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arxiv: 2504.08292 · v4 · submitted 2025-04-11 · ⚛️ physics.optics

Study of polarization-dependent band inversions and edge states from two-dimensional square lattice plasmonic crystals

T.H. Chan , Y.H. Guan , C. Liu , H.C. Ong This is my paper

Pith reviewed 2026-05-22 21:05 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords plasmonic crystalsband topologyedge statespolarizationsquare latticenanohole arraysband inversionfar-field spectroscopy
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0 comments X

The pith

Polarization-dependent band inversions at Γ and X points in square lattice plasmonic crystals enable selective 0D and 1D edge states.

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

The paper formulates far-field characteristics of eigenmodes at high symmetry points in 2D square lattice plasmonic systems. It shows that unlike the conventional tight-binding model, several polarization-dependent band inversions occur at the Γ and X points, producing subtle changes in band topology. Tuning the system geometry creates transitions between trivial and non-trivial phases. This yields polarization-selective 0D and 1D edge states that possess distinct field symmetries. The evolution of these states depends on the degree of bulk-edge overlapping, and the predictions are verified by angle- and polarization-resolved diffraction spectroscopy on Au nanohole arrays.

Core claim

Several polarization-dependent band inversions occur at the Γ and X points in 2D square lattice plasmonic systems, causing subtle changes in band topology. Tuning the system geometry facilitates trivial and non-trivial phases, realizing polarization selective 0D and 1D edge states with distinct field symmetries. The evolution of 0D or 1D edge states depends on the degree of bulk-edge overlapping, and far-field radiations allow probing of this topology in leaky electromagnetic systems.

What carries the argument

Far-field characteristics of eigenmodes at high symmetry points (HSPs) in the Brillouin zone, which retain eigenmode information to probe band topology despite leaky electromagnetic systems.

If this is right

  • Polarization selective 0D and 1D edge states with distinct field symmetries can be realized through geometry tuning.
  • The evolution of edge states depends on the degree of bulk-edge overlapping.
  • A simple far-field technique diagnoses band topology in electromagnetic and acoustic crystalline systems.
  • Transitions between trivial and non-trivial phases are controlled by system geometry adjustments.

Where Pith is reading between the lines

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

  • The far-field probing method may extend to acoustic or other classical wave systems as suggested in the abstract.
  • Polarization control of edge states could inform designs for selective light confinement in photonic devices.
  • Subtle topology changes from polarization might affect additional properties like transmission or localization not examined here.

Load-bearing premise

Topology of crystalline systems can be determined by eigenmode symmetries at high symmetry points, and far-field radiations retain sufficient eigenmode information to probe this topology.

What would settle it

Observing neither polarization-dependent band inversions at Γ and X nor the predicted polarization-selective edge states in diffraction spectroscopy of the nanohole arrays, even after geometry tuning, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2504.08292 by C. Liu, H.C. Ong, T.H. Chan, Y.H. Guan.

Figure 10
Figure 10. Figure 10: The far-field accessible eigenmodes at the  and X points are labelled together with their corresponding even (+) and odd (−) field symmetries. For the bands at other HSPs that are not far-field excited, their mode symmetries are determined by FDTD in [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 3
Figure 3. Figure 3: The plots of the FDTD simulated (a) p- and (b) s-polarized total reflectivity mappings taken at the X point as a function of R. The color dash lines are for the visualization of the A1, B1, A2 and B2 assignments [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The (black) p- and (red) s-polarized total reflectivity spectra taken at the X point for R = (a) 150, (b) 200, (c) 250, and (d) 300 nm. The (black) p- and (red) s-polarized specular reflectivity spectra taken at the X point for R = (e) 150, (f) 200, (g) 250, and (h) 300 nm. The best fits are displayed as dash lines. The (black) p- and (red) s-polarized -1 st diffraction order spectra taken at the X point f… view at source ↗
Figure 11
Figure 11. Figure 11: Inset: The schematic of the FDTD supercell for simulating the interface states. The [PITH_FULL_IMAGE:figures/full_fig_p030_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: (a) The SEM image of the heterojunction. The dash line is the location of the interface. [PITH_FULL_IMAGE:figures/full_fig_p031_12.png] view at source ↗
read the original abstract

When two topologically trivial and nontrivial systems are brought together, a localized energy state is formed at the interface. For crystalline quantum and classical systems, their topology can be determined by studying the eigenmode symmetries at high symmetry points (HSPs) in the Brillouin zone. As electromagnetic systems are usually leaky, their radiations retain the eigenmode information, thus providing a means for probing the band topology. Here, we formulate the far-field characteristics of the eigenmodes at HSPs in 2D square lattice plasmonic systems and reveals, unlike the conventional tight-binding model, several polarization-dependent band inversions occur at the{\Gamma}and X points, rendering subtle changes in their band topology. In particular, by carefully tuning the system geometry to facilitate trivial and non-trivial phases, polarization selective 0D and 1D edge states that possess distinct field symmetries are realized. The evolution of 0D or 1D edge state depends on the degree of bulk-edge overlapping. We perform angle- and polarization-resolved diffraction spectroscopy on 2D Au plasmonic nanohole arrays to verify the theory and observe such states. Our study demonstrates the applicability of simple far-field technique for diagnosing the band topology of various crystalline classical systems in electromagnetics and acoustics.

