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Delivering broadband light deep inside diffusive media

Nature Photonics volume 18, pages 744–750 (2024)Cite this article

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Abstract

Wavefront shaping enables the targeted delivery of coherent light into random-scattering media, such as biological tissue, by the constructive interference of scattered waves. However, broadband waves have short coherence times, weakening the interference effect. Here we introduce a broadband deposition matrix that identifies a single input wavefront that maximizes the broadband energy delivered to an extended target deep inside a diffusive system. We experimentally demonstrate that long-range spatial and spectral correlations result in sixfold energy enhancement for targets containing 1,700 speckle grains and located at a depth of up to ten transport mean free paths, even when the coherence time is an order of magnitude shorter than the diffusion dwell time of light in the scattering sample. In the broadband (fast decoherence) limit, enhancement of energy delivery to extended targets becomes nearly independent of the target depth and dissipation. Our experiments, numerical simulations and analytic theory establish the fundamental limit for broadband energy delivery deep into a diffusive system, which has important consequences for practical applications.

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Fig. 1: Illustration of the experimental platform.
Fig. 2: Targeted broadband energy delivery.
Fig. 3: Bandwidth dependence of targeted energy delivery.
Fig. 4: Depth dependence of broadband energy delivery.
Fig. 5: Effect of dissipation on energy delivery.

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Data availability

Source data are provided with this paper. All other data supporting the findings in this study are available from the corresponding author upon reasonable request.

References

  1. Mosk, A. P., Lagendijk, A., Lerosey, G. & Fink, M. Controlling waves in space and time for imaging and focusing in complex media. Nat. Photon. 6, 283–292 (2012).

    Article  ADS  Google Scholar 

  2. Rotter, S. & Gigan, S. Light fields in complex media: mesoscopic scattering meets wave control. Rev. Mod. Phys. 89, 015005 (2017).

    Article  ADS  Google Scholar 

  3. Cao, H., Mosk, A. P. & Rotter, S. Shaping the propagation of light in complex media. Nat. Phys. 18, 994–1007 (2022).

    Article  ADS  Google Scholar 

  4. Vellekoop, I. M. & Mosk, A. P. Focusing coherent light through opaque strongly scattering media. Opt. Lett. 32, 2309–2311 (2007).

    Article  ADS  Google Scholar 

  5. Yaqoob, Z., Psaltis, D., Feld, M. S. & Yang, C. Optical phase conjugation for turbidity suppression in biological samples. Nat. Photon. 2, 110–115 (2008).

    Article  ADS  Google Scholar 

  6. Vellekoop, I. M., van Putten, E. G., Lagendijk, A. & Mosk, A. P. Demixing light paths inside disordered metamaterials. Opt. Express 16, 67–80 (2008).

    Article  ADS  Google Scholar 

  7. Xu, X., Liu, H. & Wang, L. V. Time-reversed ultrasonically encoded optical focusing into scattering media. Nat. Photon. 5, 154–157 (2011).

    Article  ADS  Google Scholar 

  8. Judkewitz, B., Wang, Y. M., Horstmeyer, R., Mathy, A. & Yang, C. Speckle-scale focusing in the diffusive regime with time reversal of variance-encoded light (TROVE). Nat. Photon. 7, 300–305 (2013).

    Article  ADS  Google Scholar 

  9. Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nat. Photon. 9, 563–571 (2015).

    Article  ADS  Google Scholar 

  10. Vellekoop, I. M. Feedback-based wavefront shaping. Opt. Express 23, 12189–12206 (2015).

    Article  ADS  Google Scholar 

  11. Vellekoop, I. M. & Mosk, A. P. Universal optimal transmission of light through disordered materials. Phys. Rev. Lett. 101, 120601 (2008).

    Article  ADS  Google Scholar 

  12. 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).

    Article  ADS  Google Scholar 

  13. Choi, W., Mosk, A. P., Park, Q. H. & Choi, W. Transmission eigenchannels in a disordered medium. Phys. Rev. B 83, 134207 (2011).

    Article  ADS  Google Scholar 

  14. Kim, M. et al. Maximal energy transport through disordered media with the implementation of transmission eigenchannels. Nat. Photon. 6, 581–585 (2012).

    Article  ADS  Google Scholar 

  15. Yu, H. et al. Measuring large optical transmission matrices of disordered media. Phys. Rev. Lett. 111, 153902 (2013).

