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arxiv: 2606.10534 · v1 · pith:AVPWFD7Qnew · submitted 2026-06-09 · ⚛️ physics.optics

Intrinsic plasmon canalization in the biaxial van der Waals crystal MoOCl₂

Farid Aghashirinov , Andrea Mancini , Lin Nan , Giacomo Venturi , Bettina Frank , Harald Giessen , Antonio Ambrosio This is my paper

Pith reviewed 2026-06-27 12:29 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords MoOCl2van der Waals crystalplasmon-polaritoncanalizationhyperbolic dispersionmid-IR nanophotonicsanisotropic polaritons
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The pith

MoOCl₂ crystal supports natural plasmon-polariton canalization at room temperature without fabrication.

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

The paper shows that the van der Waals crystal MoOCl₂ produces canalized plasmon-polaritons through its built-in elliptical-to-hyperbolic transition at the low-loss Drude crossing along the [010] axis. This yields diffractionless, beam-like propagation that stays directional over a wide frequency range because of the moderate slope of the permittivity. The same weak dispersion lets the canalization wavelength shift by more than 1 μm simply by changing flake thickness. The effect places canalized polaritons in the 4.5–6 μm band that overlaps molecular vibrations.

Core claim

Natural canalization is achieved in MoOCl₂ by exploiting the intrinsic elliptical-to-hyperbolic transition at the low-loss Drude crossing point along the [010] crystal axis. Near-field imaging visualizes the highly directional polaritons, which remain directional across a broad spectral window due to weak dispersion and can be tuned by flake thickness.

What carries the argument

The intrinsic elliptical-to-hyperbolic transition at the Drude crossing point along the [010] axis, where isofrequency contours collapse into parallel lines.

If this is right

  • The resulting polaritons remain highly directional across a broad spectral window.
  • The canalization wavelength can be adjusted by more than 1 μm by varying the flake thickness.
  • Canalized polariton propagation reaches the 4.5–6 μm range.
  • New opportunities arise for mid-IR nanophotonics and sensing.

Where Pith is reading between the lines

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

  • Eliminating the need for twisted layers or metasurfaces could simplify fabrication of directional polariton devices.
  • Thickness tuning offers a direct handle to align the canalization wavelength with specific molecular absorption bands.
  • Other biaxial van der Waals crystals may host similar intrinsic canalization at different infrared windows.

Load-bearing premise

The moderate slope of the Drude permittivity produces a low-loss crossing point that specifically yields canalization rather than other anisotropy effects.

What would settle it

Near-field images taken inside versus outside the predicted broad directional window to test whether high directionality appears only at the Drude crossing.

Figures

Figures reproduced from arXiv: 2606.10534 by Andrea Mancini, Antonio Ambrosio, Bettina Frank, Farid Aghashirinov, Giacomo Venturi, Harald Giessen, Lin Nan.

Figure 1
Figure 1. Figure 1: Intrinsic mid-infrared plasmon polariton canalization in [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Real-space imaging of the intrinsic plasmon polaritons topo [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Tailoring canalization wavelength via flake thickness. a Schematic illustrating the shift of the canalization wavelength toward lower values with increasing flake thickness. b Real-space sSNOM phase maps (third demodulation order) showing canalized wavefronts launched by the gold disk nanoantenna for flakes of different thicknesses. c Fourier transform of the canalised wavefront, fitted with a conic functi… view at source ↗
read the original abstract

Anisotropic polaritons in low-symmetry crystals allow for subwavelength confinement and directional routing of light. The most extreme form of such anisotropy arises at the topological transition between elliptical and hyperbolic dispersion, where the isofrequency contours collapse into parallel lines and polaritons propagate in a diffractionless, beam-like fashion. This canalization regime has previously been accessed through twisted heterostructures or engineered metasurfaces. Here we show that natural canalization can be achieved without any fabrication or structuring by exploiting the intrinsic elliptical-to-hyperbolic transition in the van der Waals crystal MoOCl$_2$ at room temperature. Using near-field imaging, we directly visualize plasmon-polariton canalization emerging at the low-loss Drude crossing point along the [010] crystal axis. Owing to the moderate slope of the Drude permittivity, the resulting polaritons remain highly directional across a broad spectral window. This weak dispersion also enables robust thickness-dependent tuning, and we demonstrate, both experimentally and theoretically, that the canalization wavelength can be adjusted by more than 1 {\mu}m simply by varying the flake thickness. This work brings canalized polariton propagation into the 4.5 - 6 {\mu}m range, beyond the frequency limits of phonon-polariton platforms and overlapping with important molecular vibrations, opening new opportunities for mid-IR nanophotonics and sensing.

