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arxiv: 2604.04390 · v1 · submitted 2026-04-06 · ⚛️ physics.optics · physics.app-ph

Recognition: 2 theorem links

· Lean Theorem

Q Factors Exceeding 10⁴ in Wavelength-to-Subwavelength-Scale Free-Space Resonators

Darrell E. Omo-Lamai , Varun Dolia , Yanyu Xiong , Chih-Yi Chen , Parivash Moradifar , Priyanuj Bordoloi , Sajjad AbdollahRamezani , Sahil Dagli
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Halleh Balch Jennifer A. Dionne
Authors on Pith no claims yet

Pith reviewed 2026-05-10 20:18 UTC · model grok-4.3

classification ⚛️ physics.optics physics.app-ph
keywords free-space resonatorsQ factornanoantennasPurcell factormode volumeasymmetry controlsilicon photonicsoptical resonances
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The pith

Jointly tuning geometric and optical asymmetries unlocks high-Q free-space resonators at both wavelength and subwavelength scales.

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

The paper shows that periodically asymmetric resonators achieve high quality factors together with small mode volumes when geometric and optical asymmetries are controlled at the same time. This biaxial approach produces iso-Q contours that link different perturbation strengths to equivalent performance, solving a prior limit where designs could not reach high-Q regimes with strong field localization. A reader would care because these structures support strong light-matter interactions through simple far-field excitation, without waveguides or cavities that complicate integration. Experiments demonstrate the method with silicon nanoantenna arrays reaching Q factors of 76,000 at wavelength-scale volumes in water, while simulations show Q factors of one million at subwavelength volumes.

Core claim

By jointly tuning geometric and optical asymmetries in periodically asymmetric resonators, the authors unlock a biaxial radiative landscape with iso-Q contours that connect disparate perturbations to the same Q factor. Using VINPix structures with controlled out-of-plane perturbations of 35-150 nm made from amorphous Si, SiNx, or SiO2, they experimentally achieve Q factors up to 76,000 at mode volumes of approximately 1.7 lambda_0^3 n_eff^{-3} in simultaneously imaged arrays of more than 80 resonators in water. Computationally, 50-nm-wide slotted VINPix designs reach Q factors of 10^6 at subwavelength mode volumes of 0.2 lambda_0^3 n_eff^{-3} with 20 nm SiO2 perturbations, producing Purcell

What carries the argument

The biaxial radiative landscape with iso-Q contours, created by concurrent geometric and optical asymmetry tuning through out-of-plane perturbations in VINPix nanoantenna pixels.

Load-bearing premise

Out-of-plane perturbations of 35-150 nm can be fabricated with enough precision and uniformity across large arrays to avoid extra scattering losses or mode distortions that would lower the measured Q.

What would settle it

Fabricated arrays showing Q factors well below 76,000 or slotted VINPix simulations failing to reach Q of 10^6 when realistic fabrication errors are included.

Figures

Figures reproduced from arXiv: 2604.04390 by Chih-Yi Chen, Darrell E. Omo-Lamai, Halleh Balch, Jennifer A. Dionne, Parivash Moradifar, Priyanuj Bordoloi, Sahil Dagli, Sajjad AbdollahRamezani, Varun Dolia, Yanyu Xiong.

Figure 1
Figure 1. Figure 1: Independent control of geometric and optical asymmetries on VINPix resonators. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Simulated biaxial 𝑸𝑸 factor control via geometric and optical asymmetries. (a) Map of 𝑄𝑄 factor as a function of geometric and optical asymmetries (𝛼𝛼𝑔𝑔 and 𝛼𝛼𝑜𝑜, respectively) for infinitely periodic resonators in water. (b) Iso-𝑄𝑄 contours extracted from the (𝛼𝛼𝑔𝑔, 𝛼𝛼𝑜𝑜) landscape in (a), represented in terms of perturbation height and perturbation refractive index. The plot shows families of perturbatio… view at source ↗
Figure 3
Figure 3. Figure 3: Experimental 𝑸𝑸 factor control via perturbation height and material. (a) Representative reflection spectra for VINPix resonators with 100 nm perturbations of different materials in air. (b) Smaller refractive index asymme￾tries result in higher average quality factors across 90 resonators per condition. (c) Representative reflection spectra for VINPix resonators with silicon nitride perturbations of differ… view at source ↗
Figure 4
Figure 4. Figure 4: High-𝑸𝑸 VINPix arrays in water. (a) Wide-field optical micrograph of an array of 84 VINPix resonators with 35 nm SiO2 perturbations, showing an on-resonance intensity decrease for a selected resonator (insets). (b) Extracted spectrum for the selected resonator in (a). Circular markers indicate the wavelengths and intensities corresponding to the micrographs in insets in (a). (c) Fano fit for the resonator … view at source ↗
Figure 5
Figure 5. Figure 5: Slotted VINPix resonators with high 𝑸𝑸 factors, subwavelength mode volumes, and high Purcell factors. (a) Simulated electric near-field enhancements at the cross-sections of a 16 μm × 3.5 μm VINPix with 50 nm SiO2 perturbations and a 50-nm-wide slot, showing high enhancements in the low-index gap. Scale bar, 1.1 μm (300 nm in inset). (b) Calculated radiative 𝑄𝑄 factor as a function of perturbation height a… view at source ↗
read the original abstract

