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arxiv: 2605.18272 · v1 · pith:FHJ74WGZnew · submitted 2026-05-18 · ⚛️ physics.optics · quant-ph

Energy-Resolved Eigenmode Spectroscopy of 1-D and 2-D Non-Hermitian Skin Effects

Rohith Srikanth , Sashank Kaushik Sridhar , Avik Dutt This is my paper

Pith reviewed 2026-05-20 00:14 UTC · model grok-4.3

classification ⚛️ physics.optics quant-ph
keywords non-Hermitian skin effectfrequency synthetic dimensioneigenmode spectroscopyring resonatorboundary localizationelectro-optic modulation2D synthetic latticesdirectional transport
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The pith

Electro-optically modulated ring resonators enable energy-resolved mapping of skin modes in finite non-Hermitian lattices.

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

The paper develops a spectroscopic technique to resolve individual eigenmodes of non-Hermitian lattices that display the skin effect, in which bulk states collapse into boundary-localized modes. Strong frequency boundaries are imposed in an electro-optically modulated ring resonator to create finite lattices in a synthetic frequency dimension. Laser detuning then scans the eigenenergies while site-resolved heterodyne measurements reconstruct each mode's spatial profile. This approach reveals skin states localized at boundaries across the spectrum, with their displacement from the edge depending on energy. The same architecture, when extended with long-range couplings, produces 2D frequency lattices that exhibit tunable directional transport and edge localization.

Core claim

By introducing strong frequency-domain boundaries in an electro-optically modulated ring resonator, finite non-Hermitian lattices are realized and laser detuning is used as a spectroscopic axis for the eigenenergies of the effective Hamiltonian. Site-resolved heterodyne measurements reconstruct the spatial profile of each mode, revealing boundary-localized skin states throughout the spectrum and their eigenenergy-dependent displacement from the edge. In 2D, the frequency-boundary architecture with long-range couplings produces genuine 2D frequency lattices that display tunable directional transport and edge localization in two synthetic dimensions.

What carries the argument

Frequency synthetic dimension formed by electro-optic modulation in a ring resonator with imposed boundaries, using laser detuning and heterodyne detection to probe the eigenmodes of finite non-Hermitian Hamiltonians.

If this is right

  • Skin states appear throughout the spectrum rather than only near specific energies.
  • The position of skin-mode localization shifts systematically with eigenenergy.
  • Genuine 2D lattices arise from long-range couplings between finite 1D segments instead of folded 1D systems.
  • Directional transport becomes tunable by adjusting couplings or boundaries in the two synthetic dimensions.
  • Eigenmode spectroscopy provides direct experimental access to non-Hermitian bulk-boundary correspondence.

Where Pith is reading between the lines

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

  • The technique could be adapted to probe exceptional points or other non-Hermitian spectral features by scanning across parameter space.
  • Adding more synthetic dimensions might enable studies of non-Hermitian physics in three or higher dimensions within the same optical platform.
  • Exploiting the energy dependence of skin-mode displacement could improve sensing protocols that rely on boundary localization.
  • The method opens a route to test non-Hermitian lattice models that are difficult to realize in solid-state or atomic systems.

Load-bearing premise

The modulated ring resonator with imposed frequency boundaries accurately realizes an ideal finite non-Hermitian lattice Hamiltonian, and heterodyne measurements faithfully reconstruct mode profiles without significant artifacts or unmodeled couplings.

What would settle it

Reconstructed spatial profiles that lack boundary localization or fail to exhibit the predicted eigenenergy-dependent displacement from the edge for a range of modes would contradict the central claim.

