Abstract

In this paper, creation of pulse doublets and pulse trains by spectral phase modulation of ultrashort optical pulses is investigated. Pulse doublets with specific features are generated through step-like and triangular spectral phase modulation, whereas sequences of pulses with controllable delay and amplitude are produced via sinusoidal phase modulations. A temporal analysis of this type of tailored pulses is exposed and a complete characterization with the SPIDER technique (Spectral Phase Interferometry for Direct Electric-field Reconstruction) is presented.

© 2004 Optical Society of America

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References

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  1. A.M. Weiner, �??Femtosecond pulse shaping using spatial light modulators,�?? Rev. Sci. Instrum. 71, 1929-1960 (2000).
    [CrossRef]
  2. D. Meshulach, Y. Silberberg, �??Coherent quantum control of two-photon transitions by a femtosecond laser pulse,�?? Nature 396, 239 (1998).
    [CrossRef]
  3. T. Hornung, R. Meier, D. Zeidler, L.-L. Kompa, D Proch, M. Motzkus, �??Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,�?? Appl. Phys. B 71, 277-284 (2000).
    [CrossRef]
  4. T. Hornung, R. Meier, M. Motzkus, �??Optimal control of molecular states in a learning loop with a parametrization in frequency and time domain,�?? Chem. Phys. Lett. 326, 445-453 (2000).
    [CrossRef]
  5. T. Hornung, R. Meier, M. Motzkus, �??Coherent control of the molecular four-wave mixing response by phase and amplitude shaped pulses,�?? Chem. Phys. 267, 261-276 (2001).
    [CrossRef]
  6. M. Renard, E. Hertz, B. Lavorel, and O. Faucher, �??Controlling ground-state rotational dynamics of molecule by shaped femtosecond laser pulses,�?? Phys. Rev. A (to be published).
  7. D. Meshulach, Y. Silberberg, �??Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,�?? Phys. Rev A 60, 1287-1292 (1999).
    [CrossRef]
  8. A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Kirschner, �??Experimental observation of the fundamental dark soliton in optical fibers,�?? Phys. Rev. Lett. 61, 2445-2448 (1988).
    [CrossRef] [PubMed]
  9. Y.V. Yakovlev, C. J. Bardeen, J. Che, J. Cao and K. R. Wilson, �??Chirped pulse enhancement of multiphoton absorption in molecular iodine,�?? J. Chem. Phys. 108(6), 2309-2313 (1998).
    [CrossRef]
  10. A. M. Weiner, J. P. Heritage, and E. M. Kirschner, �?? High-resolution femtosecond pulse shaping, �?? J. Opt. Soc. Am. B 5, 1563 (1988).
    [CrossRef]
  11. A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, �?? Programmable femtosecond pulse shaping by use of a multielement liquid-crystal phase modulator, �?? Opt. Lett. 15, 326 (1990).
    [CrossRef] [PubMed]
  12. D. H. Reitze, A.M. Weiner, and D.E Leiard, �?? Shaping of wide bandwidth 20 femtosecond optical pulses,�?? Appl. Phys. Lett. 61 (11), 1260, (1992).
    [CrossRef]
  13. B. Kohler, V. V. Yakovlev, K. R. Wilson, J. Squier, K. R. DeLong, and R. Trebino, �??Phase and intensity characterization of femtosecond pulses from a chirped-pulse amplifier by frequency-resolved optical gating,�?? Opt. Lett. 20, 483 (1995).
    [CrossRef] [PubMed]
  14. P. Baum, S. Lochbrunner, L. Gallmann, G. Steinmeyer, U. Keller, and E. Riedle, �??Real-time characterization and optimal phase control of tunable visible pulses with a flexible compressor,�?? Appl. Phys. B 74, 219-224 (2002).
    [CrossRef]
  15. C. Iaconis, and I.A. Walmsley, �??Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,�?? Opt. Lett. 23, 792-794 (1998).
    [CrossRef]
  16. S. Xu, B. Lavorel, O. Faucher, and R. Chaux, �??Characterization of self-phase modulated ultrashort optical pulses by spectral phase interferometry,�?? J. Opt. Soc. Am. B 19, 165-168 (2002).
    [CrossRef]
  17. S. Vajda, A. Bartelt, E. Kaposta, T. Leisner, C. Lupulescu, S. Minemoto, P. Rosendo-Francisco and L. Wöste �??Feedback optimization of shaped femtosecond laser pulses for controlling the wavepacket dynamics and reactivity of mixed alkaline clusters,�?? Chem. Phys. 267, 231-239 (2001).
    [CrossRef]
  18. E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murname, G. Mourou, H. Kapteyn and G. Vdovin, �??Pulse compression by use of deformable mirrors,�?? Opt. Lett. 24, 493-495 (1999).
    [CrossRef]
  19. It is noticed that the energy transmittable through the LC-SLM has been recently improved with the last commercialized generation, see for instance: G. Stobrawa, M. Hacker, T. Feurer, D. Zeidler, M. Motzkus and F. Reichel, �??A new high-resolution femtosecond pulse shaper,�?? Appl. Phys. B 72, 627-630 (2001).
    [CrossRef]