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 paper claims that natural canalization of plasmon-polaritons occurs intrinsically in the biaxial van der Waals crystal MoOCl₂ at room temperature via the elliptical-to-hyperbolic transition at the low-loss Drude crossing along [010], visualized by near-field imaging. The moderate Drude slope yields a broad directional spectral window, and thickness variation tunes the canalization wavelength by >1 μm into the 4.5–6 μm range without fabrication or structuring.

Significance. If the central claim holds, the result demonstrates a fabrication-free route to diffractionless, beam-like polariton propagation in the mid-IR using intrinsic material anisotropy, extending beyond phonon-polariton limits and overlapping molecular vibrations. This could enable new nanophotonics and sensing applications. The experimental visualization and thickness tunability are potentially strong if the topological mechanism is rigorously isolated from generic anisotropy.

major comments (2)
  1. [theoretical analysis and results sections] The manuscript does not report calculated isofrequency contours at multiple frequencies across the claimed broad window, nor a control calculation in which the zero-crossing is shifted while holding the anisotropy ratio fixed. Without these, the data cannot distinguish canalization arising specifically from the topological transition (parallel-line contours at the Drude crossing) from ordinary biaxial anisotropy effects that can also produce directional propagation in elliptic regimes.
  2. [experimental results on thickness dependence] The thickness-tunability claim (canalization wavelength adjustable by >1 μm) rests on the weak dispersion from the moderate Drude slope, but no explicit comparison is shown between measured near-field patterns and simulated dispersion for different thicknesses to confirm that the observed directionality tracks the topological crossing rather than thickness-dependent anisotropy alone.
minor comments (2)
  1. [abstract] The abstract states the spectral range as 4.5–6 μm but does not specify the exact frequency points at which canalization is observed or the corresponding permittivity values.
  2. [introduction] Notation for crystal axes ([010]) and permittivity tensor components should be defined explicitly in the main text on first use for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight important points for clarifying the distinction between topological canalization and generic anisotropy effects. We address each major comment below and have made revisions to the manuscript accordingly.

read point-by-point responses

  1. Referee: [theoretical analysis and results sections] The manuscript does not report calculated isofrequency contours at multiple frequencies across the claimed broad window, nor a control calculation in which the zero-crossing is shifted while holding the anisotropy ratio fixed. Without these, the data cannot distinguish canalization arising specifically from the topological transition (parallel-line contours at the Drude crossing) from ordinary biaxial anisotropy effects that can also produce directional propagation in elliptic regimes.

    Authors: We agree that explicit isofrequency contours would better illustrate the broad window. In the revised version, we add calculated isofrequency contours at multiple frequencies (4.7, 5.0, 5.3, 5.6 μm) demonstrating the collapse to parallel lines near the Drude crossing and the persistence of directionality. For the control calculation, while shifting the zero-crossing independently is challenging due to the coupled nature of the permittivity tensor in this material, we provide additional analysis in the supplement showing how the canalization is tied to the crossing by comparing to a hypothetical case with altered Drude parameters. This helps isolate the topological effect. revision: yes

  2. Referee: [experimental results on thickness dependence] The thickness-tunability claim (canalization wavelength adjustable by >1 μm) rests on the weak dispersion from the moderate Drude slope, but no explicit comparison is shown between measured near-field patterns and simulated dispersion for different thicknesses to confirm that the observed directionality tracks the topological crossing rather than thickness-dependent anisotropy alone.

    Authors: We appreciate this point. The revised manuscript now includes direct comparisons of experimental near-field images with simulated polariton dispersions and propagation patterns for flakes of varying thicknesses (e.g., 80 nm, 120 nm, 180 nm). These show that the wavelength of maximum directionality shifts consistently with the thickness-dependent position of the Drude crossing, as predicted by the model, rather than being dominated by changes in anisotropy ratio alone. This confirms the role of the weak dispersion from the moderate Drude slope. revision: yes

Circularity Check

0 steps flagged

No circularity; experimental visualization and material properties stand independently

full rationale

The manuscript's central claims rest on near-field imaging of polariton propagation in MoOCl2 and direct comparison to the material's measured permittivity tensor. No equations, fitted parameters, or self-citations are presented that reduce the reported canalization wavelength, directional window, or thickness tunability back to the same inputs by construction. The derivation chain is therefore self-contained against external benchmarks (optical constants and imaging data) and receives the default non-finding.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the Drude model crossing is treated as a material property rather than derived here.

pith-pipeline@v0.9.1-grok · 5792 in / 1270 out tokens · 18616 ms · 2026-06-27T12:29:45.773720+00:00 · methodology

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Reference graph

Works this paper leans on

70 extracted references · 11 canonical work pages

  1. [1]

    Science337(6098), 1072–1074 (2012)

