Focusing and compression of ultrashort pulses through scattering media

Journal name:
Nature Photonics
Year published:
Published online


Light scattering in inhomogeneous media induces wavefront distortions that pose an inherent limitation in many optical applications. Examples where this occurs include microscopy, nanosurgery and astronomy. In recent years, ongoing efforts have made the correction of spatial distortions possible using wavefront-shaping techniques. However, when ultrashort pulses are used, scattering also induces temporal distortions, which hinder the use of such pulses in nonlinear processes such as multiphoton microscopy and quantum control experiments. Here, we show that correction of both spatial and temporal distortions can be achieved by manipulating only the spatial degrees of freedom of the incident wavefront. By optimizing a nonlinear signal, we demonstrate spatiotemporal focusing and compression of chirped ultrashort pulses through scattering media, and refocusing in both space and time of 100 fs pulses through thick brain and bone samples. Our results open up new possibilities for optical manipulation and nonlinear imaging in scattering media.

At a glance


  1. Spatiotemporal focusing by optimizing 2PF: spatial characterization.
    Figure 1: Spatiotemporal focusing by optimizing 2PF: spatial characterization.

    a, Experimental set-up. An ultrashort pulse is focused to a 2PF screen placed behind a scattering medium. An SLM controls the incident wavefront, optimizing the 2PF at a selected point imaged by an EMCCD (F-bandpass filter). b,c, 2PF images before (b) and after (c) optimization at the optimized plane (xy). d,e, Depth-resolved 2PF images before (d) and after (e) optimization, showing the axial (z) confinement of the optimized 2PF. The localized 2PF enhancement is estimated to be ~800. Scale bars, 25 µm. Rendered xyz field in d and e is 190 × 190 × 400 µm.

  2. Spatiotemporal characterization of the scattered and optimized fields shown in Fig. 1, demonstrating pulse compression by spatial wavefront shaping.
    Figure 2: Spatiotemporal characterization of the scattered and optimized fields shown in Fig. 1, demonstrating pulse compression by spatial wavefront shaping.

    a, Experimental set-up. Using a Michelson interferometer, spatially resolved autocorrelation is measured on the entire field simultaneously by imaging the 2PF at different delays τ. The pulse is pre-chirped by a glass slab to demonstrate temporal compression. b,c, Maps of the temporal 1/e width of the spatially resolved, background-subtracted autocorrelation, before (b) and after (c) optimization, showing temporal compression at the optimization point. Scale bars, 25 µm. d, Measured fringe-averaged, background-subtracted autocorrelation of the chirped input pulse (red; 1/e width, 715 fs), the non-optimized scattered pulse (green; 1/e width, 875 fs), the optimized pulse (blue; 1/e width, 370 fs), and the transform-limited pulse (dashed-black; 1/e width, 230 fs). e,f, Spatiotemporal renderings of the measured autocorrelations in the non-optimized (e) and optimized (f) cases (Supplementary Video 1). Dashed green and blue lines in e and f are the locations of autocorrelations plotted in corresponding colours in d. Rendered spatiotemporal volume, 200 µm × 200 µm × 2,200 fs.

  3. Mechanism for temporal compression using only spatial degrees of freedom and random scattering.
    Figure 3: Mechanism for temporal compression using only spatial degrees of freedom and random scattering.

    a,b, Much like a Fourier (frequency domain) pulse shaper32 (a), where the pixels of the SLM are coupled to the spectral degrees of freedom by scattering from a grating; coherent scattering in a random medium (b) couples each SLM pixel to a different linear combination of the spectral (also temporal) degrees of freedom, forming a new random spectral basis that is phase-controlled by the SLM. In both cases, the maximum controllable delay τmax dictates the shaping spectral resolution Δf = 1/τmax, and is determined by the optical path lengths differences in the medium/shaper.

  4. Refocusing 100 fs TL pulses through 1-mm-thick brain tissue.
    Figure 4: Refocusing 100 fs TL pulses through 1-mm-thick brain tissue.

    a,b, Two-photon fluorescence (2PF) before (a) and after (b) optimization, showing a 30-fold increase in 2PF. The 2PF image before optimization is shown with a ×10 display gain. Scale bars, 15 µm. c, Spatially resolved fringe-averaged, background-subtracted autocorrelation of the initial non-optimized pulse at the centre (blue) and top right corner (green) of the field, both with FWHM = 180 ± 10 fs, and autocorrelation of the optimized pulse (red, FWHM = 170 fs). The optimized pulse autocorrelation is identical to the TL pulse (Fig. 2d). Inset: SLM phase pattern used to generate the corrected optimized spot.