    Article  ADS  Google Scholar 

  16. Popoff, S. M., Goetschy, A., Liew, S. F., Stone, A. D. & Cao, H. Coherent control of total transmission of light through disordered media. Phys. Rev. Lett. 112, 133903 (2014).

    Article  ADS  Google Scholar 

  17. Gérardin, B., Laurent, J., Derode, A., Prada, C. & Aubry, A. Full transmission and reflection of waves propagating through a maze of disorder. Phys. Rev. Lett. 113, 173901 (2014).

    Article  ADS  Google Scholar 

  18. Davy, M., Shi, Z., Park, J., Tian, C. & Genack, A. Z. Universal structure of transmission eigenchannels inside opaque media. Nat. Commun. 6, 6893 (2015).

    Article  ADS  Google Scholar 

  19. Hsu, C. W., Liew, S. F., Goetschy, A., Cao, H. & Stone, A. D. Correlation-enhanced control of wave focusing in disordered media. Nat. Phys. 13, 497–502 (2017).

    Article  Google Scholar 

  20. Yılmaz, H., Hsu, C. W., Yamilov, A. & Cao, H. Transverse localization of transmission eigenchannels. Nat. Photon. 13, 352–358 (2019).

    Article  ADS  Google Scholar 

  21. Bender, N., Yamilov, A., Yılmaz, H. & Cao, H. Fluctuations and correlations of transmission eigenchannels in diffusive media. Phys. Rev. Lett. 125, 165901 (2020).

    Article  ADS  Google Scholar 

  22. 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, 12283–12290 (2010).

    Article  ADS  Google Scholar 

  23. Choi, Y. et al. Measurement of the time-resolved reflection matrix for enhancing light energy delivery into a scattering medium. Phys. Rev. Lett. 111, 243901 (2013).

    Article  ADS  Google Scholar 

  24. Cheng, X. & Genack, A. Z. Focusing and energy deposition inside random media. Opt. Lett. 39, 6324–6327 (2014).

    Article  ADS  Google Scholar 

  25. Chaigne, T. et al. Controlling light in scattering media non-invasively using the photoacoustic transmission matrix. Nat. Photon. 8, 58–64 (2014).

    Article  ADS  Google Scholar 

  26. Liu, Y. et al. Optical focusing deep inside dynamic scattering media with near-infrared time-reversed ultrasonically encoded (true) light. Nat. Commun. 6, 5904 (2015).

    Article  ADS  Google Scholar 

  27. Sarma, R., Yamilov, A. G., Petrenko, S., Bromberg, Y. & Cao, H. Control of energy density inside a disordered medium by coupling to open or closed channels. Phys. Rev. Lett. 117, 086803 (2016).

    Article  ADS  Google Scholar 

  28. Badon, A. et al. Smart optical coherence tomography for ultra-deep imaging through highly scattering media. Sci. Adv. 2, e1600370 (2016).

    Article  ADS  Google Scholar 

  29. Jeong, S. et al. Focusing of light energy inside a scattering medium by controlling the time-gated multiple light scattering. Nat. Photon. 12, 277–283 (2018).

    Article  ADS  Google Scholar 

  30. Katz, O., Ramaz, F., Gigan, S. & Fink, M. Controlling light in complex media beyond the acoustic diffraction-limit using the acousto-optic transmission matrix. Nat. Commun. 10, 717 (2019).

    Article  ADS  Google Scholar 

  31. Durand, M., Popoff, S. M., Carminati, R. & Goetschy, A. Optimizing light storage in scattering media with the dwell-time operator. Phys. Rev. Lett. 123, 243901 (2019).

    Article  ADS  Google Scholar 

  32. Boniface, A., Blochet, B., Dong, J. & Gigan, S. Noninvasive light focusing in scattering media using speckle variance optimization. Optica 6, 1381–1385 (2019).

    Article  ADS  Google Scholar 

  33. Horodynski, M. et al. Optimal wave fields for micromanipulation in complex scattering environments. Nat. Photon. 14, 149–153 (2020).

    Article  ADS  Google Scholar 

  34. Yang, J. et al. Focusing light inside live tissue using reversibly switchable bacterial phytochrome as a genetically encoded photochromic guide star. Sci. Adv. 5, eaay1211 (2019).

    Article  ADS  Google Scholar 

  35. Boniface, A., Dong, J. & Gigan, S. Non-invasive focusing and imaging in scattering media with a fluorescence-based transmission matrix. Nat. Commun. 11, 6154 (2020).

