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arxiv: 2605.16596 · v1 · pith:TKYBTDJJnew · submitted 2026-05-15 · 🪐 quant-ph · physics.optics

Optimization of circular cavities via guided-mode expansion method based inverse design

Abhishek Das , Neelesh Kumar Vij , Demitry Farfurnik This is my paper

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

classification 🪐 quant-ph physics.optics
keywords inverse designphotonic cavityquality factorspin-photon interfaceguided-mode expansionquantum informationnon-periodic cavityfar-field emission
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The pith

Non-periodic circular cavities optimized via guided-mode expansion reach quality factors of 9,000 with Gaussian far-field emission.

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

This paper develops a gradient-based inverse design method using guided-mode expansion and automatic differentiation to shape circular ring cavities for spin-photon interfaces in quantum information processing. The approach simultaneously raises the quality factor while shaping the far-field emission into a Gaussian-like profile and allowing arbitrary polarization. The optimized non-periodic design reaches a quality factor of about 9,000, an order of magnitude higher than a periodic bullseye cavity. The work also examines how the design performs when key dimensions vary by a few nanometers, identifying the most sensitive parameters. This supplies a direct computational route to cavities that reduce common performance trade-offs in quantum photonic hardware.

Core claim

The authors show that applying gradient-based optimization through guided-mode expansion with automatic differentiation to the ring widths and central disk radius of a circular cavity produces a non-periodic geometry that supports arbitrary polarization, delivers a quality factor of approximately 9,000, and maintains a Gaussian-like far-field emission pattern, an order-of-magnitude improvement over periodic bullseye designs.

What carries the argument

Guided-mode expansion method with automatic differentiation that supplies gradients of quality factor and far-field profile to adjust the cavity's ring widths and central radius during optimization.

Load-bearing premise

The guided-mode expansion method with automatic differentiation accurately models the quality factor and far-field profile for the non-periodic circular geometries explored.

What would settle it

Fabrication and measurement of the optimized cavity showing a quality factor well below 9,000 or a far-field pattern that deviates substantially from Gaussian would show the modeled optimization did not hold in practice.

Figures

Figures reproduced from arXiv: 2605.16596 by Abhishek Das, Demitry Farfurnik, Neelesh Kumar Vij.

Figure 1
Figure 1. Figure 1: (a) Illustration of the periodic bullseye cavity, top (x-y) view. The black areas illustrate the etched [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Optimization of the circular cavity geometry via inverse design. (a) The key metrics of gradient [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FDTD simulations of the inverse-designed cavity. (a) The normalized resonance spectra of the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Single-parameter fabrication tolerance analysis of the inverse-designed cavity. Each panel shows [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
read the original abstract

Spin-photon interfaces, realized by coupling optically active spin systems to photonic cavities, are essential for quantum networking and quantum information processing. Implementing such an interface for polarization-encoded photons requires a cavity that supports arbitrary polarization, provides efficient optical access through its far-field mode, and maintains sufficiently high quality factors to enable high cooperativity with the system's optical transitions. However, inherent trade-offs between the Q-factor and far-field emission mode make the simultaneous optimization of these parameters toward the realization of spin-photon interfaces challenging. In this work, we implement a gradient-based inverse-design framework using guided-mode expansion with automatic differentiation to obtain the geometrical features of a circular ring cavity that supports arbitrary polarization while simultaneously optimizing the cavity quality factor and far-field mode profile. The resulting optimized non-periodic cavity achieves a quality factor of approximately $9,000$, about an order-of-magnitude higher than that of a periodic ("bullseye") cavity while preserving a Gaussian-like far-field emission pattern. Furthermore, by varying the cavity geometry within a $\pm 6$ nm fabrication tolerance, we demonstrate the robustness of the design against fabrication errors and identify the innermost ring width and central disk radius as the parameters with the greatest impact on the quality factor and far-field mode. These results establish guided mode expansion-based inverse design as a powerful and computationally efficient approach for developing high-cooperativity spin-photon interfaces for quantum photonic applications.

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

2 major / 2 minor

Summary. The manuscript presents a gradient-based inverse-design framework that employs guided-mode expansion (GME) with automatic differentiation to optimize the radial geometry of non-periodic circular ring cavities. The objective is to simultaneously maximize the quality factor while preserving a Gaussian-like far-field emission pattern suitable for polarization-encoded spin-photon interfaces. The optimized design is reported to reach Q ≈ 9,000—an order-of-magnitude improvement over a periodic bullseye reference—while the authors also examine robustness under ±6 nm fabrication variations and identify the innermost ring width and central disk radius as the most sensitive parameters.

