Transverse localization of transmission eigenchannels


Transmission eigenchannels are building blocks of coherent wave transport in diffusive media, and selective excitation of individual eigenchannels can lead to diverse transport behaviour. An essential yet poorly understood property is the transverse spatial profile of each eigenchannel, which is relevant for the associated energy density and critical for coupling light into and out of it. Here, we discover that the transmission eigenchannels of a disordered slab possess exponentially localized incident and outgoing profiles, even in the diffusive regime far from Anderson localization. Such transverse localization arises from a combination of reciprocity, local coupling of spatial modes and non-local correlations of scattered waves. Experimentally, we observe signatures of such localization even with finite illumination area. The transverse localization of high-transmission channels enhances optical energy densities inside turbid media, which will be important for light–matter interactions and imaging applications.

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Fig. 1: Transverse localization of transmission eigenchannels.
Fig. 2: Bandedness of the real-space transmission matrix.
Fig. 3: Scaling of the asymptotic channel width in diffusive slabs.
Fig. 4: Experimental signatures of transverse localization for high-transmission channels.
Fig. 5: Modification of transmission eigenchannel widths by incomplete control.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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We thank A. Mosk, A. Genack, B. Shapiro, F. Scheffold, S. Skipetrov, S. Bittner, S. Rotter and T. Kottos for stimulating discussions and useful feedback. We acknowledge financial support by the Office of Naval Research (ONR) under grant no. MURI N00014-13-0649 and by the US–Israel Binational Science Foundation (BSF) under grant no. 2015509, as well as computational resources provided by the Yale High Performance Computing Cluster (Yale HPC).

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H.Y. performed the experiments and analysed the data. C.W.H. performed the numerical simulations and fabricated the samples. H.Y. analysed the numerical data. C.W.H. helped with experimental data acquisition and contributed to numerical data analysis. H.C. supervised the project. All authors contributed to the interpretation of the results. H.Y. and C.W.H. prepared the manuscript, H.C. edited it and A.Y. provided feedback.

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Correspondence to Hui Cao.

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Yılmaz, H., Hsu, C.W., Yamilov, A. et al. Transverse localization of transmission eigenchannels. Nat. Photonics 13, 352–358 (2019).

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