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 / 0 minor

Summary. The manuscript claims to formulate the far-field characteristics of eigenmodes at high-symmetry points in 2D square lattice plasmonic systems. It reveals polarization-dependent band inversions at the Γ and X points that differ from the conventional tight-binding model, leading to subtle changes in band topology. By tuning the system geometry, trivial and non-trivial phases are facilitated, realizing polarization selective 0D and 1D edge states with distinct field symmetries. The evolution of these edge states depends on bulk-edge overlapping. Experimental verification is performed using angle- and polarization-resolved diffraction spectroscopy on 2D Au plasmonic nanohole arrays.

Significance. If the central claims hold, the work is significant for showing that far-field diffraction can diagnose band topology in leaky classical electromagnetic systems, with potential extension to acoustics. The experimental realization of polarization-selective 0D/1D edge states in Au nanohole arrays provides a concrete demonstration. Credit is due for the direct experimental verification on fabricated structures and the focus on polarization dependence.

major comments (1)
  1. [Abstract and theoretical formulation] The central claim that far-field radiations retain eigenmode information sufficiently to probe band topology (as stated in the abstract) is load-bearing but rests on an unverified assumption for lossy open systems. No explicit comparison is provided between the symmetry-based classification of band inversions at Γ and X and a computed topological invariant (e.g., Wilson loop or Chern number) on the lossy band structure, raising the risk that radiation damping or absorption in Au arrays mixes parities or shifts apparent inversion points.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and the constructive comments provided. We respond to the major comment point by point below.

read point-by-point responses

  1. Referee: [Abstract and theoretical formulation] The central claim that far-field radiations retain eigenmode information sufficiently to probe band topology (as stated in the abstract) is load-bearing but rests on an unverified assumption for lossy open systems. No explicit comparison is provided between the symmetry-based classification of band inversions at Γ and X and a computed topological invariant (e.g., Wilson loop or Chern number) on the lossy band structure, raising the risk that radiation damping or absorption in Au arrays mixes parities or shifts apparent inversion points.

    Authors: We thank the referee for this insightful comment. Our approach relies on the symmetry properties of the eigenmodes at high-symmetry points, which we show through analytical formulation and numerical simulations are preserved in the far-field diffraction patterns, even in the presence of losses. While computing a topological invariant such as the Chern number for lossy, non-Hermitian systems is not straightforward and may not directly apply due to the complex eigenvalues and open boundaries, we have verified that the band inversions at Γ and X points are accompanied by clear changes in mode symmetries that are detectable experimentally. To address the potential mixing of parities by radiation damping, our simulations include the imaginary part of the dielectric function for Au, and the distinct polarization dependencies remain evident. We will revise the manuscript to include a more detailed discussion of these points, clarifying the assumptions and adding supporting data from our calculations to demonstrate the robustness of the symmetry-based classification. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on independent symmetry analysis and experimental verification.

full rationale

The paper states the general principle that topology is determined by eigenmode symmetries at HSPs and that leaky EM systems' radiations retain this information as an established starting point for classical systems, then proceeds to formulate far-field characteristics, compute polarization-dependent band inversions at Γ and X (contrasted explicitly with tight-binding models), tune geometry for trivial/non-trivial phases, and verify via angle/polarization-resolved diffraction spectroscopy on Au nanohole arrays. No equations reduce a claimed prediction to a fitted input by construction, no self-citations are invoked as load-bearing uniqueness theorems, and no ansatz or renaming occurs. The central claims rest on direct calculation, symmetry classification, and external experimental data rather than self-referential definitions.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The paper applies established topological band theory to plasmonic crystals while adding polarization dependence; it does not introduce new particles or forces but relies on symmetry-based assumptions and geometric tuning.

free parameters (1)
  • lattice geometry parameters
    Hole size, spacing, and film thickness are tuned to realize trivial versus nontrivial phases.
axioms (2)
  • domain assumption Topology of crystalline systems is determined by eigenmode symmetries at high-symmetry points in the Brillouin zone
    Invoked to link far-field observations to band topology for both quantum and classical systems.
  • domain assumption Far-field radiation from leaky electromagnetic systems retains eigenmode symmetry information
    Central premise allowing far-field diffraction spectroscopy to diagnose topology.

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