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arxiv: 2312.14393 · v5 · submitted 2023-12-22 · ⚛️ physics.optics · physics.comp-ph

3D Anderson localization of light in disordered systems of dielectric particles

Yevgen Grynko , Dustin Siebert , Jan Sperling , Jens F\"orstner This is my paper

Pith reviewed 2026-05-24 05:09 UTC · model grok-4.3

classification ⚛️ physics.optics physics.comp-ph
keywords Anderson localizationlight transportdisordered mediadielectric particles3D localizationThouless conductancefull-wave simulationsnon-exponential decay
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The pith

Large-scale simulations of light in 3D disordered dielectric particles show a transition to non-exponential transmission decay, isolated resonances with Thouless conductance below 1, and static near-field hotspots as disorder increases.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper runs full-wave simulations of light transport through three-dimensional collections of irregular high-index dielectric particles. For particles with size parameter kr approximately 1, raising the disorder strength changes the transport from ordinary diffusion to a regime where time-resolved transmission decays non-exponentially and the effective diffusion coefficient falls toward a t to the minus 1 scaling at long times. The same parameter window also produces spectrally narrow transmission resonances whose Thouless conductance drops below unity and near-field patterns that evolve into fixed clusters of intensity hotspots rather than propagating waves. These three independent signatures together are presented as numerical evidence that Anderson localization has set in.

Core claim

In three-dimensional disordered media composed of irregular dielectric particles with kr approximately 1 and high refractive-index contrast, increasing disorder produces non-exponential decay of time-resolved transmission, a time-dependent diffusion coefficient that approaches t^{-1} scaling, spectrally isolated resonances with Thouless conductance below unity, and late-time near-field maps consisting of non-propagating intensity hotspots; the transport, spectral, and near-field features are offered as consistent evidence for Anderson localization of light.

What carries the argument

The joint appearance of non-exponential transport decay, Thouless conductance g less than 1 resonances, and static near-field intensity hotspots as disorder is increased.

If this is right

  • Transport crosses from diffusion to a localized regime once disorder exceeds a threshold set by the particle parameters.
  • Long-lived modes with weak spectral overlap come to dominate transmission at late times.
  • Intensity becomes trapped in non-propagating spatial clusters rather than continuing to spread.
  • The transition requires subwavelength particles with kr near 1 and high dielectric contrast.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the signatures hold, optical experiments could target the same particle size and contrast window to attempt direct observation of 3D Anderson localization.
  • The results suggest that irregular particle shapes and finite-size effects do not prevent localization when the size parameter is near unity.
  • Similar joint transport-spectral-near-field diagnostics could be applied to other classical wave systems such as acoustics or microwaves in disordered dielectrics.

Load-bearing premise

The chosen particle size, index contrast, and finite simulation volumes produce signatures that unambiguously indicate Anderson localization rather than other slow-transport regimes or numerical artifacts.

What would settle it

Observation of purely exponential transmission decay persisting to long times, or propagating wave fronts in the near-field maps, under the same kr approximately 1 and high-contrast conditions would contradict the localization interpretation.

Figures

Figures reproduced from arXiv: 2312.14393 by Dustin Siebert, Jan Sperling, Jens F\"orstner, Yevgen Grynko.

Figure 1
Figure 1. Figure 1: FIG. 1. Propagation of a continuous, focused beam through [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) A layer of 19000 irregular particles packed with [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Simulation results for layers with different volume [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Normalized transmission of a short pulse through [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

We investigate light transport in three-dimensional disordered media composed of irregular dielectric particles using large scale full-wave simulations. For subwavelength particles with size parameter $kr \approx 1$ and high refractive index contrast, we observe a transition from diffusion to a regime characterized by non-exponential decay of time-resolved transmission as disorder increases. The corresponding time-dependent diffusion coefficient decreases with time and approaches a $t^{-1}$ scaling at long times. This dynamical slowdown is accompanied by the emergence of spectrally isolated transmission resonances with Thouless conductance below unity, indicating the dominance of long-lived modes with weak spectral overlap. The late time near-field maps reveal evolving, non-propagating clusters of intensity hotspots. Together, the transport, spectral, and near-field signatures provide consistent numerical evidence for Anderson localization of light in three-dimensional disordered dielectric media.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports large-scale full-wave simulations of Maxwell's equations for light transport through 3D disordered ensembles of irregular dielectric particles at kr ≈ 1 with high index contrast. It identifies a disorder-driven transition to non-exponential time-resolved transmission decay that approaches t^{-1} scaling, the appearance of isolated spectral resonances with Thouless conductance g < 1, and the formation of static, non-propagating near-field intensity hotspots; these three signatures are presented as consistent numerical evidence for Anderson localization.

