Abstract

We investigate the influence of the finite spatial resolution of a typical 4f pulse-shaping setup in a single- and double-pass configuration on the shaped waveforms. Specifically, we calculate and measure the space-frequency distribution at the focal plane of a lens following the shaping setup and show that steep amplitude or phase jumps, as they appear with pixelated spatial light modulators, are affected by a finite spatial resolution.

© 2010 Optical Society of America

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References

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  1. A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000).
    [CrossRef]
  2. Y. Silberberg, Annu. Rev. Phys. Chem. 60, 277 (2009).
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    [CrossRef]
  4. W. Lozovoy, X. Zhu, T. C. Gunaratne, D. A. Harris, J. C. Shane, and M. Dantus, J. Phys. Chem. A 112, 3789(2008).
    [CrossRef] [PubMed]
  5. D. Goswami, Phys. Rep. 374, 385 (2003).
    [CrossRef]
  6. M. M. Wefers and K. A. Nelson, IEEE J. Quantum Electron. 32, 161 (1996).
    [CrossRef]
  7. T. Tanabe, H. Tanabe, Y. Teramura, and F. Kannari, J. Opt. Soc. Am. B 19, 2795 (2002).
    [CrossRef]
  8. B. J. Sussman, R. Lusten, and A. Stolow, Phys. Rev. A 77, 043416 (2008).
    [CrossRef]
  9. F. Frei, A. Galler, and T. Feurer, J. Chem. Phys. 130, 034302 (2009).
    [CrossRef] [PubMed]
  10. J. C. Vaughan, T. Feurer, K. W. Stone, and K. A. Nelson, Opt. Express 14, 1314 (2006).
    [CrossRef] [PubMed]

2010 (1)

P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, Phys. Rev. A 81, 013809 (2010).
[CrossRef]

2009 (2)

Y. Silberberg, Annu. Rev. Phys. Chem. 60, 277 (2009).
[CrossRef]

F. Frei, A. Galler, and T. Feurer, J. Chem. Phys. 130, 034302 (2009).
[CrossRef] [PubMed]

2008 (2)

B. J. Sussman, R. Lusten, and A. Stolow, Phys. Rev. A 77, 043416 (2008).
[CrossRef]

W. Lozovoy, X. Zhu, T. C. Gunaratne, D. A. Harris, J. C. Shane, and M. Dantus, J. Phys. Chem. A 112, 3789(2008).
[CrossRef] [PubMed]

2006 (1)

2003 (1)

D. Goswami, Phys. Rep. 374, 385 (2003).
[CrossRef]

2002 (1)

2000 (1)

A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000).
[CrossRef]

1996 (1)

M. M. Wefers and K. A. Nelson, IEEE J. Quantum Electron. 32, 161 (1996).
[CrossRef]

Aït-Belkacem, D.

P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, Phys. Rev. A 81, 013809 (2010).
[CrossRef]

Behrndt, M.

P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, Phys. Rev. A 81, 013809 (2010).
[CrossRef]

Brasselet, S.

P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, Phys. Rev. A 81, 013809 (2010).
[CrossRef]

Dantus, M.

W. Lozovoy, X. Zhu, T. C. Gunaratne, D. A. Harris, J. C. Shane, and M. Dantus, J. Phys. Chem. A 112, 3789(2008).
[CrossRef] [PubMed]

Feurer, T.

Frei, F.

F. Frei, A. Galler, and T. Feurer, J. Chem. Phys. 130, 034302 (2009).
[CrossRef] [PubMed]

Galler, A.

F. Frei, A. Galler, and T. Feurer, J. Chem. Phys. 130, 034302 (2009).
[CrossRef] [PubMed]

Goswami, D.

D. Goswami, Phys. Rep. 374, 385 (2003).
[CrossRef]

Gunaratne, T. C.

W. Lozovoy, X. Zhu, T. C. Gunaratne, D. A. Harris, J. C. Shane, and M. Dantus, J. Phys. Chem. A 112, 3789(2008).
[CrossRef] [PubMed]

Harris, D. A.

W. Lozovoy, X. Zhu, T. C. Gunaratne, D. A. Harris, J. C. Shane, and M. Dantus, J. Phys. Chem. A 112, 3789(2008).
[CrossRef] [PubMed]

Kannari, F.