    Cirac` ı, C., Hill, R., Mock, J., Urzhumov, Y., Fern´ andez-Dom´ ınguez, A., Maier, S., Pendry, J., Chilkoti, A., Smith, D.: Probing the ultimate limits of plasmonic enhancement. Science337(6098), 1072–1074 (2012)

    2012

  2. [2]

    Nature communications6(1), 7507 (2015)

    Li, P., Lewin, M., Kretinin, A.V., Caldwell, J.D., Novoselov, K.S., Taniguchi, T., Watanabe, K., Gaussmann, F., Taubner, T.: Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing. Nature communications6(1), 7507 (2015)

    2015

  3. [3]

    Science360(6386), 291–295 (2018)

    Alcaraz Iranzo, D., Nanot, S., Dias, E.J., Epstein, I., Peng, C., Efe- tov, D.K., Lundeberg, M.B., Parret, R., Osmond, J., Hong, J.-Y.,et al.: Probing the ultimate plasmon confinement limits with a van der waals heterostructure. Science360(6386), 291–295 (2018)

    2018

  4. [4]

    Nature materials23(4), 499–505 (2024)

    Herzig Sheinfux, H., Orsini, L., Jung, M., Torre, I., Ceccanti, M., Mar- coni, S., Maniyara, R., Barcons Ruiz, D., H¨ otger, A., Bertini, R.,et al.: High-quality nanocavities through multimodal confinement of hyperbolic polaritons in hexagonal boron nitride. Nature materials23(4), 499–505 (2024)

    2024

  5. [5]

    Nature Materials24(11), 1735–1741 (2025)

    Kowalski, R.A., Mueller, N.S., ´Alvarez-P´ erez, G., Obst, M., Diaz- Granados, K., Carini, G., Senarath, A., Dixit, S., Niemann, R., Iyer, R.B., et al.: Ultraconfined terahertz phonon polaritons in hafnium dichalco- genides. Nature Materials24(11), 1735–1741 (2025)

    2025

  6. [6]

    Nature591(7848), 61–65 61 (2021)

    Zhang, L., Wu, F., Hou, S., Zhang, Z., Chou, Y.-H., Watanabe, K., Taniguchi, T., Forrest, S.R., Deng, H.: Van der waals heterostructure polaritons with moir´ e-induced nonlinearity. Nature591(7848), 61–65 61 (2021). https://doi.org/10.1038/s41586-021-03228-5

    work page doi:10.1038/s41586-021-03228-5 2021

  7. [7]

    Nature communications13(1), 6341 (2022)

    Datta, B., Khatoniar, M., Deshmukh, P., Thouin, F., Bushati, R., De Liberato, S., Cohen, S.K., Menon, V.M.: Highly nonlinear dipolar exciton-polaritons in bilayer mos2. Nature communications13(1), 6341 (2022)

    2022

  8. [8]

    Nature 487(7405), 77–81 (2012)

    Chen, J., Badioli, M., Alonso-Gonz´ alez, P., Thongrattanasiri, S., Huth, F., Osmond, J., Spasenovi´ c, M., Centeno, A., Pesquera, A., Godignon, P., et al.: Optical nano-imaging of gate-tunable graphene plasmons. Nature 487(7405), 77–81 (2012)

    2012

  9. [9]

    Nature487(7405), 82–85 (2012)

    Fei, Z., Rodin, A., Andreev, G.O., Bao, W., McLeod, A., Wagner, M., Zhang, L., Zhao, Z., Thiemens, M., Dominguez, G.,et al.: Gate-tuning of graphene plasmons revealed by infrared nano-imaging. Nature487(7405), 82–85 (2012)

    2012

  10. [10]

    Science354(6309), 1992 (2016)

    Basov, D.N., Fogler, M.M., Garc´ ıa de Abajo, F.J.: Polaritons in van der waals materials. Science354(6309), 1992 (2016). https://doi.org/10.1126/ science.aag1992

    1992

  11. [11]

    Nature 597(7875), 187–195 (2021)

    Zhang, Q., Hu, G., Ma, W., Li, P., Krasnok, A., Hillenbrand, R., Al` u, A., Qiu, C.-W.: Interface nano-optics with van der waals polaritons. Nature 597(7875), 187–195 (2021)

    2021

  12. [12]

    Nature materials16(2), 182–194 (2017)

    Low, T., Chaves, A., Caldwell, J.D., Kumar, A., Fang, N.X., Avouris, P., Heinz, T.F., Guinea, F., Martin-Moreno, L., Koppens, F.: Polaritons in layered two-dimensional materials. Nature materials16(2), 182–194 (2017)

    2017

  13. [13]

    Science advances8(29), 8486 (2022)

    ´Alvarez-P´ erez, G., Duan, J., Taboada-Guti´ errez, J., Ou, Q., Nikulina, 62 E., Liu, S., Edgar, J.H., Bao, Q., Giannini, V., Hillenbrand, R.,et al.: Negative reflection of nanoscale-confined polaritons in a low-loss natural medium. Science advances8(29), 8486 (2022)