Significance. If the signatures can be shown to survive finite-size scaling and to be incompatible with slow diffusive or resonant-tunneling regimes, the work would supply direct, parameter-free numerical support for 3D Anderson localization of electromagnetic waves—an important and still-contested result. The use of full-wave solvers without fitted quantities or self-referential definitions is a methodological strength.

major comments (2)
  1. [transport and spectral signatures sections] The central claim that the three signatures unambiguously indicate Anderson localization rests on the assumption that non-exponential decay, g < 1 resonances, and static hotspots cannot arise from slow but still diffusive transport or boundary-dominated effects in finite volumes. No systematic finite-size scaling collapse or extraction of a size-independent localization length is presented; without it the signatures remain compatible with pre-localized regimes when the localization length is comparable to the simulated system size.
  2. [time-resolved transmission analysis] The time-dependent diffusion coefficient is reported to approach t^{-1} scaling at long times, but the manuscript does not quantify how this scaling depends on system size L or demonstrate that the effective diffusion length remains bounded as L increases. This is load-bearing because t^{-1} decay can appear transiently in finite diffusive systems near the localization transition.
minor comments (2)
  1. [spectral analysis] Clarify the precise numerical definition and extraction procedure for the Thouless conductance g in the finite-system spectra (e.g., how level spacing and decay rates are obtained from the transmission resonances).
  2. [methods] Specify the ensemble size, disorder realization statistics, and convergence checks with respect to discretization and absorbing-boundary conditions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback highlighting the importance of finite-size effects. We respond point-by-point to the major comments below, providing the strongest honest defense of the manuscript while acknowledging limitations in computational scaling.

read point-by-point responses

  1. Referee: [transport and spectral signatures sections] The central claim that the three signatures unambiguously indicate Anderson localization rests on the assumption that non-exponential decay, g < 1 resonances, and static hotspots cannot arise from slow but still diffusive transport or boundary-dominated effects in finite volumes. No systematic finite-size scaling collapse or extraction of a size-independent localization length is presented; without it the signatures remain compatible with pre-localized regimes when the localization length is comparable to the simulated system size.

    Authors: We agree that a systematic finite-size scaling collapse would provide more definitive evidence for a size-independent localization length. The computational expense of full-wave Maxwell solvers at the necessary spatial resolution for kr ≈ 1 and high index contrast restricts the range of accessible system sizes L. Nevertheless, the three signatures are mutually reinforcing and difficult to reconcile with slow diffusion: isolated resonances with Thouless g < 1 directly indicate spectrally decoupled long-lived modes whose spatial extent is smaller than the simulated volume, while the static non-propagating intensity clusters observed in the near-field maps at late times contradict the continuous spreading expected even in marginally slow diffusive transport. We will revise the manuscript to add an explicit discussion of the ratio between the inferred localization length (from the long-time decay) and the simulated L, together with arguments why boundary effects alone cannot produce the observed combination of features. revision: partial

  2. Referee: [time-resolved transmission analysis] The time-dependent diffusion coefficient is reported to approach t^{-1} scaling at long times, but the manuscript does not quantify how this scaling depends on system size L or demonstrate that the effective diffusion length remains bounded as L increases. This is load-bearing because t^{-1} decay can appear transiently in finite diffusive systems near the localization transition.

    Authors: We acknowledge that explicit quantification of the L-dependence of the t^{-1} regime would address the possibility of transient behavior near the transition. Within the largest computationally feasible volumes, the approach to t^{-1} persists over more than two decades in time for the strongest disorder strengths, and the associated effective diffusion length saturates rather than continuing to grow. Transient t^{-1} scaling in finite diffusive media is typically accompanied by eventual recovery of diffusive behavior at still longer times and does not coincide with the simultaneous appearance of g < 1 resonances and static hotspots. We will revise the manuscript to include a comparison of the time-dependent diffusion coefficient across the available system sizes and to discuss the boundedness of the diffusion length in the context of these additional signatures. revision: partial

Circularity Check

0 steps flagged

No significant circularity; results from direct Maxwell simulations

full rationale

The paper derives its evidence exclusively from large-scale numerical solutions of Maxwell's equations in finite disordered particle systems. All reported signatures (non-exponential transmission decay, g<1 resonances, static near-field hotspots) are direct simulation outputs for chosen parameters (kr≈1, high contrast, irregular particles) rather than quantities fitted to subsets of data and then re-predicted. No self-citations are invoked to establish uniqueness theorems or to smuggle ansatzes; the derivation chain contains no self-definitional steps or reductions by construction. The analysis is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the interpretation of simulation outputs as localization signatures. No free parameters are fitted to data in the reported results; the size parameter kr ≈ 1 is an input choice.

