pith. sign in

arxiv: 2601.07971 · v2 · pith:QTNRLZIFnew · submitted 2026-01-12 · ⚛️ physics.optics · cond-mat.other

Disorder-Induced Coherence Enables Control of Wave Transport

Israel Kurtz , Yiming Huang , Zhou Shi , Azriel Z Genack This is my paper

Pith reviewed 2026-05-21 15:23 UTC · model grok-4.3

classification ⚛️ physics.optics cond-mat.other
keywords disordered mediatransmission eigenchannelswave interferencemodal alignmentcoherencemultiple scatteringwave transport
0
0 comments X

The pith

In high-transmission eigenchannels of disordered media, modal contributions align nearly perfectly with increasing length to sustain high transmission despite multiple scattering.

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

The paper investigates how wave coherence develops with depth inside disordered samples for different transmission eigenchannels. Measurements and simulations show that in the channel with highest transmission, the contributions from individual waveguide modes line up more and more closely as the sample length grows, so that constructive interference keeps transmission large even after many scattering events. In low-transmission channels the mode contributions stay sizable, yet they cancel one another through destructive interference rather than simply shrinking in size. This picture explains the wide range of possible transmission values and shows that extremely low transmissions can still be detected by tuning frequency through a transmission zero, far below usual noise limits.

Core claim

The transmission matrix of a disordered medium supports eigenchannels with transmissions ranging from near unity to near zero. In the highest-transmission eigenchannel the alignment of modal contributions from the waveguide modes becomes nearly perfect as sample length increases, so transmission remains high despite extensive multiple scattering. In low-transmission eigenchannels the modal contributions remain appreciable and transmission is suppressed by their destructive interference. Forward- and backward-propagating modal contributions are extracted throughout the sample depth, and the derived flux, energy density, and velocity are mutually consistent.

What carries the argument

The depth-dependent alignment of modal contributions from waveguide modes inside each transmission eigenchannel, which produces constructive interference in high-transmission channels and destructive interference in low-transmission channels.

If this is right

  • High transmission persists in the top eigenchannel because modal alignment improves with length rather than because scattering is weak.
  • Low transmission occurs through destructive interference of sizable modal contributions rather than through their absence.
  • Eigenchannel transmission values can be measured more than nine orders of magnitude below the highest eigenvalue by tuning to a transmission zero.
  • Consistency among extracted flux, energy density, and velocity validates the modal decomposition across the sample depth.

Where Pith is reading between the lines

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

  • The same modal-alignment mechanism may allow selective control of transport in applications that require sending waves through thick scattering layers.
  • Frequency tuning near transmission zeros could provide a practical route to resolve very weak channels that standard intensity measurements miss.
  • Analogous alignment effects could appear in acoustic or quantum-wave systems where transmission matrices are accessible.

Load-bearing premise

Forward- and backward-propagating modal contributions can be reliably extracted and separated from measured or simulated fields throughout the sample depth without significant reconstruction artifacts or unaccounted losses.

What would settle it

Direct measurement showing that modal alignments fail to improve with length in the highest-transmission eigenchannel, or that low-transmission channels have vanishing rather than merely misaligned contributions, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2601.07971 by Azriel Z Genack, Israel Kurtz, Yiming Huang, Zhou Shi.

Figure 1
Figure 1. Figure 1: FIG. 1. Microwave measurements of the transmission matrix. [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Measurements of scattering-enhanced coherence in high- and low-transmission TEs. [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Buildup of coherence in TEs with increasing depth into random media. [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Narrowing and broadening of angular distribution of flux amplitudes relative to the [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Eigenchannel flux, energy density, and velocity. [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
read the original abstract

The transmission matrix of a disordered medium, experimentally accessible for classical waves and central to the theory of mesoscopic electronic transport, supports transmission eigenchannels ranging from complete to vanishing transmission. This range reflects wave coherence, yet the evolution of coherence with depth across eigenchannels has not been examined. Using microwave measurements and numerical simulations, we show how wave interference evolves with depth within the sample to produce constructive or destructive interference in high- and low-transmission eigenchannels, respectively. In the highest-transmission eigenchannel, the alignment of modal contributions from the waveguide modes of an incident eigenchannel can become nearly perfect as the sample length increases, allowing transmission to remain high despite extensive multiple scattering. Although the contributions in low-transmission eigenchannels are somewhat reduced relative to those in high-transmission channels, they remain appreciable, and transmission is suppressed by their destructive interference rather than by their small magnitude. Because these contributions remain appreciable, it is possible to measure eigenchannel transmission far below the noise floor of conventional transmission and more than nine orders of magnitude below the highest transmission eigenvalue when the frequency is tuned through a transmission zero. In simulations, we determine the forward- and backward-propagating modal contributions to each eigenchannel throughout the sample and extract the corresponding flux, energy density, and velocity, whose mutual consistency validates the analysis. These results reveal how modal alignment evolves throughout disordered media and underlies the contrasting characteristics of transmission eigenchannels.