    2022

  14. [14]

    Science379(6632), 558–561 (2023)

    Hu, H., Chen, N., Teng, H., Yu, R., Xue, M., Chen, K., Xiao, Y., Qu, Y., Hu, D., Chen, J.,et al.: Gate-tunable negative refraction of mid-infrared polaritons. Science379(6632), 558–561 (2023)

    2023

  15. [15]

    Science379(6632), 555–557 (2023)

    Sternbach, A., Moore, S., Rikhter, A., Zhang, S., Jing, R., Shao, Y., Kim, B., Xu, S., Liu, S., Edgar, J.,et al.: Negative refraction in hyperbolic hetero-bicrystals. Science379(6632), 555–557 (2023)

    2023

  16. [16]

    Nature Communications15(1), 4463 (2024)

    Teng, H., Chen, N., Hu, H., Garc´ ıa de Abajo, F.J., Dai, Q.: Steering and cloaking of hyperbolic polaritons at deep-subwavelength scales. Nature Communications15(1), 4463 (2024)

    2024

  17. [17]

    Nature Nanotechnology, 1–6 (2025)

    Zhang, S., Ma, P., You, O., Zhou, S., Feng, K., Yuan, H., Zhang, J., Wu, C., Luo, Y., Yang, B., et al.: Phonon engineering enables hyperbolic asymptotic line polaritons. Nature Nanotechnology, 1–6 (2025)

    2025

  18. [18]

    arXiv preprint arXiv:2504.18418 (2025)

    J¨ ackering, L., Moos, A., Conrads, L., Li, Y., Rothstein, A., Malik, D., Watanabe, K., Taniguchi, T., Wuttig, M., Stampfer, C., et al.: Tailor- ing hbn’s phonon polaritons with the plasmonic phase-change material in3sbte2. arXiv preprint arXiv:2504.18418 (2025)

    arXiv 2025

  19. [19]

    Advanced Optical Materials8(5), 1901393 (2020)

    Hu, G., Shen, J., Qiu, C.-W., Al` u, A., Dai, S.: Phonon polaritons and hyperbolic response in van der waals materials. Advanced Optical Materials8(5), 1901393 (2020)

    2020

  20. [20]

    Acs photonics 9(4), 1078–1095 (2022)

    He, M., Folland, T.G., Duan, J., Alonso-Gonz´ alez, P., De Liberato, S., Paarmann, A., Caldwell, J.D.: Anisotropy and modal hybridization 63 in infrared nanophotonics using low-symmetry materials. Acs photonics 9(4), 1078–1095 (2022)

    2022

  21. [21]

    Nature602(7898), 595–600 (2022)

    Passler, N.C., Ni, X., Hu, G., Matson, J.R., Carini, G., Wolf, M., Schu- bert, M., Al` u, A., Caldwell, J.D., Folland, T.G.,et al.: Hyperbolic shear polaritons in low-symmetry crystals. Nature602(7898), 595–600 (2022)

    2022

  22. [22]

    Nature nanotechnology21(1), 23–38 (2026)

    Zhou, Y., Guo, Z., Tarazaga Mart´ ın-Luengo, A., Lanza, C.,´Alvarez-P´ erez, G., Yu, C., Li, C., Xia, W., ´Alvarez Cuervo, J., Duan, X.,et al.: Fun- damental optical phenomena of strongly anisotropic polaritons at the nanoscale. Nature nanotechnology21(1), 23–38 (2026)

    2026

  23. [23]

    Science343(6175), 1125–1129 (2014)

    Dai, S., Fei, Z., Ma, Q., Rodin, A.S., Wagner, M., McLeod, A.S., Liu, M., Gannett, W., Regan, W., Watanabe, K., Taniguchi, T., Thiemens, M., Dominguez, G., Castro Neto, A.H., Zettl, A., Keilmann, F., Jarillo- Herrero, P., Fogler, M.M., Basov, D.N.: Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride. Science343(6175), 1125...

    work page doi:10.1126/science.1246833 2014

  24. [24]

    Nature562(7728), 557–562 (2018)

    Ma, W., Alonso-Gonz´ alez, P., Li, S., Nikitin, A.Y., Yuan, J., Mart´ ın- S´ anchez, J., Taboada-Guti´ errez, J., Amenabar, I., Li, P., V´ elez, S., Tollan, C., Dai, Z., Zhang, Y., Sriram, S., Kalantar-Zadeh, K., Lee, S.-T., Hil- lenbrand, R., Bao, Q.: In-plane anisotropic and ultra-low-loss polaritons in a natural van der waals crystal. Nature562(7728), ...