axioms (1)
  • standard math Maxwell's equations accurately describe electromagnetic wave propagation in linear dielectric media
    Invoked implicitly by the use of full-wave simulations.

pith-pipeline@v0.9.0 · 5677 in / 1116 out tokens · 25733 ms · 2026-05-24T05:09:10.683602+00:00 · methodology

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Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages

  1. [1]

    Jeong, Y.-R

    S. Jeong, Y.-R. Lee, W. Choi, S. Kang, J. H. Hong, J.-S. Park, Y.-S. Lim, H.-G. Park, and W. Choi, Focusing of light energy inside a scattering medium by controlling the time-gated multiple light scattering, Nature Photonics 12, 277 (2018)

    work page 2018

  2. [2]

    D. S. Wiersma, The physics and applications of random lasers, Nature Physics4, 359 (2008)

    work page 2008

  3. [3]

    R. M. Nelson, M. D. Boryta, B. W. Hapke, K. S. Man- att, Y. Shkuratov, V. Psarev, K. Vandervoort, D. Kro- ner, A. Nebedum, C. L. Vides, and J. Qui˜ nones, Labo- ratory simulations of planetary surfaces: Understanding regolith physical properties from remote photopolarimet- ric observations, Icarus302, 483 (2018)

    work page 2018

  4. [4]

    Shkuratov, A

    Y. Shkuratov, A. Ovcharenko, E. Zubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, The opposition effect and negative polarization of structural analogs for planetary regoliths, Icarus159, 396 (2002)

    work page 2002

  5. [5]

    S. L. Jacques, Optical properties of biological tissues: a review, Physics in Medicine & Biology58, R37 (2013)

    work page 2013

  6. [6]

    Akkermans, E., Wolf, P.E., Maynard, R., and Maret, G., Theoretical study of the coherent backscattering of light by disordered media, J. Phys. France49, 77 (1988)

    work page 1988

  7. [7]

    C. M. Aegerter and G. Maret, Coherent backscattering 6 and anderson localization of light (Elsevier, 2009) pp. 1– 62

    work page 2009

  8. [8]

    Kaveh, M

    M. Kaveh, M. Rosenbluh, I. Edrei, and I. Freund, Weak localization and light scattering from disordered solids, Phys. Rev. Lett.57, 2049 (1986)

    work page 2049

  9. [9]

    P. W. Anderson, The question of classical localization a theory of white paint?, Philosophical Magazine B52, 505 (1985), https://doi.org/10.1080/13642818508240619

    work page doi:10.1080/13642818508240619 1985

  10. [10]

    B. A. van Tiggelen, A. Lagendijk, and D. S. Wiersma, Reflection and transmission of waves near the localization threshold, Phys. Rev. Lett.84, 4333 (2000)

    work page 2000

  11. [11]

    Cherroret and S

    N. Cherroret and S. E. Skipetrov, Microscopic derivation of self-consistent equations of anderson localization in a disordered medium of finite size, Phys. Rev. E77, 046608 (2008)

    work page 2008

  12. [12]

    Rezvani Naraghi and A

    R. Rezvani Naraghi and A. Dogariu, Phase transitions in diffusion of light, Phys. Rev. Lett.117, 263901 (2016)

    work page 2016

  13. [13]

    D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righ- ini, Localization of light in a disordered medium, Nature 390, 671 (1997)

    work page 1997

  14. [14]

    A. F. Ioffe and A. R. Regel, Non-crystalline, amor- phous, and liquid electronic semiconductors, in Progress in Semiconductors, Vol. 4, edited by A. F. Gibson (Wiley, New York, 1960) pp. 237–291

    work page 1960

  15. [15]

    S. E. Skipetrov and I. M. Sokolov, Ioffe-regel criterion for anderson localization in the model of resonant point scatterers, Phys. Rev. B98, 064207 (2018)

    work page 2018

  16. [16]

    H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. van Tiggelen, Localization of ultrasound in a three-dimensional elastic network, Nature Physics4, 945 (2008)

    work page 2008

  17. [17]

    S. S. Kondov, W. R. McGehee, J. J. Zirbel, and B. De- Marco, Three-dimensional anderson localization of ultra- cold matter, Science334, 66 (2011)

    work page 2011

  18. [18]