Significance. If the GME surrogate remains accurate for the aperiodic geometries, the work supplies a computationally efficient route to co-optimize Q and far-field properties in circular cavities, which is directly relevant to high-cooperativity spin-photon interfaces. The explicit fabrication-tolerance analysis and identification of dominant geometric parameters add practical value. The approach demonstrates the utility of GME+AD for inverse design of structures that deliberately break in-plane periodicity, a setting where more expensive full-wave methods are typically prohibitive.

major comments (2)
  1. [Abstract and Results] Abstract and Results section: The central claim that the optimized non-periodic cavity achieves Q ≈ 9,000 (an order-of-magnitude gain over the bullseye reference) rests on GME predictions without any reported cross-validation against full-wave solvers (FDTD or FEM) for the final aperiodic design. Because GME expands the field in a finite basis of slab guided modes plus a radiation-continuum approximation, small systematic errors in out-of-plane leakage can dominate at Q ∼ 10^4; independent verification is therefore required to establish that the gradient-based optimum reflects physical improvement rather than surrogate-model artifact.
  2. [Methods] Methods section: No convergence tests with respect to the number of guided modes retained in the GME basis or the discretization of the radiation continuum are provided for the non-periodic ring geometries. Such checks are load-bearing because the optimization directly ranks designs by the GME-computed Q; insufficient basis size could alter both the location of the optimum and the reported order-of-magnitude improvement.
minor comments (2)
  1. [Figures] Figure 3 (or equivalent comparison plot): the far-field intensity profiles for the optimized and bullseye cavities should be shown on the same angular scale with explicit normalization so that the preservation of the Gaussian-like shape can be quantitatively assessed.
  2. [Methods] The optimization objective function is described only qualitatively; an explicit mathematical statement of the combined Q and far-field figure of merit (including any weighting coefficients) would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our work's significance and for the constructive comments. We address each major point below and will revise the manuscript to incorporate the requested validations and tests.

read point-by-point responses

  1. Referee: [Abstract and Results] Abstract and Results section: The central claim that the optimized non-periodic cavity achieves Q ≈ 9,000 (an order-of-magnitude gain over the bullseye reference) rests on GME predictions without any reported cross-validation against full-wave solvers (FDTD or FEM) for the final aperiodic design. Because GME expands the field in a finite basis of slab guided modes plus a radiation-continuum approximation, small systematic errors in out-of-plane leakage can dominate at Q ∼ 10^4; independent verification is therefore required to establish that the gradient-based optimum reflects physical improvement rather than surrogate-model artifact.

    Authors: We agree that explicit cross-validation with full-wave solvers is important to rule out possible surrogate artifacts at Q ∼ 10^4. In the revised manuscript we will add FDTD simulations of the final optimized aperiodic design, confirming both the quality factor and the Gaussian-like far-field pattern. While GME has been benchmarked against FDTD/FEM for related photonic-crystal and cavity geometries in the literature, we accept that a direct comparison for this specific non-periodic structure will strengthen the central claim. revision: yes

  2. Referee: [Methods] Methods section: No convergence tests with respect to the number of guided modes retained in the GME basis or the discretization of the radiation continuum are provided for the non-periodic ring geometries. Such checks are load-bearing because the optimization directly ranks designs by the GME-computed Q; insufficient basis size could alter both the location of the optimum and the reported order-of-magnitude improvement.

    Authors: We acknowledge that convergence with respect to the GME basis size and radiation-continuum discretization must be demonstrated for the non-periodic geometries used in the optimization. In the revised manuscript we will include a dedicated convergence study (or appendix) showing the stability of the computed Q-factor as the number of retained guided modes is increased and as the radiation continuum discretization is refined. These tests will confirm that the basis employed is sufficient and that the reported order-of-magnitude improvement is robust. revision: yes

Circularity Check

0 steps flagged

No circularity: optimization applies external GME surrogate to geometry parameters

full rationale

The paper's central result is obtained by running gradient-based optimization of cavity ring widths and radii inside a guided-mode expansion (GME) model whose radiation-loss and far-field formulas are independent of the final Q≈9000 value. No equation is defined in terms of its own output, no fitted parameter is relabeled as a prediction, and no load-bearing premise reduces to a self-citation. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests primarily on the domain assumption that guided-mode expansion remains accurate for the optimized non-periodic structures; no explicit free parameters or new physical entities are introduced in the abstract.

axioms (1)
  • domain assumption Guided-mode expansion provides a sufficiently accurate and differentiable model of cavity Q-factor and far-field for the circular ring geometries under optimization.
    This assumption underpins the entire gradient-based inverse design loop described in the abstract.

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