    Article  ADS  Google Scholar 

  36. Lambert, W., Cobus, L. A., Frappart, T., Fink, M. & Aubry, A. Distortion matrix approach for ultrasound imaging of random scattering media. Proc. Natl Acad. Sci. USA 117, 14645–14656 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  37. Badon, A. et al. Distortion matrix concept for deep optical imaging in scattering media. Sci. Adv. 6, eaay7170 (2020).

    Article  ADS  Google Scholar 

  38. Bouchet, D., Rotter, S. & Mosk, A. P. Maximum information states for coherent scattering measurements. Nat. Phys. 17, 564–568 (2021).

    Article  Google Scholar 

  39. Lee, Y.-R. et al. Wave propagation dynamics inside a complex scattering medium by the temporal control of backscattered waves. Optica 10, 569–577 (2023).

    Article  Google Scholar 

  40. Bender, N. et al. Depth-targeted energy delivery deep inside scattering media. Nat. Phys. 18, 309–315 (2022).

    Article  Google Scholar 

  41. van Beijnum, F., van Putten, E. G., Lagendijk, A. & Mosk, A. P. Frequency bandwidth of light focused through turbid media. Opt. Lett. 36, 373–375 (2011).

    Article  ADS  Google Scholar 

  42. Paudel, H. P., Stockbridge, C., Mertz, J. & Bifano, T. Focusing polychromatic light through strongly scattering media. Opt. Express 21, 17299–17308 (2013).

    Article  ADS  Google Scholar 

  43. Andreoli, D. et al. Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix. Sci. Rep. 5, 10347 (2015).

    Article  ADS  Google Scholar 

  44. Mounaix, M. et al. Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix. Phys. Rev. Lett. 116, 253901 (2016).

    Article  ADS  Google Scholar 

  45. Mounaix, M., de Aguiar, H. B. & Gigan, S. Temporal recompression through a scattering medium via a broadband transmission matrix. Optica 4, 1289–1292 (2017).

    Article  ADS  Google Scholar 

  46. Hsu, C. W., Goetschy, A., Bromberg, Y., Stone, A. D. & Cao, H. Broadband coherent enhancement of transmission and absorption in disordered media. Phys. Rev. Lett. 115, 223901 (2015).

    Article  ADS  Google Scholar 

  47. Liew, S. F., Popoff, S. M., Mosk, A. P., Vos, W. L. & Cao, H. Transmission channels for light in absorbing random media: from diffusive to ballistic-like transport. Phys. Rev. B 89, 224202 (2014).

    Article  ADS  Google Scholar 

  48. Liew, S. F. & Cao, H. Modification of light transmission channels by inhomogeneous absorption in random media. Opt. Express 23, 11043–11053 (2015).

    Article  ADS  Google Scholar 

  49. Sarma, R., Yamilov, A., Liew, S. F., Guy, M. & Cao, H. Control of mesoscopic transport by modifying transmission channels in opaque media. Phys. Rev. B 92, 214206 (2015).

    Article  ADS  Google Scholar 

  50. Yamilov, A., Petrenko, S., Sarma, R. & Cao, H. Shape dependence of transmission, reflection, and absorption eigenvalue densities in disordered waveguides with dissipation. Phys. Rev. B 93, 100201 (2016).

    Article  ADS  Google Scholar 

  51. Sarma, R., Yamilov, A., Neupane, P. & Cao, H. Using geometry to manipulate long-range correlation of light inside disordered media. Phys. Rev. B 92, 180203 (2015).

    Article  ADS  Google Scholar 

  52. Stephen, M. J. & Cwilich, G. Intensity correlation functions and fluctuations in light scattered from a random medium. Phys. Rev. Lett. 59, 285 (1987).

    Article  ADS  Google Scholar 

  53. Berkovits, R. & Feng, S. Correlations in coherent multiple scattering. Phys. Rep. 238, 135–172 (1994).

    Article  ADS  Google Scholar 

  54. Groth, C. W., Wimmer, M., Akhmerov, A. R. & Waintal, X. Kwant: a software package for quantum transport. New J. Phys. 16, 063065 (2014).

    Article  ADS  Google Scholar 

  55. Goetschy, A. & Stone, A. D. Filtering random matrices: the effect of incomplete channel control in multiple scattering. Phys. Rev. Lett. 111, 063901 (2013).

    Article  ADS  Google Scholar 

  56. Yamilov, A. G. et al. Position-dependent diffusion of light in disordered waveguides. Phys. Rev. Lett. 112, 023904 (2014).

