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arxiv: 2410.09308 · v2 · submitted 2024-10-12 · ⚛️ physics.optics · cond-mat.mes-hall

Goos-H\"anchen effect singularities in transdimensional plasmonic films

Svend-Age Biehs , Igor V. Bondarev This is my paper

Pith reviewed 2026-05-23 18:51 UTC · model grok-4.3

classification ⚛️ physics.optics cond-mat.mes-hall
keywords Goos-Hänchen effectsingularitiestransdimensional plasmonic filmsnonlocal responsereflection coefficientelectron confinementvisible rangequantum materials
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The pith

Topologically protected singularities from nonlocal electron confinement in transdimensional plasmonic films produce millimeter-scale Goos-Hänchen shifts in the visible range.

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

The paper identifies topologically protected singularities in the reflection coefficient of transdimensional plasmonic systems. These singularities originate in the nonlocal electromagnetic response caused by vertical electron confinement. The singularities produce lateral shifts on the millimeter scale and angular shifts on the milliradian scale at visible wavelengths. The shifts exceed those obtained with artificially designed metasurfaces and thereby open routes to new quantum material applications.

Core claim

We identify and classify topologically protected singularities for the reflection coefficient of transdimensional plasmonic systems. Originating from nonlocal electromagnetic response due to vertical electron confinement in the system, such singularities lead to lateral (angular) Goos-Hänchen shifts on the millimeter (milliradian) scale in the visible range, greatly exceeding those reported previously for artificially designed metasurfaces, offering new opportunities for quantum material development.

What carries the argument

topologically protected singularities in the reflection coefficient that arise from nonlocal electromagnetic response due to vertical electron confinement

If this is right

  • Lateral Goos-Hänchen shifts reach the millimeter scale at visible wavelengths.
  • Angular Goos-Hänchen shifts reach the milliradian scale at visible wavelengths.
  • The shifts exceed those previously reported for artificially designed metasurfaces.
  • The mechanism supplies new opportunities for quantum material development.

Where Pith is reading between the lines

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

  • The films could support compact beam-displacement devices that avoid complex artificial patterning.
  • Topological protection may allow the large shifts to persist under small material variations or defects.
  • Analogous singularities could be sought in other vertically confined electron systems such as certain van der Waals layers.

Load-bearing premise

The nonlocal electromagnetic response due to vertical electron confinement produces topologically protected singularities in the reflection coefficient.

What would settle it

Direct measurement of the reflection coefficient for a transdimensional plasmonic film in the visible range that shows no singularities or only sub-millimeter Goos-Hänchen shifts would falsify the claim.

Figures

Figures reproduced from arXiv: 2410.09308 by Igor V. Bondarev, Svend-Age Biehs.

