Abstract

We analyze the spatiotemporal distortions of an ultrashort pulse focused through a thin scattering surface. We show and experimentally verify that in such a scenario temporal distortions are proportional to the distance from the optical axis and are present only outside the focal point, as result of geometrical path length differences. We use wavefront shaping to correct for the spatiotemporal distortions and to temporally compress chirped input pulses through the scattering medium.

© 2012 OSA

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  1. P. M. Johnson, A. Imhof, B. P. J. Bret, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E. 68, 016604 (2003).
    [CrossRef]
  2. M. A. Webster, T. D. Gerke, A. M. Weiner, and K. J. Webb, “Spectral and temporal speckle field measurements of a random medium,” Opt. Lett. 29, 1491–1493 (2004).
    [CrossRef] [PubMed]
  3. W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
    [CrossRef] [PubMed]
  4. A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Keifer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Annu. Rev. Phys. Chem. 60, 277–292 (2009).
  5. Y. Silberberg, “Quantum coherent control for nonlinear spectroscopy and microscopy,” Annu. Rev. Phys. Chem 60, 277–292 (1998).
  6. O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
    [CrossRef]
  7. J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett. 106, 103901 (2011).
    [CrossRef] [PubMed]
  8. D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
    [CrossRef] [PubMed]
  9. E. Small, O. Katz, Y. Eshel, and Y. Silberberg, “Spatio-temporal X-wave,” Opt. Express 17, 18659–18668 (2009).
    [CrossRef]
  10. E. Tal and Y. Silberberg, “Transformation from an ultrashort pulse to spatiotemporal speckle by a thin scattering surface,” Opt. Lett. 31, 3529–3531 (2006).
    [CrossRef] [PubMed]
  11. N. Curry, P. Bondareff, M. Leclercq, N. F. van Hulst, R. Sapienza, S. Gigan, and S. Grsillon, “Direct determination of diffusion properties of random media from speckle contrast,” Opt. Lett. 36, 3332–3334 (2011).
    [CrossRef] [PubMed]

2011 (4)

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[CrossRef]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef] [PubMed]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

N. Curry, P. Bondareff, M. Leclercq, N. F. van Hulst, R. Sapienza, S. Gigan, and S. Grsillon, “Direct determination of diffusion properties of random media from speckle contrast,” Opt. Lett. 36, 3332–3334 (2011).
[CrossRef] [PubMed]

2009 (2)

E. Small, O. Katz, Y. Eshel, and Y. Silberberg, “Spatio-temporal X-wave,” Opt. Express 17, 18659–18668 (2009).
[CrossRef]

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Keifer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Annu. Rev. Phys. Chem. 60, 277–292 (2009).

2006 (1)

2004 (1)

2003 (1)

P. M. Johnson, A. Imhof, B. P. J. Bret, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E. 68, 016604 (2003).
[CrossRef]

1998 (1)

Y. Silberberg, “Quantum coherent control for nonlinear spectroscopy and microscopy,” Annu. Rev. Phys. Chem 60, 277–292 (1998).

1990 (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Assion, A.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Keifer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Annu. Rev. Phys. Chem. 60, 277–292 (2009).

Aulbach, J.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef] [PubMed]

Austin, D. R.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

Baumert, T.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Keifer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Annu. Rev. Phys. Chem. 60, 277–292 (2009).

Bergt, M.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Keifer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Annu. Rev. Phys. Chem. 60, 277–292 (2009).

Bondareff, P.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

N. Curry, P. Bondareff, M. Leclercq, N. F. van Hulst, R. Sapienza, S. Gigan, and S. Grsillon, “Direct determination of diffusion properties of random media from speckle contrast,” Opt. Lett. 36, 3332–3334 (2011).
[CrossRef] [PubMed]

Bret, B. P. J.

P. M. Johnson, A. Imhof, B. P. J. Bret, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E. 68, 016604 (2003).
[CrossRef]

Brixner, T.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Keifer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Annu. Rev. Phys. Chem. 60, 277–292 (2009).

Bromberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[CrossRef]

Chatel, B.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

Curry, N.

Denk, W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Eshel, Y.

Gerber, G.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Keifer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Annu. Rev. Phys. Chem. 60, 277–292 (2009).

Gerke, T. D.

Gigan, S.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

N. Curry, P. Bondareff, M. Leclercq, N. F. van Hulst, R. Sapienza, S. Gigan, and S. Grsillon, “Direct determination of diffusion properties of random media from speckle contrast,” Opt. Lett. 36, 3332–3334 (2011).
[CrossRef] [PubMed]

Gjonaj, B.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef] [PubMed]

Grsillon, S.

Imhof, A.

P. M. Johnson, A. Imhof, B. P. J. Bret, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E. 68, 016604 (2003).
[CrossRef]

Johnson, P. M.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef] [PubMed]

P. M. Johnson, A. Imhof, B. P. J. Bret, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E. 68, 016604 (2003).
[CrossRef]

Katz, O.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[CrossRef]

E. Small, O. Katz, Y. Eshel, and Y. Silberberg, “Spatio-temporal X-wave,” Opt. Express 17, 18659–18668 (2009).
[CrossRef]

Keifer, B.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Keifer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Annu. Rev. Phys. Chem. 60, 277–292 (2009).