Figures

Figures reproduced from arXiv: 2605.18272 by Avik Dutt, Rohith Srikanth, Sashank Kaushik Sridhar.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Experimental schematic of a ring resonator that supports equally spaced frequency modes coupled to an auxiliary [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) The 1-D finite lattice in frequency has two frequency mirrors in a ring resonator with modest finesse, leading to [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Steady state occupations of a slightly larger bounded 7-site (a) Hermitian (H) lattice and (b) non-Hermitian (NH) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) 2-D lattice construction from finite lattice chain. The 2-D lattice on the left does not have the twisted coupling [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Non-Hermitian lattices can host the non-Hermitian skin effect, a boundary-induced collapse of all bulk eigenstates into exponentially localized edge modes. This effect underlies anomalous bulk-boundary correspondence and remarkable enhancements in non-Hermitian sensing, yet direct energy-resolved access to the eigenmodes of non-Hermitian lattices has remained limited. Here we report band- and energy-resolved eigenmode spectroscopy of skin modes in a frequency synthetic dimension. By introducing strong frequency-domain boundaries in an electro-optically modulated ring resonator, we realize finite non-Hermitian lattices and use laser detuning as a spectroscopic axis for the eigenenergies of the effective Hamiltonian. Site-resolved heterodyne measurements then reconstruct the spatial profile of each mode, revealing boundary-localized skin states throughout the spectrum and their eigenenergy-dependent displacement from the edge. Beyond 1D, the same frequency-boundary architecture, upon incorporating long-range couplings between finite lattices, produces genuine 2D frequency lattices rather than the hitherto-realized folded 1D systems on twisted tubes. In these lattices we observe tunable directional transport and edge localization in two synthetic dimensions. Our results introduce eigenmode spectroscopy as a direct probe of non-Hermitian physics and establish strongly bounded frequency lattices as a flexible platform for Hamiltonian engineering.

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

1 major / 2 minor

Summary. The manuscript reports an experimental platform for energy-resolved eigenmode spectroscopy of non-Hermitian skin effects in frequency synthetic dimensions. Using an electro-optically modulated ring resonator with strong frequency-domain boundaries, the authors realize finite 1D and 2D non-Hermitian lattices, employ laser detuning as an energy axis, and use site-resolved heterodyne detection to reconstruct mode profiles, observing boundary-localized skin states with energy-dependent displacement in 1D and tunable directional transport plus edge localization in 2D.

Significance. If the experimental system faithfully implements the target non-Hermitian Hamiltonians, the work supplies a direct spectroscopic probe of skin-mode localization across the spectrum and a scalable route to 2D frequency lattices, which could strengthen non-Hermitian sensing applications and clarify bulk-boundary correspondence in open systems.

major comments (1)
  1. [Abstract and §2] The central claim that strong frequency-domain boundaries imposed by electro-optic modulation realize a clean finite non-Hermitian lattice Hamiltonian (Abstract and §2) is load-bearing for all reported observations of energy-dependent skin-mode displacement and 2D directional transport. The manuscript does not provide quantitative bounds on deviations arising from finite modulator bandwidth, residual ring dispersion, or higher-order sideband couplings; such deviations would generically produce non-uniform hopping amplitudes or additional loss channels that alter the precise non-Hermitian structure to which the skin effect is sensitive.
minor comments (2)
  1. [Figure 3] Figure captions should explicitly state the number of independent experimental runs and the criterion used to identify a mode as 'boundary-localized' (e.g., participation ratio threshold).
  2. [Eq. (5)] Notation for the effective hopping amplitudes in the 2D lattice (Eq. (5)) should be cross-referenced to the measured modulation parameters to allow direct comparison with the 1D case.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for raising this important point about the fidelity of the effective non-Hermitian Hamiltonian. We address the major comment below and will revise the manuscript to incorporate additional quantitative analysis.

read point-by-point responses

  1. Referee: [Abstract and §2] The central claim that strong frequency-domain boundaries imposed by electro-optic modulation realize a clean finite non-Hermitian lattice Hamiltonian (Abstract and §2) is load-bearing for all reported observations of energy-dependent skin-mode displacement and 2D directional transport. The manuscript does not provide quantitative bounds on deviations arising from finite modulator bandwidth, residual ring dispersion, or higher-order sideband couplings; such deviations would generically produce non-uniform hopping amplitudes or additional loss channels that alter the precise non-Hermitian structure to which the skin effect is sensitive.