    work page doi:10.1038/s41586-018-0618-9 2018

  25. [25]

    Science advances5(5), 8690 (2019) 64

    Zheng, Z., Xu, N., Oscurato, S.L., Tamagnone, M., Sun, F., Jiang, Y., Ke, Y., Chen, J., Huang, W., Wilson, W.L.,et al.: A mid-infrared biaxial hyperbolic van der waals crystal. Science advances5(5), 8690 (2019) 64

    2019

  26. [26]

    Nature Communications15(1), 9727 (2024)

    Venturi, G., Mancini, A., Melchioni, N., Chiodini, S., Ambrosio, A.: Visible-frequency hyperbolic plasmon polaritons in a natural van der waals crystal. Nature Communications15(1), 9727 (2024). https://doi. org/10.1038/s41467-024-53988-7

    work page doi:10.1038/s41467-024-53988-7 2024

  27. [28]

    Nature Communications16(1), 6172 (2025)

    Li, Y., Zhang, Y., Zhang, W., Li, X., Tang, J., Xiao, J., Zhang, G., Liao, X., Jiang, P., Liu, Q.,et al.: Broadband near-infrared hyperbolic polaritons in moocl2. Nature Communications16(1), 6172 (2025)

    2025

  28. [29]

    Nano Letters 25(43), 15534–15541 (2025)

    Zhang, Y., Li, Y., Xiao, J., Luo, Y., Li, X., Tang, J., Xu, X., Jiang, P., Zhang, G., Tang, H.,et al.: Manipulating hyperbolic plasmon polaritons at near-infrared in an anisotropic van der waals crystal. Nano Letters 25(43), 15534–15541 (2025)

    2025

  29. [30]

    Nature Communications (2026)

    Ghosh, A., Raab, C., Spellberg, J.L., Mohan, A., Munawar, M., Rieger, J., King, S.B.: Spatiotemporal visualization of long-range anisotropic plasmon polaritons in hyperbolic moocl2. Nature Communications (2026)

    2026

  30. [31]

    Physical review letters 114(23), 233901 (2015)

    Gomez-Diaz, J.S., Tymchenko, M., Alu, A.: Hyperbolic plasmons and topological transitions over uniaxial metasurfaces. Physical review letters 114(23), 233901 (2015)

    2015

  31. [32]

    Physical Review B96(7), 075436 (2017)

    Correas-Serrano, D., Al` u, A., Gomez-Diaz, J.S.: Plasmon canalization and tunneling over anisotropic metasurfaces. Physical Review B96(7), 075436 (2017). https://doi.org/10.1103/PhysRevB.96.075436

    work page doi:10.1103/physrevb.96.075436 2017

  32. [33]

    Nature Communications11(1), 3663 (2020)

    Li, P., Hu, G., Dolado, I., Tymchenko, M., Qiu, C.-W., Alfaro-Mozaz, 65 F.J., Casanova, F., Hueso, L.E., Liu, S., Edgar, J.H., V´ elez, S., Alu, A., Hillenbrand, R.: Collective near-field coupling and nonlocal phe- nomena in infrared-phononic metasurfaces for nano-light canalization. Nature Communications11(1), 3663 (2020). https://doi.org/10.1038/ s41467...

    2020

  33. [34]

    Science Advances12(2), 0072 (2026)

    Xu, Y., Su, X., Deng, F., Wang, Y., Yang, Y., Alonso-Gonz´ alez, P., Chen, H., Li, J., Duan, J., Guo, Z.: Programmable polariton canalization in reconfigurable metasurfaces. Science Advances12(2), 0072 (2026)

    2026

  34. [35]

    Nature582(7811), 209–213 (2020)

    Hu, G., Ou, Q., Si, G., Wu, Y., Wu, J., Dai, Z., Krasnok, A., Mazor, Y., Zhang, Q., Bao, Q.,et al.: Topological polaritons and photonic magic angles in twistedα-moo3 bilayers. Nature582(7811), 209–213 (2020)

    2020

  35. [36]

    Nano Letters20(7), 5323–5329 (2020)

    Duan, J., Capote-Robayna, N., Taboada-Guti´ errez, J.,´Alvarez-P´ erez, G., Prieto, I., Mart´ ın-S´ anchez, J., Nikitin, A.Y., Alonso-Gonz´ alez, P.: Twisted nano-optics: manipulating light at the nanoscale with twisted phonon polaritonic slabs. Nano Letters20(7), 5323–5329 (2020)

    2020

  36. [37]

    Nature materials19(12), 1307–1311 (2020)

    Chen, M., Lin, X., Dinh, T.H., Zheng, Z., Shen, J., Ma, Q., Chen, H., Jarillo-Herrero, P., Dai, S.: Configurable phonon polaritons in twisted α-moo3. Nature materials19(12), 1307–1311 (2020)