Lozovoy, W.

W. Lozovoy, X. Zhu, T. C. Gunaratne, D. A. Harris, J. C. Shane, and M. Dantus, J. Phys. Chem. A 112, 3789(2008).
[CrossRef] [PubMed]

Lusten, R.

B. J. Sussman, R. Lusten, and A. Stolow, Phys. Rev. A 77, 043416 (2008).
[CrossRef]

Nelson, K. A.

Rigneault, H.

P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, Phys. Rev. A 81, 013809 (2010).
[CrossRef]

Schön, P.

P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, Phys. Rev. A 81, 013809 (2010).
[CrossRef]

Shane, J. C.

W. Lozovoy, X. Zhu, T. C. Gunaratne, D. A. Harris, J. C. Shane, and M. Dantus, J. Phys. Chem. A 112, 3789(2008).
[CrossRef] [PubMed]

Silberberg, Y.

Y. Silberberg, Annu. Rev. Phys. Chem. 60, 277 (2009).
[CrossRef]

Stolow, A.

B. J. Sussman, R. Lusten, and A. Stolow, Phys. Rev. A 77, 043416 (2008).
[CrossRef]

Stone, K. W.

Sussman, B. J.

B. J. Sussman, R. Lusten, and A. Stolow, Phys. Rev. A 77, 043416 (2008).
[CrossRef]

Tanabe, H.

Tanabe, T.

Teramura, Y.

Vaughan, J. C.

Wefers, M. M.

M. M. Wefers and K. A. Nelson, IEEE J. Quantum Electron. 32, 161 (1996).
[CrossRef]

Weiner, A. M.

A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000).
[CrossRef]

Zhu, X.

W. Lozovoy, X. Zhu, T. C. Gunaratne, D. A. Harris, J. C. Shane, and M. Dantus, J. Phys. Chem. A 112, 3789(2008).
[CrossRef] [PubMed]

Annu. Rev. Phys. Chem. (1)

Y. Silberberg, Annu. Rev. Phys. Chem. 60, 277 (2009).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Wefers and K. A. Nelson, IEEE J. Quantum Electron. 32, 161 (1996).
[CrossRef]

J. Chem. Phys. (1)

F. Frei, A. Galler, and T. Feurer, J. Chem. Phys. 130, 034302 (2009).
[CrossRef] [PubMed]

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

J. Phys. Chem. A (1)

W. Lozovoy, X. Zhu, T. C. Gunaratne, D. A. Harris, J. C. Shane, and M. Dantus, J. Phys. Chem. A 112, 3789(2008).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rep. (1)

D. Goswami, Phys. Rep. 374, 385 (2003).
[CrossRef]

Phys. Rev. A (2)

P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, Phys. Rev. A 81, 013809 (2010).
[CrossRef]

B. J. Sussman, R. Lusten, and A. Stolow, Phys. Rev. A 77, 043416 (2008).
[CrossRef]

Rev. Sci. Instrum. (1)

A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Space-frequency intensity distribution for the transmission of a single pixel set to zero—(a) experiment and (b) simulation—and for a π phase jump between two neighboring pixels—(c) experiment and (d) simulation. The dashed–dotted lines correspond to space–time coupling as predicted by Eq. (2).

Fig. 2
Fig. 2

(a) Measured and (b) simulated on-axis spectra ( x = 0 ) at the focal plane as a function of the phase step amplitude.

Fig. 3
Fig. 3

Space-frequency intensity distribution for the double-pass configuration. Left column, transmission of a single pixel set to zero. Right column, π phase step. (a), (d) Experiments. Simulations (b), (e) with and (c), (f) without a second-order spatial phase.

Equations (4)

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E ( x , Ω ) E 0 ( k c f 2 x , Ω ) M ( f γ k c Ω + f b f 2 x ) .
x = f γ k c Ω .
E 1 ( x , Ω ) = d x P ( x ) E ( x x , Ω ) .
E 2 ( x , Ω ) d x P 2 ( x ) M ( f γ k c Ω + f b f 2 ( x x ) ) × d x P 1 ( x ) E 0 ( k c b f x + k c f 2 ( x x ) , Ω ) × M ( f γ k c Ω x f b f 2 ( x x ) ) .

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