arxiv: 2605.05779 · v1 · submitted 2026-05-07 · ⚛️ physics.optics

Recognition: unknown

Robustness of bound states in the continuum in metasurface based on Ge₂Sb₂Te₅ versus structural imperfections

Alexander I. Solomonov, Ekaterina E. Maslova, Kirill A. Bronnikov, Mikhail V. Rybin, Nikolai A. Vlasov, Zarina F. Kondratenko

Pith reviewed 2026-05-08 06:48 UTC · model grok-4.3

classification ⚛️ physics.optics

keywords bound states in the continuummetasurfaceGe2Sb2Te5quality factorgeometric imperfectionsphase change materialquasi-BIC

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The pith

Quasi-BIC quality factors in GST metasurfaces stay robust to random trapezoidal shape variations

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

This paper examines the effects of lithography imperfections on quasi-bound states in the continuum in a one-dimensional metasurface made from Ge2Sb2Te5 bars that have trapezoidal cross-sections instead of perfect rectangles. It finds that random variations in the trapezoid angles from bar to bar do not significantly degrade the quality factor for either the amorphous or crystalline phases of the material. In the absence of material losses, the quality factor decreases proportionally to the square of the disorder strength, as shown by both analysis and simulations. The robustness holds particularly when the material dispersion is low near the resonance wavelength, making the structure suitable for applications requiring stable moderate quality factors and phase control.

Core claim

The quality factor of quasi-BICs supported by GST bars remains robust under random element-to-element variations of the trapezoid angle for both GST phases. Analytical and numerical estimates without material losses indicate that the Q factor scales inversely with the square of the disorder amplitude. Transition to identical isosceles trapezoids reduces the Q factor in the amorphous phase because of absorption changes linked to the resonance shift. The Q factor tolerates geometric imperfections when dispersion near the BIC wavelength is insignificant but varies when dispersion is substantial.

What carries the argument

quasi-bound states in the continuum (quasi-BICs) in a GST bar metasurface, where C2 symmetry preservation under random trapezoidal deviations enables robust Q-factor behavior against disorder

If this is right

The Q factor scales inversely quadratic with the amplitude of disorder when material losses are absent.
Both amorphous and crystalline GST phases exhibit Q-factor robustness to random trapezoid angle variations.
Substantial dispersion near the BIC wavelength alters the tolerance to geometric imperfections.
Stable moderate Q factors support phase-shifting applications in GST-based metasurfaces.

Where Pith is reading between the lines

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

Moderate fabrication variations in bar shapes may be acceptable for maintaining BIC performance in real devices.
Similar robustness properties could be tested in metasurfaces using other phase-change materials.
Practical photonic devices might benefit from relaxed precision requirements in lithography processes.

Load-bearing premise

The analysis assumes trapezoidal deviations represent the dominant imperfection and that C2 symmetry remains intact.

What would settle it

Experimental measurement of Q factors in fabricated samples with quantified random trapezoid angle variations, verifying the inverse-quadratic scaling in the absence of losses.

Figures

Figures reproduced from arXiv: 2605.05779 by Alexander I. Solomonov, Ekaterina E. Maslova, Kirill A. Bronnikov, Mikhail V. Rybin, Nikolai A. Vlasov, Zarina F. Kondratenko.

**Figure 1.** Figure 1: (a) Schematic illustration of the GST-based structure. Black bars represent GST elements, while the glass substrate is shown in blue. The period of the structure is a, and w and h are the width and height of GST bars, respectively. (b) Dispersion of q-BICs supported by crystalline- and amorphous-phase GST bars for angles of incidence from 0 ◦ to 30◦ . Blue line corresponds to the crystalline phase of GST, … view at source ↗

**Figure 2.** Figure 2: (a) SEM image of a GST-based metasurface [14]. (b) Schematic illustration of the cross-section changing from rectangular to trapezoidal. Both inclination angles of the trapezoid (left and right) are equal to α. (c) Dependence of the Q factor on α for crystalline and amorphous GST. The trend in the amorphous phase is largely governed by absorption. phous phase and εc = 43.8 + i · 3.73 for crystalline phase.… view at source ↗