Appl. Phys. B (3)

T. Hornung, R. Meier, D. Zeidler, L.-L. Kompa, D Proch, M. Motzkus, �??Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,�?? Appl. Phys. B 71, 277-284 (2000).
[CrossRef]

P. Baum, S. Lochbrunner, L. Gallmann, G. Steinmeyer, U. Keller, and E. Riedle, �??Real-time characterization and optimal phase control of tunable visible pulses with a flexible compressor,�?? Appl. Phys. B 74, 219-224 (2002).
[CrossRef]

It is noticed that the energy transmittable through the LC-SLM has been recently improved with the last commercialized generation, see for instance: G. Stobrawa, M. Hacker, T. Feurer, D. Zeidler, M. Motzkus and F. Reichel, �??A new high-resolution femtosecond pulse shaper,�?? Appl. Phys. B 72, 627-630 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

D. H. Reitze, A.M. Weiner, and D.E Leiard, �?? Shaping of wide bandwidth 20 femtosecond optical pulses,�?? Appl. Phys. Lett. 61 (11), 1260, (1992).
[CrossRef]

Chem. Phys. (2)

S. Vajda, A. Bartelt, E. Kaposta, T. Leisner, C. Lupulescu, S. Minemoto, P. Rosendo-Francisco and L. Wöste �??Feedback optimization of shaped femtosecond laser pulses for controlling the wavepacket dynamics and reactivity of mixed alkaline clusters,�?? Chem. Phys. 267, 231-239 (2001).
[CrossRef]

T. Hornung, R. Meier, M. Motzkus, �??Coherent control of the molecular four-wave mixing response by phase and amplitude shaped pulses,�?? Chem. Phys. 267, 261-276 (2001).
[CrossRef]

Chem. Phys. Lett. (1)

T. Hornung, R. Meier, M. Motzkus, �??Optimal control of molecular states in a learning loop with a parametrization in frequency and time domain,�?? Chem. Phys. Lett. 326, 445-453 (2000).
[CrossRef]

J. Chem. Phys. (1)

Y.V. Yakovlev, C. J. Bardeen, J. Che, J. Cao and K. R. Wilson, �??Chirped pulse enhancement of multiphoton absorption in molecular iodine,�?? J. Chem. Phys. 108(6), 2309-2313 (1998).
[CrossRef]

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

Nature (1)

D. Meshulach, Y. Silberberg, �??Coherent quantum control of two-photon transitions by a femtosecond laser pulse,�?? Nature 396, 239 (1998).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (2)

M. Renard, E. Hertz, B. Lavorel, and O. Faucher, �??Controlling ground-state rotational dynamics of molecule by shaped femtosecond laser pulses,�?? Phys. Rev. A (to be published).

D. Meshulach, Y. Silberberg, �??Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,�?? Phys. Rev A 60, 1287-1292 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Kirschner, �??Experimental observation of the fundamental dark soliton in optical fibers,�?? Phys. Rev. Lett. 61, 2445-2448 (1988).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

A.M. Weiner, �??Femtosecond pulse shaping using spatial light modulators,�?? Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Electric-field characteristics of a pulse shaped through step spectral phase modulation of amplitude α=-π/2 rad. : (a) spectral intensity, (b) spectral phase, (c) temporal intensity and (d) temporal phase. Measurements are represented with black lines and calculations with red lines. See text for details.

Fig. 2.
Fig. 2.