Lagendijk, A.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef] [PubMed]

P. M. Johnson, A. Imhof, B. P. J. Bret, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E. 68, 016604 (2003).
[CrossRef]

Leclercq, M.

McCabe, D. J.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

Mosk, A. P.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef] [PubMed]

Sapienza, R.

Seyfried, V.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Keifer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Annu. Rev. Phys. Chem. 60, 277–292 (2009).

Silberberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[CrossRef]

E. Small, O. Katz, Y. Eshel, and Y. Silberberg, “Spatio-temporal X-wave,” Opt. Express 17, 18659–18668 (2009).
[CrossRef]

E. Tal and Y. Silberberg, “Transformation from an ultrashort pulse to spatiotemporal speckle by a thin scattering surface,” Opt. Lett. 31, 3529–3531 (2006).
[CrossRef] [PubMed]

Y. Silberberg, “Quantum coherent control for nonlinear spectroscopy and microscopy,” Annu. Rev. Phys. Chem 60, 277–292 (1998).

Small, E.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[CrossRef]

E. Small, O. Katz, Y. Eshel, and Y. Silberberg, “Spatio-temporal X-wave,” Opt. Express 17, 18659–18668 (2009).
[CrossRef]

Strehle, M.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Keifer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Annu. Rev. Phys. Chem. 60, 277–292 (2009).

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Tajalli, A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

Tal, E.

van Hulst, N. F.

Walmsley, I. A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

Webb, K. J.

Webb, W. W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Webster, M. A.

Weiner, A. M.

Annu. Rev. Phys. Chem (1)

Y. Silberberg, “Quantum coherent control for nonlinear spectroscopy and microscopy,” Annu. Rev. Phys. Chem 60, 277–292 (1998).

Annu. Rev. Phys. Chem. (1)

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Keifer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Annu. Rev. Phys. Chem. 60, 277–292 (2009).

Nat. Commun. (1)

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

Nat. Photonics (1)

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. E. (1)

P. M. Johnson, A. Imhof, B. P. J. Bret, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E. 68, 016604 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef] [PubMed]

Science (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Numerical simulation of spatiotemporal distortions when focusing an ultrashort pulse: (a) Free-space focusing: the pulse is perfectly focused in both space and time. (b) Focusing through a thick scattering sample: the pulse is distorted in both space and time, resulting in a spatiotemporal speckle.(c) Focusing through a scattering surface: the wavefront is distorted, producing a spatiotemporal speckle field which is still temporally transform-limited (TL) near the focal spot [9], inset: zoom-in on the spatiotemporal profile near the optical axis, showing a TL pulse with speckled spatial profile.

Fig. 2
Fig. 2

(a) Geometrical sketch of focusing through a scattering surface (e.g. a diffuser). rs is a scattering point at the diffuser plane and ro is the distance from the optical axis at the observation plane. (b) Plot of the estimated pulse duration τpulse at the focal plane as function of ro, as expected from Eq. (4). (c) The result at the focal plane as seen by the naked eye: A broadband super-continuum source is focused through a diffusive piece of scotch-tape and a screen is placed at the focal plane. Near the optical axis, at the center of the image, the pulse is temporally undistorted, and the speckle contrast is high. Farther from center, the pulse is distorted, the different spectral contributions do not overlap and the speckle contrast lowers [11], as is visible by the ‘smeared’ speckle pattern [9].

Fig. 3
Fig. 3

Spatiotemporal characterization of the scattered field: (a) Experimental setup: utilizing a Michelson interferometer while imaging the two-photon fluorescence (2PF), spatially resolved autocorrelation is measured on the entire field simultaneously. (b) Map of the temporal 1 e width of the spatially resolved temporal autocorrelation; scale bar: 100μm. (c) Autocorrelation width as function of the distance from the optical axis: blue - experimental measurements, red - fit curve with two fit parameters according to Eq. (4).

Fig. 4
Fig. 4

Experimental results: 2PF intensity profile of the chirped unoptimized scattered field (a) and the optimized chirped scattered field (b), where the arrow marks the optimized point. Temporal autocorrelation width of the chirped unoptimized scattered field (c) and the optimized chirped scattered field (d), where the arrow marks the optimized point. scale bars: 100μm. All the 2PF intensity profiles are normalized to 1. Inset: optimized SLM pattern.

Equations (5)

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τ delay ( r s , r o ) = 1 c [ L ( r s , r o ) + L lens ( r s ) ]
τ spread ( r o ) = z c | 1 + ( r o z + tan φ ) 2 1 + ( r o z tan φ ) 2 |
τ spread ( r o ) = 2 r o tan φ c
τ total ( r o ) = τ 0 2 + τ spread 2
I 2 P F ( x , y ) I 2 ( x , y , y ) d t

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