Abstract

We present a theoretical model and 2D numerical simulation of cascaded four-wave mixing of femtosecond pulses in bulk χ(3) media, evidencing the importance of 2D interaction geometries in the efficient generation of frequency-converted pulses. Octave-spanning spectra and pulse synthesis down to the sub-two-cycle regime is demonstrated without the need for complex amplitude or phase control, in agreement with experimental measurements.

© 2009 Optical Society of America

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  1. D. H. Auston, Opt. Commun. 3, 272 (1971).
    [CrossRef]
  2. H. Crespo, J. T. Mendonça, and A. D. Santos, Opt. Lett. 25, 829 (2000).
    [CrossRef]
  3. L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 87, 013601 (2001).
    [CrossRef] [PubMed]
  4. T. Fuji, T. Horio, and T. Suzuki, Opt. Lett. 32, 2481 (2007).
    [CrossRef] [PubMed]
  5. H. Crespo and R. Weigand, in Ultrafast Phenomena XVI, P.Corkum, S.De Silvestri, K.A.Nelson, E.Riedle, and R.W.Schoenlein, eds., Vol. 92 of Springer Series in Chemical Physics (Springer, 2009).
    [CrossRef]
  6. R. Weigand, J. T. Mendonça, and H. Crespo, Phys. Rev. A 79, 063838 (2009).
    [CrossRef]
  7. D. L. Hart, A. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2009 (1)

R. Weigand, J. T. Mendonça, and H. Crespo, Phys. Rev. A 79, 063838 (2009).
[CrossRef]

2007 (1)

2001 (1)

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 87, 013601 (2001).
[CrossRef] [PubMed]

2000 (1)

1994 (1)

D. L. Hart, A. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef] [PubMed]

1992 (1)

1987 (1)

1971 (1)

D. H. Auston, Opt. Commun. 3, 272 (1971).
[CrossRef]

Auston, D. H.

D. H. Auston, Opt. Commun. 3, 272 (1971).
[CrossRef]

Backus, S.

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 87, 013601 (2001).
[CrossRef] [PubMed]

Bartels, R.

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 87, 013601 (2001).
[CrossRef] [PubMed]

Crespo, H.

R. Weigand, J. T. Mendonça, and H. Crespo, Phys. Rev. A 79, 063838 (2009).
[CrossRef]

H. Crespo, J. T. Mendonça, and A. D. Santos, Opt. Lett. 25, 829 (2000).
[CrossRef]

H. Crespo and R. Weigand, in Ultrafast Phenomena XVI, P.Corkum, S.De Silvestri, K.A.Nelson, E.Riedle, and R.W.Schoenlein, eds., Vol. 92 of Springer Series in Chemical Physics (Springer, 2009).
[CrossRef]

Durfee, C. G.

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 87, 013601 (2001).
[CrossRef] [PubMed]

Friesem, A. A.

Fuji, T.

Hadley, G.

Hart, D. L.

D. L. Hart, A. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef] [PubMed]

Horio, T.

Judy, A.

D. L. Hart, A. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef] [PubMed]

Kapteyn, H. C.

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 87, 013601 (2001).
[CrossRef] [PubMed]

Kennedy, T. A. B.

D. L. Hart, A. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef] [PubMed]

Lichtman, E.

Mendonça, J. T.

R. Weigand, J. T. Mendonça, and H. Crespo, Phys. Rev. A 79, 063838 (2009).
[CrossRef]

H. Crespo, J. T. Mendonça, and A. D. Santos, Opt. Lett. 25, 829 (2000).
[CrossRef]

Misoguti, L.

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 87, 013601 (2001).
[CrossRef] [PubMed]

Murnane, M. M.

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 87, 013601 (2001).
[CrossRef] [PubMed]

Roy, R.

D. L. Hart, A. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef] [PubMed]

Santos, A. D.

Stoev, K.

D. L. Hart, A. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef] [PubMed]

Suzuki, T.

Waarts, R. G.

Weigand, R.

R. Weigand, J. T. Mendonça, and H. Crespo, Phys. Rev. A 79, 063838 (2009).
[CrossRef]

H. Crespo and R. Weigand, in Ultrafast Phenomena XVI, P.Corkum, S.De Silvestri, K.A.Nelson, E.Riedle, and R.W.Schoenlein, eds., Vol. 92 of Springer Series in Chemical Physics (Springer, 2009).
[CrossRef]

Yaffe, H. H.

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

Opt. Commun. (1)

D. H. Auston, Opt. Commun. 3, 272 (1971).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (2)

R. Weigand, J. T. Mendonça, and H. Crespo, Phys. Rev. A 79, 063838 (2009).
[CrossRef]

D. L. Hart, A. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 87, 013601 (2001).
[CrossRef] [PubMed]

Other (1)

H. Crespo and R. Weigand, in Ultrafast Phenomena XVI, P.Corkum, S.De Silvestri, K.A.Nelson, E.Riedle, and R.W.Schoenlein, eds., Vol. 92 of Springer Series in Chemical Physics (Springer, 2009).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Spectrum of the multiple CFWM orders generated in fused silica spanning 1.5 octaves (the two pump frequencies correspond to the two larger peaks). Dashed curve, experimental results (see [6]); solid curve, numerical simulation; dotted curve, numerical simulation for collinear pumps.

Fig. 2
Fig. 2

Simulated θ λ spectrum of the CFWM beams, clipped at 10 6 of the maximum.

Fig. 3
Fig. 3

Recombined and focused CFWM pulses. (a) Electric field as a function of the delay (in femtoseconds). (b) Intensity. (c) Power spectrum (logarithmic scale).

Fig. 4
Fig. 4

Experimental (measured and retrieved) and simulated PG-XFROG traces of the second frequency-upshifted pulse (top row) and first downshifted pulse (bottom row). The retrieved pulse durations are 30.7 and 40.2 fs for the second upshift and the first downshift, respectively (FROG errors were 0.014 and 0.008 for a 128 × 128 grid).

Fig. 5
Fig. 5

Simulated PG-XFROG, clipped at 10 4 of the maximum, for the recombined and focused CFWM field, assuming 20 fs (left) and 80 fs (right) gate pulses.

Equations (2)

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2 i [ k 0 + k 1 Δ ω ] A ( r , Δ ω ) z + [ k 2 ( ω ) k 0 2 2 k 0 k 1 Δ ω k 1 2 Δ ω 2 + 2 ] A ( r , Δ ω ) = 2 μ 0 ω 2 P NL ( ω ) e i k 0 z ,
A ( r , t ) z = μ 0 ω 0 2 i k 0 ( 1 + i ω 0 t ) 2 p ( r , t ) ,

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