  5. Spatiotemporal refocusing of 100 fs pulses through 500-[micro]m-thick bone sample.
    Figure 5: Spatiotemporal refocusing of 100 fs pulses through 500-µm-thick bone sample.

    a,b, Imaged 2PF before (a) and after (b) optimization. c,d, Spatially resolved 1/e2 width of the background-subtracted autocorrelation for the initial non-optimized (c) and optimized (d) fields. Scale bars, 10 µm. e, Measured fringe-averaged, background-subtracted 2PF autocorrelation of the non-optimized scattered pulse (blue; 1/e width, 315 fs), the optimized pulse (red; 1/e width, 250 fs) and the TL pulse (dashed black; 1/e width, 230 fs). Inset: transmission microscope image of the bone sample surface. Scale bar, 100 µm.


  1. Sebbah, P. Waves and Imaging Through Complex Media (Kluwer Academic Publishers, 2001).
  2. Goodman, J. W. Speckle Phenomena in Optics: Theory and Applications (Roberts & Co., 2007).
  3. Tal, E. & Silberberg, Y. Transformation from an ultrashort pulse to a spatiotemporal speckle by a thin scattering surface. Opt. Lett. 31, 35293531 (2006).
  4. Bruce, N. C. et al. Investigation of the temporal spread of an ultrashort light pulse on transmission through a highly scattering medium. Appl. Opt. 34, 58235828 (1995).
  5. Webster, M. A., Gerke, T. D., Weiner, A. M. & Webb, K. J. Spectral and temporal speckle field measurements of a random medium. Opt. Lett. 29, 14911493 (2004).
  6. Johnson, P. M. et al. Time-resolved pulse propagation in a strongly scattering material. Phys. Rev. E 68, 016604 (2003).
  7. Szmacinski, H., Gryczynski, I. & Lakowicz, J. R. Spatially localized ballistic two-photon excitation in scattering media. Biospectroscopy 4, 303310 (1998).
  8. Dela Cruz, J. M., Pastirk, I., Comstock, M., Lozovoy, V. V. & Dantus, M. Use of coherent control methods through scattering biological tissue to achieve functional imaging. Proc. Natl Acad. Sci. USA 101, 1699617001 (2004).
  9. Tyson, R. K. Principles of Adaptive Optics 2nd edn (Academic Press, 1998).
  10. Nature Photon. Technology focus: Adaptive optics. Nature Photon. 5, 1528 (2011).
  11. Booth, M. J. Adaptive optics in microscopy. Phil.Trans. R. Soc. A 365, 28292843 (2007).
  12. Rueckel, M., Mack-Bucher, J. A. & Denk, W. Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing. Proc. Natl Acad. Sci. USA 103, 1713717142 (2006).
  13. Vellekoop, I. M. & Mosk, A. P. Focusing coherent light through opaque strongly scattering media. Opt. Lett. 32, 23092311 (2007).
  14. Vellekoop, I. M., van Putten, E. G., Lagendijk, A. & Mosk, A. P. Demixing light paths inside disordered metamaterials. Opt. Express 16, 6780 (2008).
  15. Vellekoop, I. M., Lagendijk, A. & Mosk, A. P. Exploiting disorder for perfect focusing. Nature Photon. 4, 320322 (2010).
  16. Vellekoop, I. M. & Aegerter, C. M. Scattered light fluorescence microscopy: imaging through turbid layers. Opt. Lett. 35, 12451247 (2010).
  17. Popoff, S. M. et al. Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media. Phys. Rev. Lett. 104, 100601 (2010).
  18. Popoff, S., Lerosey, G., Fink, M., Boccara, A. C. & Gigan, S. Image transmission through an opaque material. Nature Commun. 1, 81. doi:10.1038/ncomms1078 (2010).
  19. Čižmár, T., Mazilu, M. & Dholakia, K. In situ wavefront correction and its application to micromanipulation. Nature Photon. 4, 388394 (2010).
  20. Yaqoob, Z., Psaltis, D., Feld, M. S. & Yang, C. Optical phase conjugation for turbidity suppression in biological samples. Nature Photon. 2, 110115 (2008).
  21. Denk, W., Strickler, J. H. & Webb, W. W. Two-photon laser scanning fluorescence microscopy. Science 248, 7376 (1990).
  22. Oheim, M., Beaurepaire, E., Chaigneau, E., Mertz, J. & Charpak, S. Two-photon microscopy in brain tissue: parameters influencing the imaging depth. J. Neurosci. Methods 111, 2937 (2001).
