χ SH Δ k w 2 w 2 j δ χ FF χ SH Δ k 2 w 2 w t = 0
ρ 2 = f ( t + z γ ρ 2 )
φ=zκ ρ 2 +g(t+zγ ρ 2 )
δ ω = ϕ t = z κ ρ 2 t

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