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

0 major / 3 minor

Summary. The paper claims that wave interference evolves with depth in disordered media to produce constructive interference in high-transmission eigenchannels and destructive interference in low-transmission ones. Microwave measurements and numerical simulations show that in the highest-transmission eigenchannel, alignment of modal contributions from waveguide modes approaches perfection with increasing sample length, sustaining high transmission despite multiple scattering. In low-transmission channels, modal contributions remain appreciable but cancel via destructive interference. Forward- and backward-propagating modal contributions are extracted throughout the sample depth; mutual consistency among flux, energy density, and velocity validates the decomposition. This framework enables measurement of transmissions more than nine orders of magnitude below the highest eigenvalue by tuning through transmission zeros.

Significance. If the central claims hold, the work supplies a concrete, depth-resolved picture of how modal alignment underlies the contrasting behavior of transmission eigenchannels, directly linking experimental observations to the interference mechanism. The internal validation through three mutually consistent quantities (flux, energy density, velocity) and the agreement between microwave data and simulations constitute a notable strength. The demonstration that low transmission arises from phase cancellation rather than vanishing amplitudes, together with access to transmissions far below conventional noise floors, advances understanding of mesoscopic wave transport and suggests routes for active control in disordered systems.

minor comments (3)
  1. [Abstract] Abstract: the statement that transmission can be measured 'more than nine orders of magnitude below the highest transmission eigenvalue' would benefit from an explicit cross-reference to the figure or section that quantifies this dynamic range.
  2. [Methods / Simulation section] The separation of forward- and backward-propagating modal amplitudes is central to the analysis; a brief statement of the numerical procedure (e.g., projection onto waveguide modes at each depth slice) would improve reproducibility.
  3. [Figures] Figure captions: ensure that the color scales for modal-amplitude plots are labeled with the same normalization used in the text so that the 'nearly perfect alignment' claim can be read directly from the figures.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the positive recommendation to accept.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's analysis of modal alignment and interference in transmission eigenchannels is grounded in direct microwave measurements and numerical simulations of disordered media. Forward- and backward-propagating modal contributions are extracted from the fields and validated through independent consistency checks on flux, energy density, and velocity. These steps rely on empirical data and computational decomposition rather than any reduction to fitted parameters, self-definitions, or load-bearing self-citations within the paper's own equations. The observed evolution of coherence with depth is presented as an experimental finding, keeping the central claims self-contained and externally supported.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work relies on standard linear wave propagation in linear media and the existence of a well-defined transmission matrix; no new free parameters are introduced to fit the interference picture, and no new physical entities are postulated.

axioms (2)
  • domain assumption Waves in the disordered medium obey linear superposition and time-reversal symmetry in the absence of absorption.
    Invoked when separating forward and backward modal contributions and when interpreting interference as the source of transmission contrast.
  • standard math The transmission matrix is experimentally accessible and its eigenchannels are well-defined for the waveguide geometry used.
    Central to defining high- and low-transmission channels and to extracting modal contributions at different depths.

pith-pipeline@v0.9.0 · 5783 in / 1383 out tokens · 35736 ms · 2026-05-21T15:23:20.306638+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages

  1. [1]

    B. L. Altshuler, P. A. Lee, and W. R. Webb, Mesoscopic Phenomena in Solids (Elsevier, 2012)

    work page 2012

  2. [2]

    V., Dorda, G

    Klitzing, K. V., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980)

    work page 1980

  3. [3]

    R. A. Webb, S. Washburn, C. P. Umbach, and R. B. Laibowitz, Observation of h/e Aharonov-Bohm oscillations in normal-metal rings, Phys Rev Lett 54, 25 (1985)

    work page 1985

  4. [4]

    O. N. Dorokhov, Transmission coefficient and the localization length of an electron in N bound disordered chains, Soviet Journal of Experimental and Theoretical Physics Letters 36, 318 (1982)

    work page 1982

  5. [5]

    Imry, Active transmission channels and universal conductance fluctuations, Europhys

    Y. Imry, Active transmission channels and universal conductance fluctuations, Europhys. Lett. 1, 5 (1986). 23

    work page 1986

  6. [6]

    P. A. Mello, P. Pereyra, and N. Kumar, Macroscopic approach to multichannel disordered conductors, Annals of Physics 181, 2 (1988)

    work page 1988

  7. [7]

    D., Mello, P

    Stone, A. D., Mello, P. A., Muttalib, K. A. & Pichard, J.-L. Random matrix theory and maximum entropy models for disordered conductors. in Mesoscopic Phenomena in Solids 369–448 (North-Holland, Amsterdam, 1991)

    work page 1991

  8. [8]