    Authors: We agree that explicit quantitative bounds on deviations from the ideal model are valuable for rigorously validating the effective Hamiltonian. The original manuscript derives the target non-Hermitian lattice from the modulated ring resonator under the assumption of strong boundaries and limited sideband generation, with experimental results shown to be consistent with this model. However, we did not include a dedicated quantitative error analysis for finite modulator bandwidth, residual dispersion, or higher-order couplings. In the revised manuscript we will add a new subsection (or appendix) to §2 that provides these bounds. Using our experimental parameters, we will estimate the resulting non-uniformity in hopping amplitudes (expected to remain below a few percent) and show that any additional loss channels are negligible relative to the designed non-Hermitian gain/loss terms. This analysis will confirm that the observed energy-dependent skin-mode displacement and 2D directional transport arise from the intended Hamiltonian structure. revision: yes

Circularity Check

0 steps flagged

No circularity: direct experimental measurements of skin modes

full rationale

This is an experimental paper whose central claims consist of direct observations via laser detuning spectroscopy and site-resolved heterodyne measurements in a modulated ring resonator. No derivation chain, first-principles prediction, or fitted parameter is presented that reduces by construction to the inputs; the effective non-Hermitian lattice is realized physically and its eigenmodes are read out experimentally rather than derived mathematically. The mapping from setup to Hamiltonian is an empirical assumption tested by the measurements themselves, not a self-referential definition or self-citation load-bearing step. Score remains at the low end appropriate for self-contained experimental work.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work rests on standard assumptions of synthetic dimension physics and non-Hermitian effective Hamiltonians, with experimental parameters such as modulation depth tuned to realize desired boundaries and couplings.

free parameters (1)
  • modulation amplitude and frequency
    Tuned to set the strength of frequency-domain couplings and boundaries in the effective lattice model.
axioms (1)
  • domain assumption The electro-optically modulated ring resonator dynamics are well-approximated by a non-Hermitian tight-binding Hamiltonian in the frequency synthetic dimension.
    Invoked when mapping the physical system to finite 1D and 2D lattices with skin effect.

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Works this paper leans on

49 extracted references · 49 canonical work pages

  1. [1]

    Hatano and D

    N. Hatano and D. R. Nelson, Localization Transitions in Non-Hermitian Quantum Mechanics, Phys. Rev. Lett. 77, 570 (1996). 7

    work page 1996

  2. [2]

    V. M. Martinez Alvarez, J. E. Barrios Vargas, and L. E. F. Foa Torres, Non-hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points, Phys. Rev. B97, 121401(R) (2018)

    work page 2018

  3. [3]

    Yao and Z

    S. Yao and Z. Wang, Edge states and topological in- variants of non-hermitian systems, Phys. Rev. Lett.121, 086803 (2018)

    work page 2018

  4. [4]

    Okuma, K

    N. Okuma, K. Kawabata, K. Shiozaki, and M. Sato, Topological Origin of Non-Hermitian Skin Effects, Phys. Rev. Lett.124, 086801 (2020)

    work page 2020

  5. [5]

    McDonald and A

    A. McDonald and A. A. Clerk, Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics, Nat Commun11, 5382 (2020)

    work page 2020

  6. [6]

    S. Liu, R. Shao, S. Ma, L. Zhang, O. You, H. Wu, Y. J. Xiang, T. J. Cui, and S. Zhang, Non-hermitian skin ef- fect in a non-hermitian electrical circuit, Research2021, 10.34133/2021/5608038 (2021)

    work page doi:10.34133/2021/5608038 2021

  7. [7]

    H. Yuan, W. Zhang, Z. Zhou, W. Wang, N. Pan, Y. Feng, H. Sun, and X. Zhang, Non-hermitian topolectrical cir- cuit sensor with high sensitivity, Advanced Science10, 10.1002/advs.202301128 (2023)

    work page doi:10.1002/advs.202301128 2023

  8. [8]

    Parto, C

    M. Parto, C. Leefmans, J. Williams, R. M. Gray, and A. Marandi, Enhanced sensitivity via non- hermitian topology, Light: Science & Applications14, 10.1038/s41377-024-01667-z (2025)

    work page doi:10.1038/s41377-024-01667-z 2025

  9. [9]

    Q. Wang, Z. Fu, L. Ye, H. He, W. Deng, J. Lu, M. Ke, and Z. Liu, Observation of supersensitivity of non-hermitian skin effect, Phys. Rev. Res.7, L042057 (2025)

    work page 2025

  10. [10]