    Crespi, R

    A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, and P. Mataloni, Anderson localization of entangled photons in an integrated quantum walk, Nature Photonics7, 322 (2013)

    work page 2013

  19. [19]

    Riboli, P

    F. Riboli, P. Barthelemy, S. Vignolini, F. Intonti, A. D. Rossi, S. Combrie, and D. S. Wiersma, Anderson local- ization of near-visible light in two dimensions, Opt. Lett. 36, 127 (2011)

    work page 2011

  20. [20]

    Schwartz, G

    T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Transport and anderson localization in disordered two- dimensional photonic lattices, Nature446, 52 (2007)

    work page 2007

  21. [21]

    Haberko, L

    J. Haberko, L. S. Froufe-P´ erez, and F. Scheffold, Tran- sition from light diffusion to localization in three- dimensional amorphous dielectric networks near the band edge, Nature Communications11, 4867 (2020)

    work page 2020

  22. [22]

    Yamilov, S

    A. Yamilov, S. E. Skipetrov, T. W. Hughes, M. Minkov, Z. Yu, and H. Cao, Anderson localization of electromag- netic waves in three dimensions, Nature Physics19, 1308 (2023)

    work page 2023

  23. [23]

    Yılmaz, C

    H. Yılmaz, C. W. Hsu, A. Yamilov, and H. Cao, Trans- verse localization of transmission eigenchannels, Nature Photonics13, 352 (2019)

    work page 2019

  24. [24]

    Wang and X

    C. Wang and X. Liu, The transition of lateral spreading to localization in 3d disordered medium, Physics Letters A400, 127321 (2021)

    work page 2021

  25. [25]

    S. E. Skipetrov and B. A. van Tiggelen, Dynamics of anderson localization in open 3d media, Phys. Rev. Lett. 96, 043902 (2006)

    work page 2006

  26. [26]

    A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Statis- tical signatures of photon localization, Nature404, 850 (2000)

    work page 2000

  27. [27]

    D. J. Thouless, Maximum metallic resistance in thin wires, Phys. Rev. Lett.39, 1167 (1977)

    work page 1977

  28. [28]

    M. C. W. van Rossum and T. M. Nieuwenhuizen, Multi- ple scattering of classical waves: microscopy, mesoscopy, and diffusion, Rev. Mod. Phys.71, 313 (1999)

    work page 1999

  29. [29]

    Mondal, R

    S. Mondal, R. Kumar, M. Kamp, and S. Mujumdar, Op- tical thouless conductance and level-spacing statistics in two-dimensional anderson localizing systems, Phys. Rev. B100, 060201 (2019)

    work page 2019

  30. [30]

    St¨ orzer, P

    M. St¨ orzer, P. Gross, C. M. Aegerter, and G. Maret, Ob- servation of the critical regime near anderson localization of light, Phys. Rev. Lett.96, 063904 (2006)

    work page 2006

  31. [31]

    Sperling, W

    T. Sperling, W. B¨ uhrer, C. M. Aegerter, and G. Maret, Direct determination of the transition to localization of light in three dimensions, Nature Photonics7, 48 (2013)

    work page 2013

  32. [32]

    Scheffold, R

    F. Scheffold, R. Lenke, R. Tweer, and G. Maret, Local- ization or classical diffusion of light?, Nature398, 206 (1999)

    work page 1999

  33. [33]

    Scheffold and D

    F. Scheffold and D. Wiersma, Inelastic scattering puts in question recent claims of anderson localization of light, Nature Photonics7, 934 (2013)

    work page 2013

  34. [34]

    S. E. Skipetrov and J. H. Page, Red light for anderson localization, New Journal of Physics18, 021001 (2016)

    work page 2016

  35. [35]

    Sperling, L

    T. Sperling, L. Schertel, M. Ackermann, G. J. Aubry, C. M. Aegerter, and G. Maret, Can 3d light localization be reached in ‘white paint’?, New Journal of Physics18, 013039 (2016)

    work page 2016

  36. [36]

    Grynko, Y

    Y. Grynko, Y. Shkuratov, and J. F¨ orstner, Light backscattering from large clusters of densely packed ir- regular particles, Journal of Quantitative Spectroscopy and Radiative Transfer255, 107234 (2020)

    work page 2020

  37. [37]

    Rezvani Naraghi, S

    R. Rezvani Naraghi, S. Sukhov, J. J. S´ aenz, and A. Doga- riu, Near-field effects in mesoscopic light transport, Phys. Rev. Lett.115, 203903 (2015)

    work page 2015

  38. [38]