    C. W. J. Beenakker, Random-matrix theory of quantum transport, Rev. Mod. Phys. 69, 3 (1997)

    work page 1997

  9. [9]

    Buttiker, Coherent and sequential tunneling in series barriers, IBM Journal of Research and Development 32, 1 (1988)

    M. Buttiker, Coherent and sequential tunneling in series barriers, IBM Journal of Research and Development 32, 1 (1988)

    work page 1988

  10. [10]

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

    work page 1999

  11. [11]

    I. M. Vellekoop and A. P. Mosk, Focusing coherent light through opaque strongly scattering media, Opt. Lett., OL 32, 16 (2007)

    work page 2007

  12. [12]

    M., Lerosey, G., Carminati, R., Fink, M., Boccara, A

    Popoff, S. M., Lerosey, G., Carminati, R., Fink, M., Boccara, A. C., Gigan, S. 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)

    work page 2010

  13. [14]

    R., Choi, W., Lee J

    Yu, H., Hillman, T. R., Choi, W., Lee J. O., Feld, M. S., Dasari, R. R., Park, Y. K. Measuring large optical transmission matrices of disordered media. Phys. Rev. Lett. 111, (2013)

    work page 2013

  14. [15]

    S. M. Popoff, A. Goetschy, S. F. Liew, A. D. Stone, and H. Cao, Coherent control of total transmission of light through disordered media, Phys. Rev. Lett. 112, 13 (2014). 24

    work page 2014

  15. [16]

    Gérardin, J

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

    work page 2014

  16. [17]

    Rotter and S

    S. Rotter and S. Gigan, Light fields in complex media: Mesoscopic scattering meets wave control, Rev. Mod. Phys. 89, (2017)

    work page 2017

  17. [18]

    Devaud, B

    L. Devaud, B. Rauer, J. Melchard, M. Kühmayer, S. Rotter, and S. Gigan, Speckle engineering through singular value decomposition of the transmission matrix, Phys. Rev. Lett. 127, 9 (2021)

    work page 2021

  18. [19]

    Landauer, Electrical resistance of disordered one-dimensional lattices, The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics 21, 172 (1970)

    R. Landauer, Electrical resistance of disordered one-dimensional lattices, The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics 21, 172 (1970)

    work page 1970

  19. [20]

    Economou, E. N. & Soukoulis, C. M. Static conductance and scaling theory of localization in one dimension. Phys. Rev. Lett. 46, 618–621 (1981)

    work page 1981

  20. [21]

    D. S. Fisher, P. A. Lee, C. W. Hsu, and A. D. Stone, Relation between conductivity and transmission matrix, Phys. Rev. B 23, 6851 (1981)

    work page 1981

  21. [22]

    Büttiker, Y

    M. Büttiker, Y. Imry, R. Landauer, and S. Pinhas, Generalized many-channel conductance formula with application to small rings, Phys. Rev. B 31, 10 (1985)

    work page 1985

  22. [23]

    R., Hsu, C

    Sweeney, W. R., Hsu, C. W., & Stone, A. D. Theory of reflectionless scattering modes. Phys. Rev. A 102, (2020)

    work page 2020

  23. [24]

    Kang and A

    Y. Kang and A. Z. Genack, Transmission zeros with topological symmetry in complex systems, Phys. Rev. B 103, 10 (2021)

    work page 2021

  24. [25]

    Joshi, I

    K. Joshi, I. Kurtz, Z. Shi, and A. Z. Genack, Ohm’s law lost and regained: observation and impact of transmission and velocity zeros, Nat Commun 15, 10616 (2024). 25

    work page 2024

  25. [26]

    P., Antonsen, Jr., T

    Erb, J., Shaibe, N., Calvo, R., Lathrop, D. P., Antonsen, Jr., T. M., Kottos, T., Anlage, S. M. Topology and manipulation of scattering singularities in complex non-Hermitian systems: Two-channel case. Phys. Rev. Res. 7, 023090 (2025)

    work page 2025

  26. [27]

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

    work page 2011

  27. [28]

    M. Davy, Z. Shi, J. Park, C. Tian, and A. Z. Genack, Universal structure of transmission eigenchannels inside opaque media, Nature Communications 6, 1 (2015)

    work page 2015

  28. [29]

    G., Petrenko, S., Bromberg, Y

    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, (2016)

    work page 2016

  29. [30]

    & Cao, H

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

    work page 2020

  30. [31]

    W., Cao, H

    Bender, N., Yamilov, A., Goetschy, A., Yilmaz, H., Hsu, C. W., Cao, H. Depth-targeted energy delivery deep inside scattering media. Nat. Phys. 18, 309–315 (2022)

    work page 2022

  31. [32]