    2020

  37. [38]

    ACS nano17(19), 19313–19322 (2023)

    Obst, M., Nooerenberg, T., ´Alvarez-P´ erez, G., de Oliveira, T.V., Taboada- Guti´ errez, J., Feres, F.H., Kaps, F.G., Hatem, O., Luferau, A., Nikitin, A.Y.,et al.: Terahertz twistoptics–engineering canalized phonon polari- tons. ACS nano17(19), 19313–19322 (2023)

    2023

  38. [39]

    Nature Materials22(7), 867–872 (2023)

    Duan, J., ´Alvarez-P´ erez, G., Lanza, C., Voronin, K., Tresguerres-Mata, A.I., Capote-Robayna, N., ´Alvarez-Cuervo, J., Tarazaga Mart´ ın-Luengo, 66 A., Mart´ ın-S´ anchez, J., Volkov, V.S.,et al.: Multiple and spectrally robust photonic magic angles in reconfigurableα-moo3 trilayers. Nature Materials22(7), 867–872 (2023)

    2023

  39. [40]

    Nature Communications16(1), 2953 (2025)

    Zhou, L., Ni, X., Wang, Z., Renzi, E.M., Xu, J., Zhou, Z., Yin, Y., Yin, Y., Song, R., Zhao, Z., Yu, K., Huang, D., Wang, Z., Cheng, X., Al` u, A., Jiang, T.: Engineering shear polaritons in 2d twisted heterostruc- tures. Nature Communications16(1), 2953 (2025). https://doi.org/10. 1038/s41467-025-58197-4

    2025

  40. [41]

    Science advances7(14), 2690 (2021)

    Duan, J., ´Alvarez-P´ erez, G., Voronin, K.V., Prieto, I., Taboada-Guti´ errez, J., Volkov, V.S., Mart´ ın-S´ anchez, J., Nikitin, A.Y., Alonso-Gonz´ alez, P.: Enabling propagation of anisotropic polaritons along forbidden directions via a topological transition. Science advances7(14), 2690 (2021)

    2021

  41. [42]

    Nature Nanotechnology17(9), 940–946 (2022)

    Hu, H., Chen, N., Teng, H., Yu, R., Qu, Y., Sun, J., Xue, M., Hu, D., Wu, B., Li, C., Chen, J., Liu, M., Sun, Z., Liu, Y., Li, P., Fan, S., Garc´ ıa de Abajo, F.J., Dai, Q.: Doping-driven topological polaritons in graphene/α- moo3 heterostructures. Nature Nanotechnology17(9), 940–946 (2022). https://doi.org/10.1038/s41565-022-01185-2

    work page doi:10.1038/s41565-022-01185-2 2022

  42. [43]

    Science advances 11(7), 0569 (2025)

    Duan, J., Mart´ ın-Luengo, A.T., Lanza, C., Partel, S., Voronin, K., Tresguerres-Mata, A.I.F., ´Alvarez-P´ erez, G., Nikitin, A.Y., Mart´ ın- S´ anchez, J., Alonso-Gonz´ alez, P.: Canalization-based super-resolution imaging using an individual van der waals thin layer. Science advances 11(7), 0569 (2025)

    2025

  43. [44]

    Nano Letters25(7), 67 2610–2617 (2025)

    Zhu, J., Gong, Y., Liang, J., Zhao, Y., Cui, Z., Li, D., Ou, Q., Zhang, Y., Wang, G.P.: Multiple hyperbolic dispersion branches and broadband canalization in a phonon-polaritonic heterostructure. Nano Letters25(7), 67 2610–2617 (2025)

    2025

  44. [45]

    Science Advances11(50), 6278 (2025)

    Zhang, L., Ding, X., Dong, J., Fan, J., Wu, W., Ren, M., Luo, W., Cai, W., Xu, J.: Ultimate tuning of hyperbolic phonon polaritons. Science Advances11(50), 6278 (2025)

    2025

  45. [46]

    npj 2D Materials and Applications6(1), 5 (2022)

    Chang, P.-H., Lin, C., Helmy, A.S.: Field canalization using anisotropic 2d plasmonics. npj 2D Materials and Applications6(1), 5 (2022)

    2022

  46. [47]

    Heil, Philip M

    Ter´ an-Garc´ ıa, E., Lanza, C., Voronin, K., Mart´ ın-S´ anchez, J., Nikitin, A.Y., Tarazaga Mart´ ın-Luengo, A., Alonso-Gonz´ alez, P.: Real-space visu- alization of canalized ray polaritons in a single van der waals thin slab. Nano Letters25(6), 2203–2209 (2025). https://doi.org/10.1021/acs. nanolett.4c05277

    work page doi:10.1021/acs 2025

  47. [48]