    Ghatak, M

    A. Ghatak, M. Brandenbourger, J. van Wezel, and C. Coulais, Observation of non-Hermitian topology and its bulk–edge correspondence in an active mechanical metamaterial, Proceedings of the National Academy of Sciences117, 29561 (2020)

    work page 2020

  11. [11]

    Cost function dependent barren plateaus in shallow parametrized quan- tum circuits

    X. Zhang, Y. Tian, J.-H. Jiang, M.-H. Lu, and Y.-F. Chen, Observation of higher-order non-hermitian skin effect, Nature Communications12, 10.1038/s41467-021- 25716-y (2021)

    work page doi:10.1038/s41467-021- 2021

  12. [12]

    Z. Gu, H. Gao, H. Xue, J. Li, Z. Su, and J. Zhu, Transient non-hermitian skin effect, Nature Communications13, 10.1038/s41467-022-35448-2 (2022)

    work page doi:10.1038/s41467-022-35448-2 2022

  13. [13]

    Helbig, T

    T. Helbig, T. Hofmann, S. Imhof, M. Abdelghany, T. Kiessling, L. W. Molenkamp, C. H. Lee, A. Szameit, M. Greiter, and R. Thomale, Generalized bulk–boundary correspondence in non-hermitian topolectrical circuits, Nature Physics16, 747–750 (2020)

    work page 2020

  14. [14]

    Zhu, X.-Q

    P. Zhu, X.-Q. Sun, T. L. Hughes, and G. Bahl, Higher rank chirality and non-Hermitian skin effect in a topolec- trical circuit, Nat Commun14, 720 (2023)

    work page 2023

  15. [15]

    Liang, D

    Q. Liang, D. Xie, Z. Dong, H. Li, H. Li, B. Gadway, W. Yi, and B. Yan, Dynamic signatures of non-hermitian skin effect and topology in ultracold atoms, Phys. Rev. Lett.129, 070401 (2022)

    work page 2022

  16. [16]

    E. Zhao, Z. Wang, C. He, T. F. J. Poon, K. K. Pak, Y.- J. Liu, P. Ren, X.-J. Liu, and G.-B. Jo, Two-dimensional non-hermitian skin effect in an ultracold fermi gas, Na- ture637, 565–573 (2025)

    work page 2025

  17. [17]

    Weidemann, M

    S. Weidemann, M. Kremer, T. Helbig, T. Hofmann, A. Stegmaier, M. Greiter, R. Thomale, and A. Szameit, Topological funneling of light, Science368, 311 (2020)

    work page 2020

  18. [18]

    L. Xiao, T. Deng, K. Wang, G. Zhu, Z. Wang, W. Yi, and P. Xue, Non-hermitian bulk–boundary correspondence in quantum dynamics, Nature Physics16, 761–766 (2020)

    work page 2020

  19. [19]

    K. Wang, A. Dutt, K. Y. Yang, C. C. Wojcik, J. Vuˇ ckovi´ c, and S. Fan, Generating arbitrary topologi- cal windings of a non-Hermitian band, Science371, 1240 (2021)

    work page 2021

  20. [20]

    K. Wang, A. Dutt, C. C. Wojcik, and S. Fan, Topological complex-energy braiding of non-Hermitian bands, Nature 598, 59 (2021)

    work page 2021

  21. [21]

    R. Ye, Y. He, G. Li, L. Wang, X. Wu, X. Qiao, Y. Zheng, L. Jin, D.-W. Wang, L. Yuan, and X. Chen, Observ- ing non-hermiticity induced chirality breaking in a syn- thetic hall ladder, Light: Science & Applications14, 10.1038/s41377-024-01700-1 (2025)

    work page doi:10.1038/s41377-024-01700-1 2025

  22. [22]

    O. E. ¨Orsel, J. Noh, P. Zhu, J. Yim, T. L. Hughes, R. Thomale, and G. Bahl, Giant Nonreciprocity and Gy- ration through Modulation-Induced Hatano-Nelson Cou- pling in Integrated Photonics, Phys. Rev. Lett.134, 153801 (2025)

    work page 2025

  23. [23]