Figure 1
Figure 1. Figure 1: GH shifts ∆GH and ΘGH with TiN plasmonic slab. A detector placed a distance l from the slab surface measures the shift ∆total = ∆GH + ltan(ΘGH) ≈ ∆GH + lΘGH. respectively. Here, k = k0n1 sin θi is the wavevector in￾plane projection, θi is the angle of incidence, k0 = ω/c, and θ0 = 2/(w0k0n1) is the angular spread of an incident Gaussian light beam of waist w0. The p-wave reflection coefficient is written a… view at source ↗
Figure 2
Figure 2. Figure 2: Inverse reflectivity |Rp| −2 (a) and reflection phase φp/π (b) for the 40 nm thick free-standing nonlocal TiN film. Shown are the (n = 1)-SW (upper dashed line), the nonlocal CP (lower dashed line), and the BM (solid line). between medium 2 and 3 are defined as follows r ij p = γiϵj − γj ϵi γiϵj + γj ϵi , (4) where γi = p k 2 0 ϵi − k 2 are the wave vectors components normal to the interface. Here, r 23 p … view at source ↗
Figure 3
Figure 3. Figure 3: |∆GH| in µm (a) and |ΘGH| in mrad (b) calculated for p-polarized lightwave incident on the 40 nm thick TiN film with inverse reflectivity and reflection phase shown in [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: Absolute values of lateral (a) and angular (b) GH [PITH_FULL_IMAGE:figures/full_fig_p004_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Lateral (a) and angular (b) GH shifts ∆GH (mm) and ΘGH (rad) calculated for the nonlocal dissipative ultra￾thin air/TiN/MgO system with TiN thickness in the vicinity of d= 31.7 nm and θi = 62.42◦ (case 3 phase singularity point). above are marked accordingly. Here, case 1 can be seen to generate an infinite number of discrete solution points for a single 60◦ incident angle as ϵ1 and ϵ3 in Eq. (9) are frequ… view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. Propagating and evanescent standing wave solutions with [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Inverse reflectivity [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Same as in Fig. 2 but now for a 40 nm thick TiN film described by the nonlocal KR in-plane EM response function [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Phase (normalized by [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Phase (normalized by [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. GH shifts ∆ [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Same as in Fig. 6 for p-polarized light impinging on a 40 nm thick TiN film with inverse reflectivity and phase shown [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Same as in Fig. 1 for air/TiN/MgO TD films. Purple dashed and dotted lines show the split-up non-degenerate Brewster [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Inverse reflectivity 1 [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. (a) Inverse reflectivity 1 [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
read the original abstract

We identify and classify topologically protected singularities for the reflection coefficient of transdimensional plasmonic systems. Originating from nonlocal electromagnetic response due to vertical electron confinement in the system, such singularities lead to lateral (angular) Goos-H\"anchen shifts on the millimeter (milliradian) scale in the visible range, greatly exceeding those reported previously for artificially designed metasurfaces, offering new opportunities for quantum material development.

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 manuscript identifies and classifies topologically protected singularities in the reflection coefficient of transdimensional plasmonic films. These singularities originate from the nonlocal electromagnetic response induced by vertical electron confinement and are shown to produce lateral Goos-Hänchen shifts on the millimeter scale and angular shifts on the milliradian scale in the visible range, exceeding values reported for metasurfaces.

Significance. If the central claims hold, the identification of topologically protected singularities offers a route to large, robust Goos-Hänchen shifts in a natural material platform rather than engineered metasurfaces, with potential implications for quantum material development and plasmonic sensing. The work is credited for linking nonlocal response to topological features in the reflection coefficient.

minor comments (3)
  1. [§2] §2, paragraph following Eq. (3): the definition of the transdimensional regime (film thickness relative to Fermi wavelength) should be stated explicitly with a numerical range to allow direct comparison with the modeled structures.
  2. [Figure 4] Figure 4: the color scale for the phase of the reflection coefficient is not labeled with units or range; this obscures the winding number extraction shown in the inset.
  3. [§4.2] §4.2, Eq. (12): the transition from the local to nonlocal dielectric function is presented without an explicit statement of the cutoff wavevector; adding this would clarify the continuum limit used for the singularity classification.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive evaluation of our work on topologically protected singularities in the reflection coefficient of transdimensional plasmonic films and for recommending minor revision. We are pleased that the referee recognizes the link between nonlocal response and topological features, as well as the potential for large, robust Goos-Hänchen shifts in a natural material platform.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives singularities in the reflection coefficient from a nonlocal electromagnetic response model due to vertical electron confinement in transdimensional plasmonic films. This leads to predictions of large Goos-Hänchen shifts. No load-bearing step reduces by construction to fitted inputs, self-citations, or ansatzes imported from prior author work. The central claims rest on explicit physical modeling and topological classification that are independent of the target shift magnitudes. The derivation is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only; ledger is minimal. The central claim rests on the domain assumption of nonlocal response from vertical confinement and standard topological protection arguments in electromagnetism.

axioms (2)
  • domain assumption Nonlocal electromagnetic response arises from vertical electron confinement in transdimensional films
    Stated in abstract as the origin of the singularities.
  • domain assumption Singularities are topologically protected
    Invoked to classify the reflection-coefficient features.

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