    Article  ADS  Google Scholar 

  57. Hong, P., Ojambati, O. S., Lagendijk, A., Mosk, A. P. & Vos, W. L. Three-dimensional spatially resolved optical energy density enhanced by wavefront shaping. Optica 5, 844–849 (2018).

    Article  ADS  Google Scholar 

  58. Uppu, R., Adhikary, M., Harteveld, C. A. & Vos, W. L. Spatially shaping waves to penetrate deep inside a forbidden gap. Phys. Rev. Lett. 126, 177402 (2021).

    Article  ADS  Google Scholar 

  59. Yu, H. et al. Recent advances in wavefront shaping techniques for biomedical applications. Curr. Appl. Phys. 15, 632–641 (2015).

    Article  ADS  Google Scholar 

  60. Yoon, S. et al. Deep optical imaging within complex scattering media. Nat. Rev. Phys. 2, 141–158 (2020).

    Article  Google Scholar 

  61. Fenno, L., Yizhar, O. & Deisseroth, K. The development and application of optogenetics. Annu. Rev. Neurosci. 34, 389–412 (2011).

    Article  Google Scholar 

  62. Yoon, J. et al. Optogenetic control of cell signaling pathway through scattering skull using wavefront shaping. Sci. Rep. 5, 13289 (2015).

    Article  ADS  Google Scholar 

  63. Pégard, N. C. et al. Three-dimensional scanless holographic optogenetics with temporal focusing (3D-SHOT). Nat. Commun. 8, 1228 (2017).

    Article  ADS  Google Scholar 

  64. Ruan, H. et al. Deep tissue optical focusing and optogenetic modulation with time-reversed ultrasonically encoded light. Sci. Adv. 3, eaao5520 (2017).

    Article  Google Scholar 

  65. Yanik, M. F. et al. Neurosurgery: functional regeneration after laser axotomy. Nature 432, 822 (2004).

    Article  ADS  Google Scholar 

  66. Pernot, M. et al. In vivo transcranial brain surgery with an ultrasonic time reversal mirror. J. Neurosurg. 106, 1061–1066 (2007).

    Article  Google Scholar 

  67. Bender, N. et al. Coherent enhancement of optical remission in diffusive media. Proc. Natl Acad. Sci. USA 119, e2207089119 (2022).

    Article  Google Scholar 

  68. Srivastava, A. & Klassen, E. Monte Carlo extrinsic estimators of manifold-valued parameters. IEEE Trans. Signal Process. 50, 299–308 (2002).

    Article  Google Scholar 

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Acknowledgements

We thank C.-W. Chen, K. Kim, S. Han, L. Shaughnessy, P. Miao, S. Halladay and Z. Lai for valuable discussions. This work is supported partly by the National Science Foundation (NSF) under grant nos. DMR-1905465 (R.M. and H.C.) and no. DMR-1905442 (A.Y.) and the Office of Naval Research (ONR) under grant no. N00014-221-1-2026 (H.C.). It has also received support under the program Investissements d’Avenir launched by the French Government (A.G.).

Author information

Authors and Affiliations

  1. Department of Physics, Yale University, New Haven, CT, USA

    Rohin McIntosh

  2. Institut Langevin, ESPCI Paris, PSL University, CNRS, Paris, France

    Arthur Goetschy

  3. School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA

    Nicholas Bender

  4. Physics Department, Missouri University of Science & Technology, Rolla, MO, USA

    Alexey Yamilov

  5. Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA

    Chia Wei Hsu

  6. Institute of Materials Science and Nanotechnology, National Nanotechnology Research Center (UNAM), Bilkent University, Ankara, Turkey

    Hasan Yılmaz

  7. Department of Applied Physics, Yale University, New Haven, CT, USA

    Hui Cao

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  1. Rohin McIntosh
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Contributions

R.M. and N.B. performed the experiments. R.M. analysed the data. N.B. fabricated the samples. A.G. developed the analytic theory. C.W.H. contributed to the theoretical analysis. H.Y. contributed to the experimental analysis. R.M. and A.Y. performed the numerical simulations. H.C. initiated the project and supervised the research. All authors contributed to the interpretation of the results. R.M. and A.G. prepared the paper, H.C. edited it and all authors provided feedback.

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Correspondence to Hui Cao.

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Nature Photonics thanks Jacopo Bertolotti, Roarke Horstmeyer and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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McIntosh, R., Goetschy, A., Bender, N. et al. Delivering broadband light deep inside diffusive media. Nat. Photon. 18, 744–750 (2024). https://doi.org/10.1038/s41566-024-01446-7

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