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Delivering broadband light deep inside diffusive media

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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.

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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.).

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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. (2024). https://doi.org/10.1038/s41566-024-01446-7

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