  23. Rabitz, H., de Vivie-Riedle, R., Motzkus, M. & Kompa, K. Whither the future of controlling quantum phenomena? Science 288, 824828 (2000).
  24. Assion, A. et al. Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses Science 30, 919922 (1998).
  25. Pearson, B. J., White, J. L., Weinacht, T. C. & Bucksbaum, P. H. Coherent control using adaptive learning algorithms. Phys. Rev. A 63, 063412 (2001).
  26. Stockman, M. I., Faleev, S. V. & Bergman, D. J. Coherent control of femtosecond energy localization in nanosystems. Phys. Rev. Lett. 88, 067402 (2002).
  27. Aeschlimann, M. et al. Adaptive subwavelength control of nano-optical fields. Nature 446, 301304 (2007).
  28. Oron, D., Dudovich, N. & Silberberg, Y. All-optical processing in coherent nonlinear spectroscopy. Phys. Rev. A 70, 023415 (2004).
  29. Fink, M. Time reversed acoustics. Phys. Today 50, 3440 (1997).
  30. Lerosey, G. et al. Time reversal of electromagnetic waves. Phys. Rev. Lett. 92, 193904 (2004).
  31. Derode, A. et al. Taking advantage of multiple scattering to communicate with time-reversal antennas. Phys. Rev. Lett. 90, 014301 (2003).
  32. Weiner, A. M. Femtosecond pulse shaping using spatial light modulators. Rev. Sci. Instrum. 71, 19291960 (2000).
  33. McCabe, D. J. et al. Shaping speckles: spatio-temporal focussing of an ultrafast pulse through a multiply scattering medium. arXiv:1101.0976 (2011).
  34. Jiang, Y., Narushima, T. & Okamoto, H. Nonlinear optical effects in trapping nanoparticles with femtosecond pulses. Nature Phys. 6, 10051009 (2010).
  35. Andrasfalvy, B. K., Zemelman, B. V., Tang, J. & Vaziri, A. Two-photon single-cell optogenetic control of neuronal activity by sculpted light. Proc. Natl Acad. Sci. USA 107, 1198111986 (2010).
  36. Vellekoop, I. M. & Mosk, A. P. Phase control algorithms for focusing light through turbid media. Opt. Commun. 281, 30713080 (2008).
  37. Diels, J. C., Fontaine, J. J., McMichael, I. C. & Simoni, F. Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy. Appl. Opt. 24, 12701282 (1985).
  38. Yelin, D., Meshulach, D. & Silberberg, Y. Adaptive femtosecond pulse compression. Opt. Lett. 22, 17931795 (1997).
  39. Lemoult, F., Lerosey, G., de Rosny, J. & Fink, M. Manipulating spatiotemporal degrees of freedom of waves in random media. Phys. Rev. Lett. 103, 173902 (2009).
  40. Aulbach, J., Gjonaj, B., Johnson, P. M., Mosk, A. P. & Lagendijk, A. Control of light transmission through opaque scattering media in space and time. Phys. Rev. Lett. 106, 103901 (2011).
  41. Small, E., Katz, O., Eshel, Y., Silberberg, Y. & Oron, D. Spatio-temporal X-wave. Opt. Express 17, 1865918668 (2009).
  42. Oron, D., Tal, E. & Silberberg, Y. Scanningless depth-resolved microscopy. Opt. Express 13, 14681476 (2005).
  43. Wilt, B. A. et al. Advances in light microscopy for neuroscience. Annu. Rev. Neurosci. 32, 435506 (2009).
  44. Cui, M. A high speed wavefront determination method based on spatial frequency modulations for focusing light through random scattering media. Opt. Express 19, 29892995 (2011).
  45. Hsieh, C.-L., Pu, Y., Grange, R. & Psaltis, D. Digital phase conjugation of second harmonic radiation emitted by nanoparticles in turbid media. Opt. Express 18, 1228312290 (2010).

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  1. Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel

    • Ori Katz,
    • Eran Small,
    • Yaron Bromberg &
    • Yaron Silberberg


O.K. conceived the idea. O.K., Y.B., E.S. and Y.S. designed the experiments. O.K., E.S. and Y.B. performed the experiments, analysed the data and carried out numerical simulations. All authors contributed to the writing of the paper.

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