**Figure 3.** Figure 3: Scheme of perturbed cross-sections of the structure with random disorder. Each bar has random sidewall inclination angles αℓ and αℓ+1 uniformly distributed within a given range. Coordinates of the bar beginning and end at height y are xℓ and xℓ+1, respectively. In real structures, the inclination angle varies from bar to bar. The disordered cross-sections are illustrated in view at source ↗

**Figure 5.** Figure 5: Dependence of the Q factor on the disorder amplitude σ in (a) crystalline and (b) amorphous GST with material loss. Bars indicate the spread of Q factors for each σ. The Q factor weakly depends on σ. V. CONCLUSION We have quantified the impact of lithography-induced geometric imperfections on the Q factor of symmetryprotected BICs in a GST-based metasurface. We have uncovered the interplay between materi… view at source ↗

**Figure 6.** Figure 6: Q factor dependencies (log–log scale) on the mean inclination angle α0 in crystalline GST without material loss. Three series correspond to σ = 0.001, 0.05, 0.1 from top to bottom. Lines correspond to inverse-quadratic fits view at source ↗

read the original abstract

We study the impact of lithography imperfections on quasi-bound states in the continuum (quasi-BICs) supported by a one-dimensional metasurface of Ge$_2$Sb$_2$Te$_5$ (GST) bars with trapezoidal deviations from rectangular cross-sections. Several mechanisms of quality ($Q$) factor scaling, including the impact of material losses, dispersion, and geometric imperfections are established. We demonstrate that transition to identical isosceles trapezoids, despite preserving the required $C_2$ symmetry, reduces the $Q$ factor in the amorphous phase due to absorption changes accompanying the resonance shift. Further, the $Q$ factor remains robust for both GST phases under random element-to-element variations of the trapezoid angle, while analytical and numerical estimations in the absence of material losses show inverse-quadratic scaling of the Q factor with the disorder amplitude. We reveal that in the GST-based metasurface, the $Q$ factor is tolerant to geometric imperfections for insignificant dispersion near the BIC wavelength, but changes in case of substantial dispersion. The phase shifting and established robustness of BICs in GST can be useful for applications where stable moderate $Q$ factors are essential.

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.

Desk Editor's Note private letter to a colleague

The paper shows inverse-quadratic Q-factor scaling with trapezoid-angle disorder in GST metasurfaces when losses are ignored, plus phase-dependent tolerance tied to dispersion, but only under symmetry-preserving imperfections.

read the letter

The core result is that random bar-to-bar changes in trapezoid angle leave the quasi-BIC Q factor fairly stable in both amorphous and crystalline GST, while uniform trapezoids shift the resonance and cut Q in the amorphous phase due to higher absorption. Without material losses the drop follows an inverse-quadratic law with disorder amplitude, and low dispersion near the BIC wavelength preserves that tolerance. These are concrete numbers for a phase-change material that prior BIC robustness papers did not supply for GST.

Referee Report

1 major / 2 minor

Summary. The manuscript studies the impact of lithography imperfections, modeled as trapezoidal deviations from rectangular cross-sections in a 1D metasurface of Ge2Sb2Te5 bars, on quasi-bound states in the continuum. It claims that the Q factor remains robust under random element-to-element trapezoid angle variations for both GST phases, exhibits inverse-quadratic scaling with disorder amplitude in the absence of material losses, reduces for identical isosceles trapezoids in the amorphous phase due to resonance shift and absorption, and is tolerant to geometric imperfections when dispersion near the BIC wavelength is insignificant but changes with substantial dispersion.