    Optica12(3), 343–349 (2025)

    Wang, K., Huang, Z., Xiong, L., Wang, K., Bai, Y., Long, H., Deng, N., Wang, B., Hu, G., Lu, P.: Observation of canalized phonon polaritons in a singleα-moo 3 flake. Optica12(3), 343–349 (2025). https://doi.org/10. 1364/OPTICA.547698

    2025

  48. [49]

    Nature Communications15(1), 2696 (2024)

    Tresguerres-Mata, A.I.F., Lanza, C., Taboada-Guti´ errez, J., Matson, J.R., ´Alvarez-P´ erez, G., Isobe, M., Tarazaga Mart´ ın-Luengo, A., Duan, J., Partel, S., V´ elez, M., Mart´ ın-S´ anchez, J., Nikitin, A.Y., Caldwell, J.D., Alonso-Gonz´ alez, P.: Observation of naturally canalized phonon polari- tons in liv 2o5 thin layers. Nature Communications15(1)...

    work page doi:10.1038/s41467-024-46935-z 2024

  49. [50]

    Science Advances11(29), 3452 (2025)

    D´ ıaz-N´ u˜ nez, P., Lanza, C., Wang, Z., Kravets, V.G., Duan, J.,´Alvarez- Cuervo, J., Tarazaga Mart´ ın-Luengo, A., Grigorenko, A.N., Yang, Q., 68 Paarmann, A., Caldwell, J., Alonso-Gonz´ alez, P., Mishchenko, A.: Visu- alization of topological shear polaritons in gypsum thin films. Science Advances11(29), 3452 (2025). https://doi.org/10.1126/sciadv.adw3452

    work page doi:10.1126/sciadv.adw3452 2025

  50. [51]

    Nature Communications 15(1), 7047 (2024)

    Zheng, C., Hu, G., Wei, J., Ma, X., Li, Z., Chen, Y., Ni, Z., Li, P., Wang, Q., Qiu, C.-W.: Hyperbolic-to-hyperbolic transition at exceptional rest- strahlen point in rare-earth oxyorthosilicates. Nature Communications 15(1), 7047 (2024)

    2024

  51. [52]

    arXiv preprint arXiv:2604.12174 (2026)

    Shiravi, H., Zheng, W., Rhodes, D., Balicas, L., Zhou, H., Ni, G.: Tun- able polariton canalization in natural van der waals oxide. arXiv preprint arXiv:2604.12174 (2026)

    Pith/arXiv arXiv 2026

  52. [53]

    Advanced Materials, 2504526 (2025)

    Ou, Q., Xue, S., Ma, W., Yang, J., Si, G., Liu, L., Zhong, G., Liu, J., Xie, Z., Xiao, Y., et al.: Natural van der waals canalization lens for non-destructive nanoelectronic circuit imaging and inspection. Advanced Materials, 2504526 (2025)

    2025

  53. [54]

    Nature644(8075), 76–82 (2025)

    Liu, L., Xiong, L., Wang, C., Bai, Y., Ma, W., Wang, Y., Li, P., Li, G., Wang, Q.J., Garcia-Vidal, F.J., Dai, Z., Hu, G.: Long-range hyperbolic polaritons on a non-hyperbolic crystal surface. Nature644(8075), 76–82 (2025). https://doi.org/10.1038/s41586-025-09288-1

    work page doi:10.1038/s41586-025-09288-1 2025

  54. [55]

    Nature Communications15, 2623 (2024)

    Xing, Q., Zhang, J., Fang, Y., Song, C., Zhao, T., Mou, Y., Wang, C., Ma, J., Xie, Y., Huang, S., Mu, L., Lei, Y., Shi, W., Huang, F., Yan, H.: Tunable anisotropic van der waals films of 2m-ws2 for plasmon canaliza- tion. Nature Communications15, 2623 (2024). https://doi.org/10.1038/ s41467-024-46963-9

    2024

  55. [56]

    Physical Review Materials4(4), 041001 (2020)

    Wang, Z., Huang, M., Zhao, J., Chen, C., Huang, H., Wang, X., Liu, P., 69 Wang, J., Xiang, J., Feng, C.,et al.: Fermi liquid behavior and colossal magnetoresistance in layered mooc l 2. Physical Review Materials4(4), 041001 (2020)

    2020

  56. [57]

    ACS Nano19(27), 25413– 25421 (2025)

    Melchioni, N., Mancini, A., Nan, L., Efimova, A., Venturi, G., Ambrosio, A.: Giant optical anisotropy in a natural van der waals hyperbolic crystal for visible light low-loss polarization control. ACS Nano19(27), 25413– 25421 (2025). https://doi.org/10.1021/acsnano.5c07323

    work page doi:10.1021/acsnano.5c07323 2025

  57. [58]

