Abstract

We exploit the close similarities between time–frequency and position–wave-vector correspondences to control the spatiotemporal diffraction pattern of ultrashort laser pulses. This approach permits novel, automated generation of sophisticated two-dimensional femtosecond waveforms. A two-dimensional space–time version of a Gerchberg–Saxton algorithm is used to iteratively determine the phase pattern in position-frequency space that produces a user-defined intensity profile in wave-vector–time space.

© 2003 Optical Society of America

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  1. J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, Appl. Phys. Lett. 47, 87 (1985).
    [CrossRef]
  2. A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000).
    [CrossRef]
  3. T. Feurer, J. C. Vaughan, and K. A. Nelson, Science 299, 374 (2003).
    [CrossRef] [PubMed]
  4. T. Feurer, J. C. Vaughan, R. Koehl, and K. A. Nelson, Opt. Lett. 27, 652 (2002).
    [CrossRef]
  5. J. C. Vaughan, T. Feurer, and K. A. Nelson, J. Opt. Soc. Am. B 19, 2489 (2002).
    [CrossRef]
  6. S. H. Lee, ed., Selected Papers on Computer-Generated Holograms and Diffractive Optics (SPIE Optical Engineering Press, Bellingham, Wash., 1992).
  7. M. C. Nuss and R. L. Morrison, Opt. Lett. 20, 740 (1995).
    [CrossRef] [PubMed]
  8. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, Rev. Sci. Instrum. 68, 3277 (1997).
    [CrossRef]
  9. R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 34, 275 (1971).
  10. M. Hacker, G. Stobrawa, and T. Feurer, Opt. Express 9, 191 (2001), http://www.opticsexpress.org.
    [CrossRef] [PubMed]

2003 (1)

T. Feurer, J. C. Vaughan, and K. A. Nelson, Science 299, 374 (2003).
[CrossRef] [PubMed]

2002 (2)

J. C. Vaughan, T. Feurer, and K. A. Nelson, J. Opt. Soc. Am. B 19, 2489 (2002).
[CrossRef]

T. Feurer, J. C. Vaughan, R. Koehl, and K. A. Nelson, Opt. Lett. 27, 652 (2002).
[CrossRef]

2001 (1)

2000 (1)

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

1997 (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

1995 (1)

1985 (1)

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, Appl. Phys. Lett. 47, 87 (1985).
[CrossRef]

1971 (1)

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 34, 275 (1971).

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Feurer, T.

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 34, 275 (1971).

Hacker, M.

Heritage, J. P.

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, Appl. Phys. Lett. 47, 87 (1985).
[CrossRef]

Koehl, R.

Krumbugel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Morrison, R. L.

Nelson, K. A.

T. Feurer, J. C. Vaughan, and K. A. Nelson, Science 299, 374 (2003).
[CrossRef] [PubMed]

T. Feurer, J. C. Vaughan, R. Koehl, and K. A. Nelson, Opt. Lett. 27, 652 (2002).
[CrossRef]

J. C. Vaughan, T. Feurer, and K. A. Nelson, J. Opt. Soc. Am. B 19, 2489 (2002).
[CrossRef]

Nuss, M. C.

Richman, B. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 34, 275 (1971).

Stobrawa, G.

Stolen, R. H.

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, Appl. Phys. Lett. 47, 87 (1985).
[CrossRef]

Sweetser, J. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Thurston, R. N.

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, Appl. Phys. Lett. 47, 87 (1985).
[CrossRef]

Tomlinson, W. J.

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, Appl. Phys. Lett. 47, 87 (1985).
[CrossRef]

Trebino, R.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Vaughan, J. C.

T. Feurer, J. C. Vaughan, and K. A. Nelson, Science 299, 374 (2003).
[CrossRef] [PubMed]

T. Feurer, J. C. Vaughan, R. Koehl, and K. A. Nelson, Opt. Lett. 27, 652 (2002).
[CrossRef]

J. C. Vaughan, T. Feurer, and K. A. Nelson, J. Opt. Soc. Am. B 19, 2489 (2002).
[CrossRef]

Weiner, A. M.

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

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, Appl. Phys. Lett. 47, 87 (1985).
[CrossRef]

Appl. Phys. Lett. (1)

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, Appl. Phys. Lett. 47, 87 (1985).
[CrossRef]

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

J. C. Vaughan, T. Feurer, and K. A. Nelson, J. Opt. Soc. Am. B 19, 2489 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Optik (Stuttgart) (1)

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 34, 275 (1971).

Rev. Sci. Instrum. (2)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

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

Science (1)

T. Feurer, J. C. Vaughan, and K. A. Nelson, Science 299, 374 (2003).
[CrossRef] [PubMed]

Other (1)

S. H. Lee, ed., Selected Papers on Computer-Generated Holograms and Diffractive Optics (SPIE Optical Engineering Press, Bellingham, Wash., 1992).

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Figures (4)

Fig. 1
Fig. 1

(a) Setup for the generation and measurement of spatiotemporally shaped femtosecond laser pulses. b.s., beam splitter; c.l., cylindrical lens; 2D, two-dimensional. (b) Phase pattern corresponding to temporally separated double slits along the vertical dimension with increasing spatial separation. Note that the phase is modulo 2π, black corresponds to zero phase, and white to 2π. (c) Spatially resolved cross correlation of the waveform generated by the phase pattern shown in (b).

Fig. 2
Fig. 2

(a) Measured and (b) calculated SR-FROG trace. In both cases an isosurface corresponding to half the maximum value is shown. The three faces show the projections along the corresponding axis. The spot in the center of the measured SR-FROG is the zeroth-order diffraction.

Fig. 3
Fig. 3

A single pulse, originally centered in space and time, has been steered around to different positions all located on a circle in space–time.

Fig. 4
Fig. 4

Cross correlation of a waveform generated through wave-vector shaping. The corresponding phase pattern was calculated through a space–time version of a Gerchberg–Saxton algorithm.

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