Significance. If the results on robustness and scaling hold under the modeled conditions, this provides useful insights into fabrication tolerances for BIC-based tunable metasurfaces using phase-change materials, supporting applications needing stable moderate Q factors such as sensors or modulators. The combination of analytical estimations and numerical simulations for disorder effects is a strength.

major comments (1)

[§3] §3 (modeling of geometric imperfections): The robustness and inverse-quadratic Q scaling are demonstrated only for random trapezoid-angle fluctuations that preserve C2 symmetry (isosceles trapezoids in a periodic supercell). The central claim of robustness versus 'structural imperfections' and 'lithography imperfections' is load-bearing on this assumption, yet the manuscript provides no analysis or simulations for symmetry-breaking defects (e.g., left/right base-angle mismatch or sidewall tilt) that lift BIC protection even at zero disorder amplitude, especially when material dispersion and GST-phase absorption are present.

minor comments (2)

[Abstract] Abstract: The statement on inverse-quadratic scaling and robustness lacks any mention of the specific disorder amplitude range, numerical error analysis, or full parameter specifications used in the estimations.
[Throughout] Throughout: Clarify in text and figures whether the scaling laws are purely analytical derivations or involve fitting, and ensure consistent notation for Q factor and disorder amplitude when dispersion is included.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive and detailed review of our manuscript on the robustness of quasi-BICs in GST metasurfaces. The feedback highlights an important scope limitation in our modeling of imperfections, which we address below. We are prepared to revise the manuscript to improve clarity without overstating our results.

read point-by-point responses

Referee: §3 (modeling of geometric imperfections): The robustness and inverse-quadratic Q scaling are demonstrated only for random trapezoid-angle fluctuations that preserve C2 symmetry (isosceles trapezoids in a periodic supercell). The central claim of robustness versus 'structural imperfections' and 'lithography imperfections' is load-bearing on this assumption, yet the manuscript provides no analysis or simulations for symmetry-breaking defects (e.g., left/right base-angle mismatch or sidewall tilt) that lift BIC protection even at zero disorder amplitude, especially when material dispersion and GST-phase absorption are present.

Authors: We thank the referee for this observation. Our study deliberately models trapezoidal deviations as random element-to-element variations of the base angle while enforcing isosceles shapes (preserving C2 symmetry) within a periodic supercell. This corresponds to a common class of lithography imperfections that do not immediately destroy the underlying symmetry protection of the BIC. We focused on this regime because it allows the quasi-BIC to survive with a finite but reduced Q factor, enabling the study of disorder-induced scaling (inverse-quadratic in the lossless limit) and the interplay with material losses and dispersion. Symmetry-breaking defects, such as left/right angle mismatch or non-uniform sidewall tilt, would indeed lift the C2 symmetry and eliminate the BIC even at zero disorder amplitude; this is a fundamental property of symmetry-protected BICs and was outside the intended scope of examining how disorder perturbs an existing quasi-BIC. We acknowledge that the manuscript language referring to 'structural imperfections' and 'lithography imperfections' could be read more broadly than intended. To address the referee's concern, we will revise the abstract, introduction, and conclusions to explicitly state that the modeled imperfections preserve C2 symmetry, add a brief discussion of why symmetry-breaking cases are excluded (as they trivially suppress the BIC), and note that real fabrication may include a mixture of both types. This constitutes a partial revision that clarifies the claims without requiring new extensive simulations. revision: partial

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper derives the inverse-quadratic Q-factor scaling with disorder amplitude via explicit analytical and numerical estimations performed in the absence of material losses. This scaling is obtained from perturbation analysis of the symmetry-protected BIC under C2-preserving trapezoid-angle variations and does not reduce to a fitted parameter or input data by construction. No self-definitional loops, fitted inputs renamed as predictions, load-bearing self-citations, or ansatz smuggling are present in the provided claims or abstract. The robustness statements rest on independent numerical simulations and standard BIC perturbation theory that remain externally verifiable.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis builds on standard nanophotonics modeling without new postulates.

axioms (1)

domain assumption Electromagnetic theory and material dispersion relations for GST in amorphous and crystalline phases
Invoked to model resonance shifts and absorption changes with geometry and phase.

pith-pipeline@v0.9.0 · 5548 in / 1233 out tokens · 42208 ms · 2026-05-08T06:48:52.498426+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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