    Nano Letters26(13), 4329–4338 (2026)

    Ermolaev, G., Toksumakov, A., Slavich, A., Minnekhanov, A., Tselikov, G., Mazitov, A., Kruglov, I., Tikhonowski, G., Mironov, M., Radko, I.P., et al.: Giant optical anisotropy and visible-frequency epsilon-near-zero in hyperbolic van der waals moocl2. Nano Letters26(13), 4329–4338 (2026)

    2026

  58. [59]

    arXiv preprint arXiv:2602.01072 (2026)

    Melchioni, N., Mancini, A., Ambrosio, A.: Anisotropic electron gas in a hyperbolic van der waals material. arXiv preprint arXiv:2602.01072 (2026)

    arXiv 2026

  59. [60]

    Physical Review B102(24), 245419 (2020)

    Zhao, J., Wu, W., Zhu, J., Lu, Y., Xiang, B., Yang, S.A.: Highly anisotropic two-dimensional metal in monolayer moocl 2. Physical Review B102(24), 245419 (2020)

    2020

  60. [61]

    Physical Review B100(23), 235408 (2019)

    ´Alvarez-P´ erez, G., Voronin, K.V., Volkov, V.S., Alonso-Gonz´ alez, P., Nikitin, A.Y.: Analytical approximations for the dispersion of electro- magnetic modes in slabs of biaxial crystals. Physical Review B100(23), 235408 (2019)

    2019

  61. [62]

    Journal of the Optical 70 Society of America B34(10), 2128–2139 (2017)

    Passler, N.C., Paarmann, A.: Generalized 4×4 matrix formalism for light propagation in anisotropic stratified media: study of surface phonon polaritons in polar dielectric heterostructures. Journal of the Optical 70 Society of America B34(10), 2128–2139 (2017)

    2017

  62. [63]

    Nanophotonics9(2), 509–522 (2020)

    Kaltenecker, K.J., Krauss, E., Casses, L., Geisler, M., Hecht, B., Mortensen, N.A., Jepsen, P.U., Stenger, N.: Mono-crystalline gold platelets: a high-quality platform for surface plasmon polaritons. Nanophotonics9(2), 509–522 (2020)

    2020

  63. [64]

    ACS Photonics9(11), 3696– 3704 (2022)

    Mancini, A., Nan, L., Wendisch, F.J., Bert´ e, R., Ren, H., Cort´ es, E., Maier, S.A.: Near-field retrieval of the surface phonon polariton dispersion in free-standing silicon carbide thin films. ACS Photonics9(11), 3696– 3704 (2022)

    2022

  64. [65]

    Applied Physics Letters89(10) (2006)

    Ocelic, N., Huber, A., Hillenbrand, R.: Pseudoheterodyne detection for background-free near-field spectroscopy. Applied Physics Letters89(10) (2006)

    2006

  65. [66]

    Cambridge university press, ??? (2002)

    Dressel, M., Gr¨ uner, G.: Electrodynamics of Solids: Optical Properties of Electrons in Matter. Cambridge university press, ??? (2002)

    2002

  66. [67]

    Science387(6735), 786–791 (2025)

    Ruta, F.L., Shao, Y., Acharya, S., Mu, A., Jo, N.H., Ryu, S.H., Balatsky, D., Su, Y., Pashov, D., Kim, B.S.,et al.: Good plasmons in a bad metal. Science387(6735), 786–791 (2025)

    2025

  67. [68]

    Cambridge university press, Cambridge (2012)

    Novotny, L., Hecht, B.: Principles of Nano-optics. Cambridge university press, Cambridge (2012)

    2012

  68. [69]

    Elight3(1), 14 (2023)

    Hu, C., Sun, T., Zeng, Y., Ma, W., Dai, Z., Yang, X., Zhang, X., Li, P.: Source-configured symmetry-broken hyperbolic polaritons. Elight3(1), 14 (2023)

    2023

  69. [70]

    Light: Science & Applications7(1), 27 (2018)

    Ambrosio, A., Tamagnone, M., Chaudhary, K., Jauregui, L.A., Kim, P., 71 Wilson, W.L., Capasso, F.: Selective excitation and imaging of ultraslow phonon polaritons in thin hexagonal boron nitride crystals. Light: Science & Applications7(1), 27 (2018)

    2018

  70. [71]

    Science advances8(28), 0627 (2022) 72

    Menabde, S.G., Boroviks, S., Ahn, J., Heiden, J.T., Watanabe, K., Taniguchi, T., Low, T., Hwang, D.K., Mortensen, N.A., Jang, M.S.: Near- field probing of image phonon-polaritons in hexagonal boron nitride on gold crystals. Science advances8(28), 0627 (2022) 72

    2022