Marchal 2026 QNM cavity reproduction — 2026-08-10¶
Outcome¶
The paper's high-Q optimization is not reproduced. The campaign did validate cavitygrad's local QNM boundary formula, but it also showed that the current unstructured CSG/NGSolve pole loss is too sensitive to discretization and remeshing to serve as a trustworthy Q objective.
The benchmark is Marchal et al., “Nanobeam laser cavities with high quality-factor and near-unity outcoupling efficiency” (journal, arXiv, supplement). The retained reconstruction uses the published 600 × 250 nm InP nanobeam, NB6 defect, 75→100 nm hole-radius taper, 330→380 nm period taper, and 20 initial holes per side. The unpublished taper count, final coordinates, mesh/PML settings, and exact indices are explicit campaign assumptions.
What passed¶
On one fixed P2 mesh, the QNM prediction for translating the innermost symmetric hole pair agrees with a completely independent ALE derivative:
| check | value |
|---|---|
analytic dQ/dx |
+32,047.89 / nm |
ALE dQ/dx |
+31,842.77 / nm |
| relative disagreement | 0.64% |
| wall-motion realization error | 0.032% |
The analytic theorem, wall normal/sign convention, symmetric-coordinate projection, and complex-frequency-to-Q conversion therefore work locally. The low-order “noise floor at a few thousand Q” is also explained: P1 gives Q=2,818, while P2 gives Q=176,400 and reverses the strongest gradient ordering.
What failed¶
The imaginary frequency does not converge smoothly even though wavelength, residual, and localization identify the same branch:
| configuration | DOF | Q | peak RSS |
|---|---|---|---|
| all P1 | 150,478 | 2,818 | 2.3 GB |
| all P2 | 630,534 | 176,400 | 20.8 GB |
| P2, finer hole curvature 2.5 | 875,892 | 62,179 | 29.2 GB |
| P2, finer hole curvature 3.0 | 1,104,918 | 87,892 | 39.1 GB |
| P2 cavity, P3 PML | 733,533 | 51,146 | 23.3 GB |
| selective P3 cavity + P3 PML | 936,047 | 136,025 | 35.4 GB |
The first P2 optimizer looked successful: it moved two hole pairs and raised same-mesh Q from 176,400 to 451,009. Under the matched selective-P3 certification configuration, however, that geometry has Q=131,476, slightly worse than the Q=136,025 initial geometry. It optimized discretization error.
Refreshed high-order trust steps¶
The repaired workflow uses selective P3 in the cavity and PML, stops after one accepted move, bakes the geometry, rebuilds a reference, and requires a fresh mesh certification before continuing.
| stage | geometry change | fixed Q | fresh-mesh Q | result |
|---|---|---|---|---|
| baseline | — | — | 136,025 | baseline |
| 1 | inner pair +0.25 nm | 138,299 | 145,434 | pass |
| 2 | inner pair +0.50 nm | 150,365 | 154,478 | pass |
| 3 | inner pair +1.00 nm | 162,467 | 120,188 | reject |
| 3b | inner pair +0.50 nm | 159,039 | 129,512 | reject |
| 4 | fourth pair −0.25 nm | 156,348 | 130,870 | reject |
The best retained design has the inner pair displaced outward by 0.75 nm and Q=154,478 at 1532.54 nm, with 0.9887 monitor localization and a 1.29×10⁻¹⁴ relative residual. This is a real 13.57% gain over the matched high-order baseline, but it is 6.33× below the paper's reported NB6-0F Q=978,000 and does not survive enough independent directions to qualify as a useful optimizer.
Blocker and next step¶
The blocker is now specific: fresh OCC/Netgen connectivity changes move the tiny imaginary frequency by 15–30% for 0.25–1 nm geometry changes. The next global refinement already approaches the hardware ceiling: 39.1 GB peak RSS on a 45 GiB machine, with system swap use observed after the sustained run.
Do not spend more time on CSG-remeshed Q ascent. Build the next acceptance loop around a topology-invariant objective:
- use structured-grid FDTD (Tidy3D or Meep) with subpixel smoothing and two resolutions for Q and branch acceptance;
- use QNM/ALE boundary density only to propose a contour step;
- compensate resonance motion by tracking complex frequency, not by sampling at a fixed real frequency;
- accept only if the lower-confidence Q gain is positive at both FDTD resolutions;
- require three consecutive independently re-solved steps before adding arbitrary contours, then V, then physical desired-mode beta.
An alternative is a universal/topology-stable high-order mesh, but it needs a second certification level with Q uncertainty below the requested gain. The current host cannot supply that with global refinement, so structured FDTD is the practical next route.
The retained source contract, designs, trajectories, failed controls, and
machine-readable summary live under
engines/quan_loncar_meep_lab/campaigns/marchal_2026_qnm_reproduction/.
Structured-FDTD gate now ready¶
The no-submit Tidy3D gate has now been implemented and retained. It compares
the initial cavity, the +0.75 nm accepted inner-hole-pair design, and the
+1.75 nm rejected control on two frozen Cartesian grids. Within each
resolution, all three simulations reuse the exact same x/y/z cell-boundary
arrays, so a boundary move changes subpixel material fractions without
changing grid topology. The frozen grid is generated from an unperforated
substrate-backed InP guide, preventing preferential alignment to the initial
hole interfaces.
The model includes the SiO2 lower half-space and through-PML InP waveguide; holes stop at the substrate. Because the substrate breaks midplane parity, the simulations use x/y symmetry only. They run in double precision with subpixel smoothing, four pole probes, and a vector-field branch monitor.
| gate | 20 steps/wavelength | 24 steps/wavelength |
|---|---|---|
| active grid points | 1,848,825 | 2,814,924 |
| time steps (12 ps) | 269,381 | 317,280 |
| exact-grid identity across three designs | pass | pass |
| local pre-upload validation | pass | pass |
No cloud task has been uploaded or started. An empirical projection from
retained Tidy3D jobs is 2.1883 FlexCredits for all six double-precision
tasks, versus 5.1126 remaining in the project ledger. The authoritative
maximum cost is available only after upload and must be reserved before paid
execution. The next scientific result is therefore a bounded six-task
decision, not another NGSolve remesh: both grids must preserve the expected
best > initial > rejected Q ordering, agree on Q within 15%, and identify
the same field branch.
The preflight audit reconstructs both neutral grids and verifies all six simulation hashes, materials, etch depths, symmetries, monitors, and expected hole displacements. Synthetic multi-mode fitting also exposed and repaired a would-be Nyquist alias from excessive post-monitor downsampling. The final sampling margin is 1.71x above the fit-window maximum. Across retained stress cases, the protocol preserves the known three-device Q ordering with noise and a resolvable 50 GHz contaminant, while rejecting unresolved 20 GHz and frequency-degenerate two-decay signals.