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Anderson localization of electromagnetic waves in three dimensions

Nature Physics volume 19, pages 1308–1313 (2023)Cite this article

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Abstract

Anderson localization is a halt of diffusive wave propagation in disordered systems. Despite extensive studies over the past 40 years, Anderson localization of light in three dimensions has remained elusive, leading to the question of its very existence. Recent advances have enabled finite-difference time-domain calculations to be sped up by orders of magnitude, allowing us to conduct brute-force numerical simulations of light transport in fully disordered three-dimensional systems with unprecedented dimension and refractive index difference. We show numerically three-dimensional localization of vector electromagnetic waves in random aggregates of overlapping metallic spheres, in sharp contrast to the absence of localization for dielectric spheres with a refractive index up to 10 in air. Our work opens a wide range of avenues in both fundamental research related to Anderson localization and potential applications using three-dimensional localized light.

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Fig. 1: Absence of non-diffusive transport in random dielectric systems with a refractive index of 3.5.
Fig. 2: AL of light in 3D disordered PEC.
Fig. 3: The transition from diffusion to AL in 3D disordered PEC.
Fig. 4: Arrest of transverse spreading of transmitted beam in 3D localized PEC systems.

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Data availability

Figures reported in this work, containing the source data, are available via download from https://scholarsmine.mst.edu/phys_facwork/2259/. All other data that support the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

The simulation project and associated codes can be found at https://www.flexcompute.com/userprojects/anderson-localization-of-electromagnetic-waves-in-three-dimensions. A Tidy3D software license can be requested from Flexcompute Inc to reproduce simulation results.

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Acknowledgements

This work is supported by the National Science Foundation under grant nos. DMR-1905442 and DMR-1905465 and the Office of Naval Research (ONR) under grant no. N00014-20-1-2197. We thank S. Fan and B. van Tiggelen for enlightening discussions. A.Y. expresses gratitude to LPMMC (CNRS) for hospitality.

Author information

Authors and Affiliations

  1. Physics Department, Missouri University of Science and Technology, Rolla, MO, USA

    Alexey Yamilov

  2. Univ. Grenoble Alpes, CNRS, LPMMC, Grenoble, France

    Sergey E. Skipetrov

  3. Flexcompute Inc, Belmont, MA, USA

    Tyler W. Hughes & Momchil Minkov

  4. Department of Electrical and Computer Engineering, University of Wisconsin, Madison, WI, USA

    Zongfu Yu

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

    Hui Cao

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Contributions

A.Y. performed numerical simulations, analysed the data and compiled all results. S.E.S. conducted theoretical study and guided data interpretation. T.W.H. and M.M. implemented the hardware-accelerated FDTD method and aided in the setup of the numerical simulations. Z.Y. and H.C. initiated this project and supervised the research. A.Y. wrote the first draft, S.E.S. and H.C. revised the content and scope, and T.W.H., M.M. and Z.Y. edited the manuscript. All co-authors discussed and approved the content.

Corresponding authors

Correspondence to Alexey Yamilov, Zongfu Yu or Hui Cao.

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Competing interests

T.W.H., M.M. and Z.Y. have financial interest in Flexcompute Inc., which develops the software Tidy3D used in this work.

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Nature Physics thanks Luis Froufe-Pérez, Diederik Wiersma and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary material, Table 1, Figs. 1–20 and Videos 1−6.

Supplementary Video 1

Variation of the x–z cross section of intensity inside f = 15% PEC aggregate with wavelength.

Supplementary Video 2

Variation of the x–z cross section of intensity inside f = 48% PEC aggregate with wavelength.

Supplementary Video 3

Transverse spreading of transmitted beam in n = 3.5, f = 29% dielectric aggregate with time.

Supplementary Video 4

Transverse spreading of transmitted beam in f = 15% PEC aggregate with time.

Supplementary Video 5

Halt of transverse spreading of transmitted beam in f = 48% PEC aggregate with time.

Supplementary Video 6

3D localized mode in disordered PEC slab with f = 33%.

Source data

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Source Data Fig. 2

Source data for Fig. 2.

Source Data Fig. 3

Source data for Fig. 3.

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Yamilov, A., Skipetrov, S.E., Hughes, T.W. et al. Anderson localization of electromagnetic waves in three dimensions. Nat. Phys. 19, 1308–1313 (2023). https://doi.org/10.1038/s41567-023-02091-7

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