Creation of pulse doublets with adjustable maxima intensity ratio through spectral phase step modulation. (a) Examples of temporal intensity of pulse doublets generated through step modulation of amplitude α and characterised by a SPIDER apparatus : (i) α=-π/2 rad., (ii) α=-2π/3 rad. and (iii) α=-3π/4 rad.. Measurements (black lines) and calculated results (red lines). (b) Evolution of the maxima intensity ratio versus modulation magnitude α. Measurements (blue circles) and calculated results (solid line). See text for details.

Fig. 3.
Fig. 3.

Same as fig.1 with a centered triangular spectral phase modulation (δω=0) of spectral phase slope Δτ=193 fs.

Fig. 4.
Fig. 4.

Tailoring of pulse doublets through triangular spectral phase modulation. (a) Temporal intensity of pulse doublets generated through triangular spectral phase modulation with spectral phase slope Δτ : (i) Δτ=193 fs, (ii) Δτ=258 fs and (iii) Δτ=396 fs. (b) Temporal intensity of pulse doublets generated through triangular spectral phase modulation with relative phase breakpoint position δω/Δω. The spectral phase slope Δτ is fixed to 193 fs. (i) δω/Δω=-0.3, (ii) δω/Δω=-0.2, (iii) δω/Δω=-0.1. (c) Evolution of maxima intensity ratio versus relative phase breakpoint position δω/Δω (Δτ=193fs). (a–b) Experimental (black lines) and calculated results (red lines). (c) Experimental (blue circles) and calculated results (black lines).

Fig. 5.
Fig. 5.

Same as in fig.1 with a sinusoidal spectral phase modulation. The modulation amplitude β and the spectral modulation frequency Δτ are respectively fixed to 0.5 rad. and 330 fs.

Fig. 6.
Fig. 6.

Pulse trains generation through sinusoidal spectral phase modulation. (a) Calculated evolution of maxima intensity versus modulation amplitude β. (b) Temporal intensity of pulse train generated through sinusoidal spectral phase modulation for different values of modulation amplitude β. The spectral modulation frequency Δτ is 211 fs. (i) β=0.5 rad., (ii) β=1 rad., (iii) β=1.2 rad., (iv) β=1.5 rad. and (v) β=2 rad.. (c) Temporal intensity of pulse train generated through sinusoidal spectral phase modulation for different values of spectral modulation frequency Δτ. The modulation amplitude β is fixed to 0.5 rad.. (i) Δτ=211 fs, (ii) Δτ=310 fs and (iii) Δτ=405 fs. See text for details.

Equations (13)

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φ ( ω ) = α H ( ω ω 0 ) ,
E ( t ) = ( E 0 σ 2 π ) cos ( α 2 ) exp [ ( σt 2 ) 2 ] [ 1 + t g ( α 2 ) erfi ( σ t 2 ) ] exp ( i ω 0 t )
= A ( t ) exp ( i ω 0 t ) ,
erfi ( x ) = 2 π 1 2 0 x exp ( y 2 ) dy ,
φ ( ω ) = sgn [ ω ( ω 0 + δ ω ) ] Δ τ [ ω ( ω 0 + δ ω ) ] ,
E ( t ) = ( E 0 σ 4 π ) exp ( i ω 0 t ) { exp [ ( σ ( t + Δ τ ) 2 ) 2 ] [ 1 erf ( i σ ( t + Δ τ ) 2 + δ ω σ ) ]
+ exp [ ( σ ( t Δ τ ) 2 ) 2 ] [ 1 erf ( i σ ( t Δ τ ) 2 δ ω σ ) ] } ,
erf ( x ) = 2 π 1 2 0 x exp ( y 2 ) dy .
E 1,2 ( t ) = ( E 0 σ 4 π ) exp ( i ω 0 t ) exp [ ( σ ( t ± Δ τ ) 2 ) 2 ] [ 1 i erf i ( σ ( t ± Δ τ ) 2 ) ] .
A 1,2 ( t ) = ( E 0 σ 4 π ) exp [ ( σ ( t ± Δ τ ) 2 ) 2 ] [ 1 + { erfi ( σ ( t ± Δ τ ) 2 ) } 2 ] 1 2 ,
φ 1,2 ( t ) = t g 1 [ erfi ( σ ( t ± Δ τ ) 2 ) ] .
φ ( ω ) = β cos [ Δ τ ( ω ω 0 ) ] ,
E ( t ) n = + J n ( β ) exp [ i ( n π 2 ) ] exp [ ( t n Δ τ ) 2 σ 2 4 ] ,

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