    Blanchard, A

    P.-E. Blanchard, A. McDonald, and P. St-Jean, Expo- nentially enhanced sensing through nonreciprocal light propagation (2025), arXiv:2511.16895 [physics]

    work page arXiv 2025

  24. [24]

    D. Yu, W. Song, L. Wang, R. Srikanth, S. K. Sridhar, T. Chen, C. Huang, G. Li, X. Qiao, X. Wu, Z. Dong, Y. He, M. Xiao, X. Chen, A. Dutt, B. Gadway, and L. Yuan, Comprehensive review on developments of syn- thetic dimensions, pi4, R06 (2025)

    work page 2025

  25. [25]

    Koch and J

    R. Koch and J. C. Budich, Bulk-boundary correspon- dence in non-Hermitian systems: stability analysis for generalized boundary conditions, Eur. Phys. J. D74, 70 (2020)

    work page 2020

  26. [26]

    H. Wang, J. Zhong, and S. Fan, Non-hermitian photonic band winding and skin effects: a tutorial, Advances in Optics and Photonics16, 659 (2024)

    work page 2024

  27. [27]

    S. K. Sridhar, R. Srikanth, A. R. Miller, F. J. McComb, and A. Dutt, Measuring Z2 invariants in dimer models and cross-coupled ladders with a programmable photonic molecule (2025)

    work page 2025

  28. [28]

    A. Dutt, L. Yuan, K. Y. Yang, K. Wang, S. Buddhiraju, J. Vuˇ ckovi´ c, and S. Fan, Creating boundaries along a synthetic frequency dimension, Nat Commun13, 3377 (2022)

    work page 2022

  29. [29]

    Y. Hu, M. Yu, N. Sinclair, D. Zhu, R. Cheng, C. Wang, and M. Lonˇ car, Mirror-induced reflection in the fre- quency domain, Nat Commun13, 6293 (2022), number: 1

    work page 2022

  30. [30]

    A. Dutt, M. Minkov, Q. Lin, L. Yuan, D. A. B. Miller, and S. Fan, Experimental band structure spectroscopy along a synthetic dimension, Nature Communications10, 3122 (2019)

    work page 2019

  31. [31]

    A. Dutt, Q. Lin, L. Yuan, M. Minkov, M. Xiao, and S. Fan, A single photonic cavity with two independent physical synthetic dimensions, Science367, 59 (2020)

    work page 2020

  32. [32]

    G. Li, Y. Zheng, A. Dutt, D. Yu, Q. Shan, S. Liu, L. Yuan, S. Fan, and X. Chen, Dynamic band structure measurement in the synthetic space, Science Advances7, eabe4335 (2021)

    work page 2021

  33. [33]

    Balˇ cytis, T

    A. Balˇ cytis, T. Ozawa, Y. Ota, S. Iwamoto, J. Maeda, and T. Baba, Synthetic dimension band structures on a Si CMOS photonic platform, Science Advances8, eabk0468 (2022)

    work page 2022

  34. [34]

    Senanian, L

    A. Senanian, L. G. Wright, P. F. Wade, H. K. Doyle, and P. L. McMahon, Programmable large-scale simulation of bosonic transport in optical synthetic frequency lattices, Nat. Phys.19, 1333 (2023). 8

    work page 2023

  35. [35]

    G. Li, L. Wang, R. Ye, Y. Zheng, D.-W. Wang, X.-J. Liu, A. Dutt, L. Yuan, and X. Chen, Direct extraction of topological Zak phase with the synthetic dimension, Light Sci Appl12, 81 (2023)

    work page 2023

  36. [36]

    Cheng, E

    D. Cheng, E. Lustig, K. Wang, and S. Fan, Multi- dimensional band structure spectroscopy in the synthetic frequency dimension, Light: Science & Applications12, 158 (2023)

    work page 2023

  37. [37]

    H. X. Dinh, A. Balˇ cytis, T. Ozawa, Y. Ota, G. Ren, T. Baba, S. Iwamoto, A. Mitchell, and T. G. Nguyen, Reconfigurable synthetic dimension frequency lattices in an integrated lithium niobate ring cavity, Commun Phys 7, 1 (2024)

    work page 2024

  38. [38]