    V. N. Astratov and S. P. Ashili, Percolation of light through whispering gallery modes in 3d lattices of cou- pled microspheres, Opt. Express15, 17351 (2007)

    work page 2007

  39. [39]

    S. E. Skipetrov and I. M. Sokolov, Absence of anderson localization of light in a random ensemble of point scat- terers, Phys. Rev. Lett.112, 023905 (2014)

    work page 2014

  40. [40]

    B. A. van Tiggelen and S. E. Skipetrov, Longitudinal modes in diffusion and localization of light, Phys. Rev. B 103, 174204 (2021)

    work page 2021

  41. [41]

    Grynko, Y

    Y. Grynko, Y. Shkuratov, S. Alhaddad, and J. F¨ orstner, Light scattering by large densely packed clusters of particles, in Springer Series in Light Scattering: Volume 8: Light Polarization and Multiple Scattering in Turbid Media, edited by A. Kokhanovsky (Springer International Pub- lishing, Cham, 2022) pp. 125–155

    work page 2022

  42. [42]

    Grynko, Y

    Y. Grynko, Y. Shkuratov, S. Alhaddad, and J. F¨ orstner, Negative polarization of light at backscattering from a numerical analog of planetary regoliths, Icarus384, 115099 (2022)

    work page 2022

  43. [43]

    Conti and A

    C. Conti and A. Fratalocchi, Dynamic light diffusion, three-dimensional anderson localization and lasing in in- verted opals, Nature Physics4, 794 (2008)

    work page 2008

  44. [44]

    Hesthaven and T

    J. Hesthaven and T. Warburton, Nodal high-order meth- ods on unstructured grids: I. time-domain solution of maxwell’s equations, Journal of Computational Physics 181, 186 (2002)

    work page 2002

  45. [45]

    Grynko and J

    Y. Grynko and J. F¨ orstner, Simulation of second har- monic generation from photonic nanostructures us- 7 ing the discontinuous galerkin time domain method, in Recent Trends in Computational Photonics, edited by A. Agrawal, T. Benson, R. M. De La Rue, and G. A. Wurtz (Springer International Publishing, Cham, 2017) pp. 261–284

    work page 2017

  46. [46]

    Busch, M

    K. Busch, M. K¨ onig, and J. Niegemann, Discontinuous galerkin methods in nanophotonics, Laser & Photonics Reviews5, 773 (2011)

    work page 2011

  47. [47]

    Torquato and F

    S. Torquato and F. H. Stillinger, Local density fluctua- tions, hyperuniformity, and order metrics, Phys. Rev. E 68, 041113 (2003)

    work page 2003

  48. [48]

    Ch´ eron, S

    E. Ch´ eron, S. F´ elix, J.-P. Groby, V. Pagneux, and V. Romero-Garc´ ıa, Wave transport in stealth hyperuni- form materials: The diffusive regime and beyond, Ap- plied Physics Letters121, 061702 (2022)

    work page 2022

  49. [49]

    Grynko, Y

    Y. Grynko, Y. Shkuratov, and J. F¨ orstner, Intensity surge and negative polarization of light from compact irregular particles, Opt. Lett.43, 3562 (2018)

    work page 2018

  50. [50]

    Coumans and Y

    E. Coumans and Y. Bai, Pybullet, a python module for physics simulation for games, robotics and machine learn- ing,http://pybullet.org(2016–2021)

    work page 2016

  51. [51]

    S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Whispering-gallery mode microdisk lasers, Applied Physics Letters60, 289 (1992)

    work page 1992

  52. [52]

    J. M. Escalante and S. E. Skipetrov, Longitu- dinal optical fields in light scattering from di- electric spheres and anderson localization of light, Annalen der Physik529, 1700039 (2017), https://onlinelibrary.wiley.com/doi/pdf/10.1002/andp.201700039

    work page doi:10.1002/andp.201700039 2017

  53. [53]

    Warburton, Mini discontinuous galerkin maxwells time-domain solver,https://github.com/tcew

    T. Warburton, Mini discontinuous galerkin maxwells time-domain solver,https://github.com/tcew

    work page

  54. [54]

    C ¸ apo˘ glu, A

    ˙Ilker R. C ¸ apo˘ glu, A. Taflove, and V. Backman, Genera- tion of an incident focused light pulse in fdtd, Opt. Ex- press16, 19208 (2008). SUPPLEMENT AR Y MA TERIAL I. NUMERICAL MODEL We performed numerical simulations using a self- developed light scattering code based on the open source DGTD Maxwell solver MIDG published by Tim Warbur- ton [53]. TheCS...

    work page 2008