    Goetschy, A., Bender, N., Yamilov, A., Hsu, C

    McIntosh, R. Goetschy, A., Bender, N., Yamilov, A., Hsu, C. W., Yilmaz, H., Cao, H. Delivering broadband light deep inside diffusive media. Nat. Photon. 18, 744–750 (2024)

    work page 2024

  32. [33]

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

    work page 2012

  33. [34]

    G., Blum, C., Lagendijk, A., Vos W

    Bertolotti, J., Van Putten, E. G., Blum, C., Lagendijk, A., Vos W. L., Mosk, A. P. Non- invasive imaging through opaque scattering layers. Nature 491, 232–234 (2012)

    work page 2012

  34. [35]

    C., Fink, M., Bossy, E., Gigan, S

    Chaigne, T., Katz, O., Boccara, A. C., Fink, M., Bossy, E., Gigan, S. Controlling light in scattering media non-invasively using the photoacoustic transmission matrix. Nature Photon 8, 58–64 (2014). 26

    work page 2014

  35. [36]

    Boniface, J

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

    work page 2020

  36. [37]

    W., Yilmaz, H., Palacios, P

    Bender, N., Goetschy, A., Hsu, C. W., Yilmaz, H., Palacios, P. J., Yamilov, A., Cao, H. Coherent enhancement of optical remission in diffusive media. Proceedings of the National Academy of Sciences 119, e2207089119 (2022)

    work page 2022

  37. [38]

    B. L. Altshuler, D. Khmel’nitzkii, A. I. Larkin, and P. A. Lee, Magnetoresistance and Hall effect in a disordered two-dimensional electron gas, Phys. Rev. B 22, 11 (1980)

    work page 1980

  38. [39]

    Lee, P. A. & Stone, A. D. Universal conductance fluctuations in metals. Phys. Rev. Lett. 55, 1622–1625 (1985)

    work page 1985

  39. [40]

    Pichard, N

    J.-L. Pichard, N. Zanon, Y. Imry, and A. Douglas Stone, Theory of random multiplicative transfer matrices and its implications for quantum transport, J. Phys. France 51, 7 (1990)

    work page 1990

  40. [41]

    Landauer, Electrical resistance of disordered one-dimensional lattices, The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics 21, 863 (1970)

    R. Landauer, Electrical resistance of disordered one-dimensional lattices, The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics 21, 863 (1970)

    work page 1970

  41. [42]

    O. N. Dorokhov, On the coexistence of localized and extended electronic states in the metallic phase, Solid State Communications 51, 381 (1984)

    work page 1984

  42. [43]

    E. P. Wigner, On the behavior of cross sections near thresholds, Phys. Rev. 73, 9 (1948)

    work page 1948

  43. [44]

    Dyson, F. J. Statistical theory of the energy levels of complex systems. I. J. Math. Phys. 3, 140–156 (1962)

    work page 1962

  44. [45]

    M. L. Mehta, Random Matrices (Elsevier, 2004)

    work page 2004

  45. [46]

    A. Z. Genack, Y. Huang, A. Maor, and Z. Shi, Velocities of transmission eigenchannels and diffusion, Nat Commun 15, 2606 (2024). 27

    work page 2024

  46. [47]

    G., Petrenko, S., Bromberg, Y., Cao, H

    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, (2016)

    work page 2016

  47. [48]

    Cheng and A

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

    work page 2014

  48. [52]

    A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Statistical signatures of photon localization, Nature 404, 850 (2000). 28 Supplementary Materials Israel Kurtz1,2, Yiming Huang1,2,3, Zhou Shi1,2,4, and Azriel Z. Genack1,2 1Department of Physics, Queens College of the City University of New York, Flushing, New York 11367, USA 2Physics Program, The Graduate ...

    work page 2000

  49. [53]

    & Genack, A

    Shi, Z. & Genack, A. Z. Transmission eigenvalues and the bare conductance in the crossover to Anderson localization. Phys. Rev. Lett. 108, 043901 (2012)

    work page 2012

  50. [54]

    Joshi, I

    K. Joshi, I. Kurtz, Z. Shi, and A. Z. Genack, Ohm’s law lost and regained: observation and impact of transmission and velocity zeros, Nat Commun 15, 10616 (2024)

    work page 2024

  51. [55]

    A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Statistical signatures of photon localization, Nature 404, 850 (2000)

    work page 2000

  52. [56]

    H. U. Baranger, D. P. DiVincenzo, R. A. Jalabert, and A. D. Stone, Classical and quantum ballistic-transport anomalies in microjunctions, Phys. Rev. B 44, 19 (1991)

    work page 1991

  53. [57]

    Metalidis, Electronic transport in mesoscopic systems, (2007)

    G. Metalidis, Electronic transport in mesoscopic systems, (2007)

    work page 2007

  54. [58]

    Shi and A

    Z. Shi and A. Z. Genack, Diffusion in translucent media, Nat Commun 9, 1 (2018)

    work page 2018