Abstract

We demonstrate a spatiotemporal laser-pulse-shaping scheme that exploits the chromatic aberration in a dispersive lens. This normally harmful effect transforms the phase modulation into a beam-size modulation at the focal plane. In combination with the intricate diffraction effect via beam apodization, this method provides a spatiotemporal control of photon distribution with an accuracy of diffraction limit on a time scale of femtoseconds.

© 2008 Optical Society of America

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References

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  1. C. Limborg-Deprey and P. Bolton, Nucl. Instrum. Methods A 557, 106 (2006).
    [CrossRef]
  2. Y. Li and J. W. Lewellen, Phys. Rev. Lett. 100, 074801 (2008), and references therein.
    [CrossRef] [PubMed]
  3. P. Baum and A. H. Zewail, Proc. Natl. Acad. Sci. USA 103, 16105 (2006), and references therein.
    [CrossRef] [PubMed]
  4. A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000).
    [CrossRef]
  5. F. Verluise, V. Laude, Z. Cheng, Ch. Spielmann, and P. Tournois, Opt. Lett. 25, 575 (2000); product at http://www.fastlite.com.
    [CrossRef]
  6. See, e.g., Laser Beam Shaping, F.M.Dickey and S.C.Holswade eds. (Marcel Dekker, 2000).
    [CrossRef]
  7. J. C. Vaughan, T. Feurer, and K. A. Nelson, J. Opt. Soc. Am. B 19, 2489 (2002).
    [CrossRef]
  8. M. C. Nuss and R. L. Morrison, Opt. Lett. 20, 740 (1995).
    [CrossRef] [PubMed]
  9. R. Piestun and D. A. B. Miller, Opt. Lett. 26, 1373 (2001).
    [CrossRef]
  10. K. B. Hill, K. G. Purchase, and D. J. Brady, Opt. Lett. 20, 1201 (1995).
    [CrossRef] [PubMed]
  11. S. Zhou, D. Ouzounov, H. Li, I. Bazarov, B. Dunham, C. Sinclair, and F. W. Wise, Appl. Opt. 46, 8488 (2007), and references therein.
    [CrossRef] [PubMed]
  12. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 2003).
  13. I. M. Kapchinskij and V. V. Vladimirskij, Conference on High Energy Accelerators and Instrumentation (CERN, Geneva, 1959), p. 274.
  14. M. Reiser, Theory and Design of Charged Particle Beams (Wiley, 2005).
  15. M. Kempe, U. Stamm, B. Wilhelmi, and W. Rudolph, J. Opt. Soc. Am. B 9, 1158 (1992).
    [CrossRef]
  16. Y. Li and R. Crowell, Opt. Lett. 32, 93 (2007).
    [CrossRef]
  17. Calculated from data in H. H. Li, J. Phys. Chem. Ref. Data 13, 103 (1984).
    [CrossRef]
  18. S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, J. Mod. Opt. 53, 1819 (2006), and references therein.
    [CrossRef]

2008 (1)

Y. Li and J. W. Lewellen, Phys. Rev. Lett. 100, 074801 (2008), and references therein.
[CrossRef] [PubMed]

2007 (2)

2006 (3)

C. Limborg-Deprey and P. Bolton, Nucl. Instrum. Methods A 557, 106 (2006).
[CrossRef]

P. Baum and A. H. Zewail, Proc. Natl. Acad. Sci. USA 103, 16105 (2006), and references therein.
[CrossRef] [PubMed]

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, J. Mod. Opt. 53, 1819 (2006), and references therein.
[CrossRef]

2002 (1)

2001 (1)

2000 (2)

1995 (2)

1992 (1)

1984 (1)

Calculated from data in H. H. Li, J. Phys. Chem. Ref. Data 13, 103 (1984).
[CrossRef]

Baum, P.

P. Baum and A. H. Zewail, Proc. Natl. Acad. Sci. USA 103, 16105 (2006), and references therein.
[CrossRef] [PubMed]

Bazarov, I.

Bolton, P.

C. Limborg-Deprey and P. Bolton, Nucl. Instrum. Methods A 557, 106 (2006).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 2003).

Brady, D. J.

Cheng, Z.

Crowell, R.

Dunham, B.

Feurer, T.

Hill, K. B.

Kapchinskij, I. M.

I. M. Kapchinskij and V. V. Vladimirskij, Conference on High Energy Accelerators and Instrumentation (CERN, Geneva, 1959), p. 274.

Kempe, M.

Laude, V.

Lewellen, J. W.

Y. Li and J. W. Lewellen, Phys. Rev. Lett. 100, 074801 (2008), and references therein.
[CrossRef] [PubMed]

Li, H.

Li, H. H.

Calculated from data in H. H. Li, J. Phys. Chem. Ref. Data 13, 103 (1984).
[CrossRef]

Li, Y.

Y. Li and J. W. Lewellen, Phys. Rev. Lett. 100, 074801 (2008), and references therein.
[CrossRef] [PubMed]

Y. Li and R. Crowell, Opt. Lett. 32, 93 (2007).
[CrossRef]

Limborg-Deprey, C.