Free-space-addressable optical resonators that combine long photon lifetimes (high $Q$ factors) with strong spatial localization of optical fields (small mode volumes, $V_m$) enhance light-matter interactions with facile far-field excitation. The Purcell factor governing spontaneous emission enhancement scales as $Q\,V_m^{-1}$. Periodically asymmetric resonators, in which perturbations convert bound modes into radiating modes, offer a route to free-space resonances, with the radiative $Q$ factor tuned by the geometric and optical strength of the asymmetry-inducing perturbations. However, free-space resonators that simultaneously achieve high $Q$ and small $V_m$ have remained rare. This limitation arises in part because existing designs do not tailor geometric and optical asymmetries concurrently, thus limiting access to high-$Q$ regimes. Here, we show that jointly tuning geometric and optical asymmetries unlocks a biaxial radiative landscape with iso-$Q$ contours that connect disparate perturbations with equivalent $Q$ factors. We demonstrate this framework with very-large-scale-integrated single-crystalline Si nanoantenna pixels (VINPix) with out-of-plane perturbations of 35-150 nm amorphous Si, SiN$_x$, and SiO$_2$. We experimentally establish biaxial $Q$ factor control in air and achieve $Q$ factors up to $76,000$ at wavelength-scale mode volumes ($V_m \sim 1.7\,\lambda_0^3\,n_{\mathrm{eff}}^{-3}$) in simultaneously imaged arrays of $>80$ resonators in water. Furthermore, we computationally demonstrate 50-nm-wide slotted VINPix that reach $Q$ factors of $10^6$ at subwavelength mode volumes ($V_m \sim 0.2\,\lambda_0^3\,n_{\mathrm{eff}}^{-3}$) with 20 nm SiO$_2$ perturbations, yielding Purcell factors as high as $5 \times 10^5$ in an all-dielectric free-space resonator.

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

3 major / 2 minor

Summary. The paper introduces a biaxial radiative landscape for free-space optical resonators achieved by jointly tuning geometric and optical asymmetries via out-of-plane perturbations in very-large-scale-integrated single-crystalline Si nanoantenna pixels (VINPix). It experimentally reports Q factors up to 76,000 at wavelength-scale mode volumes (V_m ~ 1.7 λ_0^3 n_eff^{-3}) in water using simultaneously imaged arrays of >80 resonators with 35-150 nm amorphous Si/SiN_x/SiO_2 perturbations, demonstrates biaxial Q control in air, and computationally shows slotted VINPix reaching Q=10^6 at subwavelength volumes (V_m ~ 0.2 λ_0^3 n_eff^{-3}) with 20 nm SiO_2 perturbations and Purcell factors up to 5×10^5.

Significance. If the central claims hold, this advances free-space-addressable high-Q resonators with small mode volumes, a longstanding challenge in nanophotonics. The biaxial control framework, experimental array-scale demonstration, and computational extension to subwavelength scales with high Purcell factors represent a meaningful step toward enhanced light-matter interactions in all-dielectric systems. The conceptual unification of geometric and optical asymmetry tuning is a strength.

major comments (3)
  1. [Abstract] Abstract and experimental results: The reported experimental Q up to 76,000 at V_m ~1.7 λ_0^3 n_eff^{-3} in arrays of >80 resonators lacks error bars, statistical distribution across the array, or direct quantification of fabricated perturbation heights/positions (35-150 nm range). This is load-bearing because the skeptic concern on uniformity directly impacts whether the measured Q reflects the designed radiative landscape or includes unaccounted scattering from fabrication variations.
  2. [Abstract] Abstract and computational section: The claim of Q=10^6 for 50-nm-wide slotted VINPix with 20 nm SiO_2 perturbations yielding Purcell factors of 5×10^5 provides no simulation parameters (mesh resolution, boundary conditions, material dispersion models) or convergence checks, making it impossible to assess if the subwavelength volume and high-Q regime are robust.
  3. [Results] Results on biaxial control: The iso-Q contours connecting disparate perturbations (e.g., different materials/heights) are presented as a key advance, but without tabulated or plotted quantitative agreement between measured Q values and simulated radiative Q for the specific fabricated devices, it is unclear whether the biaxial landscape holds under real fabrication tolerances.
minor comments (2)
  1. [Abstract] The acronym VINPix is used in the abstract before being defined in the main text; a parenthetical expansion on first use would improve clarity.
  2. [Abstract] Notation for effective index n_eff in the mode volume expression is not defined on first appearance, which could confuse readers unfamiliar with the effective-medium approximation used.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have helped us strengthen the manuscript. We address each major comment below and have incorporated revisions to provide the requested data, parameters, and comparisons.

read point-by-point responses

  1. Referee: [Abstract] Abstract and experimental results: The reported experimental Q up to 76,000 at V_m ~1.7 λ_0^3 n_eff^{-3} in arrays of >80 resonators lacks error bars, statistical distribution across the array, or direct quantification of fabricated perturbation heights/positions (35-150 nm range). This is load-bearing because the skeptic concern on uniformity directly impacts whether the measured Q reflects the designed radiative landscape or includes unaccounted scattering from fabrication variations.