    Pellerin, R

    F. Pellerin, R. Houvenaghel, W. Coish, I. Carusotto, and P. St-Jean, Wave-Function Tomography of Topological Dimer Chains with Long-Range Couplings, Phys. Rev. Lett.132, 183802 (2024)

    work page 2024

  39. [39]

    Ch` enier, B

    A. Ch` enier, B. d’Aligny, F. Pellerin, P.-E. Blanchard, T. Ozawa, I. Carusotto, and P. St-Jean, Quantized Hall drift in a frequency-encoded photonic Chern insulator, arXiv:2412.04347 10.48550/arXiv.2412.04347 (2024)

    work page doi:10.48550/arxiv.2412.04347 2024

  40. [40]

    Wang, X.-D

    Z.-A. Wang, X.-D. Zeng, Y.-T. Wang, J.-M. Ren, C. Ao, Z.-P. Li, W. Liu, N.-J. Guo, L.-K. Xie, J.-Y. Liu, Y.-H. Ma, Y.-Q. Wu, X.-W. Luo, S. Wang, J.-S. Tang, C.-F. Li, and G.-C. Guo, Versatile photonic frequency synthetic dimensions using a single programmable on-chip device, Nature Communications16, 10.1038/s41467-025-63114- w (2025)

    work page doi:10.1038/s41467-025-63114- 2025

  41. [41]

    R. Ye, G. Li, S. Wan, X. Xue, P.-Y. Wang, X. Qiao, L. Wang, H. Li, S. Liu, J. Wang, R. Ma, F. Bo, Y. Zheng, C.-H. Dong, L. Yuan, and X. Chen, Construction of var- ious time-varying hamiltonians on thin-film lithium nio- bate chip, Phys. Rev. Lett.134, 163802 (2025)

    work page 2025

  42. [42]

    Zhang, B

    M. Zhang, B. Buscaino, C. Wang, A. Shams-Ansari, C. Reimer, R. Zhu, J. M. Kahn, and M. Lonˇ car, Broadband electro-optic frequency comb generation in a lithium niobate microring resonator, Nature568, 373 (2019)

    work page 2019

  43. [43]

    A. Yang, Z. Fang, K. Zhang, and C. Fang, Tailoring bound state geometry in high-dimensional non-hermitian systems, Communications Physics8, 10.1038/s42005- 025-02037-w (2025)

    work page doi:10.1038/s42005- 2025

  44. [44]

    Montag and F

    A. Montag and F. K. Kunst, Symmetry-induced higher- order exceptional points in two dimensions, Phys. Rev. Res.6, 023205 (2024)

    work page 2024

  45. [45]

    H. Zhao, X. Qiao, T. Wu, B. Midya, S. Longhi, and L. Feng, Non-Hermitian topological light steering, Sci- ence365, 1163 (2019)

    work page 2019

  46. [46]

    D. Zou, T. Chen, W. He, J. Bao, C. H. Lee, H. Sun, and X. Zhang, Observation of hybrid higher-order skin- topological effect in non-hermitian topolectrical circuits, Nature Communications12, 10.1038/s41467-021-26414- 5 (2021)

    work page doi:10.1038/s41467-021-26414- 2021

  47. [47]

    Zheng, M

    X. Zheng, M. Jalali Mehrabad, J. Vannucci, K. Li, A. Dutt, M. Hafezi, S. Mittal, and E. Waks, Dynamic control of 2D non-Hermitian photonic corner skin modes in synthetic dimensions, Nat Commun15, 10881 (2024)

    work page 2024

  48. [48]

    L. Yuan, M. Xiao, Q. Lin, and S. Fan, Synthetic-space with arbitrary dimensions in a few rings undergoing dy- namic modulation, Physical Review B97, 104105 (2018)

    work page 2018

  49. [49]

    K. Wang, B. A. Bell, A. S. Solntsev, D. N. Neshev, B. J. Eggleton, and A. A. Sukhorukov, Multidimensional syn- thetic chiral-tube lattices via nonlinear frequency conver- sion, Light: Science & Applications9, 132 (2020)

    work page 2020