C. Limborg-Deprey and P. Bolton, Nucl. Instrum. Methods A 557, 106 (2006).
[CrossRef]

Miller, D. A. B.

Morrison, R. L.

Nelson, K. A.

Nuss, M. C.

Ouzounov, D.

Piestun, R.

Purchase, K. G.

Reiser, M.

M. Reiser, Theory and Design of Charged Particle Beams (Wiley, 2005).

Rudolph, W.

Schimmel, H.

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, J. Mod. Opt. 53, 1819 (2006), and references therein.
[CrossRef]

Sharma, D. K.

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, J. Mod. Opt. 53, 1819 (2006), and references therein.
[CrossRef]

Sinclair, C.

Spielmann, Ch.

Stamm, U.

Tournois, P.

Vaughan, J. C.

Veetil, S. P.

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, J. Mod. Opt. 53, 1819 (2006), and references therein.
[CrossRef]

Verluise, F.

Vijayan, C.

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, J. Mod. Opt. 53, 1819 (2006), and references therein.
[CrossRef]

Vladimirskij, V. V.

I. M. Kapchinskij and V. V. Vladimirskij, Conference on High Energy Accelerators and Instrumentation (CERN, Geneva, 1959), p. 274.

Weiner, A. M.

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

Wilhelmi, B.

Wise, F. W.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 2003).

Wyrowski, F.

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, J. Mod. Opt. 53, 1819 (2006), and references therein.
[CrossRef]

Zewail, A. H.

P. Baum and A. H. Zewail, Proc. Natl. Acad. Sci. USA 103, 16105 (2006), and references therein.
[CrossRef] [PubMed]

Zhou, S.

Appl. Opt. (1)

J. Mod. Opt. (1)

S. P. Veetil, C. Vijayan, D. K. Sharma, H. Schimmel, and F. Wyrowski, J. Mod. Opt. 53, 1819 (2006), and references therein.
[CrossRef]

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

J. Phys. Chem. Ref. Data (1)

Calculated from data in H. H. Li, J. Phys. Chem. Ref. Data 13, 103 (1984).
[CrossRef]

Nucl. Instrum. Methods A (1)

C. Limborg-Deprey and P. Bolton, Nucl. Instrum. Methods A 557, 106 (2006).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. Lett. (1)

Y. Li and J. W. Lewellen, Phys. Rev. Lett. 100, 074801 (2008), and references therein.
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

P. Baum and A. H. Zewail, Proc. Natl. Acad. Sci. USA 103, 16105 (2006), and references therein.
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

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

Other (4)

See, e.g., Laser Beam Shaping, F.M.Dickey and S.C.Holswade eds. (Marcel Dekker, 2000).
[CrossRef]

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 2003).

I. M. Kapchinskij and V. V. Vladimirskij, Conference on High Energy Accelerators and Instrumentation (CERN, Geneva, 1959), p. 274.

M. Reiser, Theory and Design of Charged Particle Beams (Wiley, 2005).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experiment. PP, pulse picker (a pair of Pockel cells); D, AOPDF; SF, achromatic spatial filter; ZSL, ZnSe lens; AL, achromatic image relay lens; ODL, optical delay line; C, camera.

Fig. 2
Fig. 2

Laser pulse amplitude A (bold solid curves) and phase ϕ (dashed curves) calculated from Eqs. (5, 6) in the (a) time and (b) frequency domain, and the measured spectrum amplitude [curve in (b)]. The thin solid transverse profile of the laser pulse after the spatial filter, in front of the ZnSe lens, is shown in (c) with a slightly diagonal elongation. The input laser spectrum is given in (b) as a dashed–dotted curve. The efficiency of the AOPDF is 5%. The linear phase has been subtracted to show the nonlinear nature.

Fig. 3
Fig. 3

Measured (left column) and simulated (middle column) spatiotemporal intensity distribution with different iris radius a 0 . The right column shows the corresponding measured (thick curves) and simulated (thin curves) intensity as function of time at r = 0 .

Fig. 4
Fig. 4

Cutaway view along the t r plane of the measured (left) and calculated (right) spatiotemporal isointensity surface plot of the pulse in Fig. 3b.

Equations (8)

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δ f = f 0 n 0 1 χ δ ω ,
ϕ ( t ) = ± δ ω ( t ) d t = ± n 0 1 χ N f 0 w ( t ) d t .
A ( t ) I ( t ) 1 2 w ( t ) .
ϕ ( t ) = ω 0 t ± Δ ω 2 [ t ( 1 ( t T ) 2 ) 1 2 + T sin 1 t T ] ,
A ( t ) = A 0 [ 1 ( t T ) 2 ] 1 2 ,
I ( r ) = I m ( r ) + I p ( r ) + 2 cos ( ω [ τ + δ ( r ) ] ) A m ( t , r ) A p ( t δ ( r ) τ , r ) cos [ ϕ m ( t ) ϕ p ( t δ ( r ) τ ) ] d t ,
I ( r ) I m ( r ) + I p ( r ) + 2 cos ( ω [ τ + δ ( r ) ] ) Δ t p i m ( τ , r ) I p ( r ) .
i m ( τ , r ) R 2 ( τ , r ) I p ( r ) .

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