    Authors: We agree that error bars, statistical distributions, and direct fabrication metrology are essential to substantiate uniformity. In the revised manuscript, we have added error bars to all reported Q values (representing one standard deviation across the >80 resonators in each array) and included a histogram of the Q-factor distribution in the supplementary information. We have also incorporated AFM and SEM measurements quantifying the actual perturbation heights and lateral positions for the 35-150 nm range, with mean values and standard deviations now reported. These data confirm that fabrication variations remain within tolerances that do not introduce significant additional scattering, thereby validating that the measured Q factors arise from the designed biaxial radiative landscape. revision: yes

  2. Referee: [Abstract] Abstract and computational section: The claim of Q=10^6 for 50-nm-wide slotted VINPix with 20 nm SiO_2 perturbations yielding Purcell factors of 5×10^5 provides no simulation parameters (mesh resolution, boundary conditions, material dispersion models) or convergence checks, making it impossible to assess if the subwavelength volume and high-Q regime are robust.

    Authors: We acknowledge the need for full simulation transparency. The revised manuscript now includes a dedicated methods subsection detailing the simulation parameters: finite-difference time-domain mesh resolution of 5 nm in the resonator region (with adaptive refinement), perfectly matched layer boundaries with 1 μm thickness and 0.1% reflection coefficient, and material dispersion models based on ellipsometry-measured refractive indices for Si, SiN_x, and SiO_2. We have added convergence plots demonstrating that both Q and mode volume stabilize for mesh densities finer than 10 nm, confirming the robustness of the Q=10^6 and Purcell factor results in the subwavelength regime. revision: yes

  3. Referee: [Results] Results on biaxial control: The iso-Q contours connecting disparate perturbations (e.g., different materials/heights) are presented as a key advance, but without tabulated or plotted quantitative agreement between measured Q values and simulated radiative Q for the specific fabricated devices, it is unclear whether the biaxial landscape holds under real fabrication tolerances.

    Authors: The referee correctly identifies that quantitative validation strengthens the biaxial framework. We have added a new figure panel and accompanying table in the revised Results section that directly compares experimentally measured Q factors (for devices with AFM-quantified perturbations of specific heights and materials) against the corresponding simulated radiative Q values. The agreement is within 15% across the iso-Q contours, with minor deviations attributable to the small fabrication tolerances already quantified. This explicit comparison confirms that the biaxial radiative landscape remains valid under realistic fabrication conditions. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on new experimental measurements and simulations

full rationale

The paper presents experimental Q-factor measurements from fabricated VINPix arrays with 35-150 nm perturbations and computational results for slotted designs. These values are obtained directly from device fabrication, imaging, and simulation rather than from any self-referential equations, fitted parameters renamed as predictions, or load-bearing self-citations. The biaxial radiative landscape arises from explicit joint tuning of geometric and optical asymmetries in the described structures, with no reduction of the reported Q or Purcell factors to prior inputs by construction. The work is self-contained against external benchmarks of fabrication and electromagnetic simulation.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 2 invented entities

The central claim rests on the domain assumption that small out-of-plane perturbations convert bound modes to tunable radiating modes while preserving localization, plus the design choice of specific perturbation materials and heights as free parameters.

free parameters (2)
  • perturbation height = 35-150 nm
    35-150 nm range chosen to set asymmetry strength for target Q values.
  • perturbation material
    a-Si, SiNx, SiO2 selected to provide optical contrast variation.
axioms (1)
  • domain assumption Perturbations convert bound modes into radiating modes whose radiative Q is tunable by geometric and optical strength of the asymmetry.
    Invoked in the introduction to justify the biaxial landscape approach.
invented entities (2)
  • VINPix no independent evidence
    purpose: Name for the very-large-scale-integrated single-crystalline Si nanoantenna pixel arrays with out-of-plane perturbations.
    Device platform introduced to implement the asymmetry tuning.
  • biaxial radiative landscape no independent evidence
    purpose: Concept of iso-Q contours connecting disparate geometric and optical perturbations.
    New organizing framework for Q control.

pith-pipeline@v0.9.0 · 5720 in / 1604 out tokens · 49320 ms · 2026-05-10T20:18:45.137655+00:00 · methodology

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Reference graph

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