Source
Engine majumdar_lab · package package/multilayer_autonomous_optimizer · assembled 2026-07-29 15:57 UTC.
Majumdar multilayer phase-16 validation¶
Decision¶
Continue the local analytical/FDTD trust-region approach. The first proposed geometry change improves the fitted FDTD Q, the matched core-center mode volume, the anthracene-center mode volume, and both core- and anthracene-referenced Purcell proxies. The wavelength and spatial localization remain essentially fixed, so this is the same cavity branch.
This is one local direction confirmation, not proof that the surrogate remains accurate over a long trajectory. The next decision point is one five-step analytical block plus its FDTD checkpoint.
Corrected observables¶
The original report's missing V and coupling values were caused by boundary NaNs from permittivity interpolation. The field and flux monitor data were finite. The corrected procedure uses nearest-neighbor extrapolation for the sub-grid homogeneous boundary continuation and exact plane monitors for the oriented point denominators.
| Observable | Baseline | Phase 16 | Relative/change |
|---|---|---|---|
| FDTD Q | 5383.0195 | 5601.2129 | +4.0534% |
| analytical Q | 6733.6407 | 7117.8640 | +5.7060% |
| wavelength (nm) | 778.46203 | 778.46628 | +0.00425 nm |
| resonance-fit error | 0.002519 | 0.002071 | improved |
| localization fraction | 0.686081 | 0.685713 | -0.000368 |
| peak V / (lambda/nSiN)^3 | 3.45807 | 3.46177 | +0.1068% |
| core-center Ey V / (lambda/nSiN)^3 | 7.78028 | 7.71508 | -0.8380% |
| anthracene-center Ey V / (lambda/nAnth)^3 | 11.77512 | 11.69859 | -0.6500% |
| total x-plane-flux external Q | 6271.70 | 6422.22 | +2.40% |
| non-x-radiation Q | 42135.68 | 52430.89 | +24.43% |
| total x-plane flux decay fraction | 0.85830 | 0.87216 | +0.01386 |
| directional-Q / fitted-Q | 1.01414 | 1.02146 | within 2.2% |
| peak Purcell proxy | 118.29 | 122.95 | +3.94% |
| core-center Purcell proxy | 52.58 | 55.17 | +4.93% |
| anthracene-center Purcell proxy | 34.74 | 36.38 | +4.73% |
The FDTD-to-analytical log-Q response ratio is 0.7160. After the exact phase-16 analytical refresh, the analytical normalized core-point volume is 3.08834 versus 3.10219 at baseline. Its fundamental-feed-pole fraction is 0.60919 versus 0.57604, but the existing FDTD files do not contain mode monitors, so that coupling direction is not yet independently validated.
The absolute analytical and FDTD mode-volume values should not be equated: the analytical value uses QNM residue normalization in a truncated basis, whereas the FDTD value uses a late-time real-field electric-energy integral. The useful validation signal is their local response to the same geometry.
What the multilayer physics is doing¶
The finite-volume z partition of the electric-energy density is nearly unchanged between the two designs:
| z region | Baseline fraction | Phase-16 fraction |
|---|---|---|
| substrate | 0.03219 | 0.03199 |
| SiN-height slice | 0.56166 | 0.56218 |
| anthracene | 0.36736 | 0.36714 |
| PVA | 0.03793 | 0.03784 |
| upper air | 0.00086 | 0.00086 |
Roughly 37% of this electric-energy measure lies in anthracene, so the film stack is not a perturbative afterthought. Its layered eigenproblem must remain inside the resonance engine and its benchmark definition.
Coupling limitation and the v0.3 measurement¶
The imported confirmation reports
for the sum of the two x-directed flux planes. Those planes collect TE0, any other guided or film/slab modes, and x-directed radiation. Therefore the old 0.85830 and 0.87216 values are useful directional-loss diagnostics but are not evidence for TE0 coupling.
Version 0.3 adds a ringdown-apodized ModeMonitor and matching spectral
FluxMonitor in the straight +x feed section. It explicitly selects and
records the highest-real-neff propagating Ey-like mode, checks that Tidy3D's
x-plane TE fraction is at least 0.5, checks incoming contamination and modal
power closure, and infers the -x port from exact x symmetry. This yields
beta_TE0 = Q_total / Q_TE0. The next paid checkpoint will be the first FDTD
test of the analytical TE0 objective.
This remains a cavity-decay-channel metric. A port-excited S-parameter simulation is required for driven transmission or input-to-cavity efficiency.
Stop/rebuild conditions¶
Do not abandon the approach now. Rebuild or demote the analytical engine if any of these occur:
- two FDTD checkpoints give the opposite sign from a predicted positive composite objective change;
- branch localization/overlap fails or the resonance jumps outside the target wavelength window;
- directional loss accounting differs from ResonanceFinder Q by more than about 15% after monitor convergence;
- core-center V repeatedly changes in the opposite direction from its analytical prediction by more than the FDTD convergence uncertainty;
- centered finite differences fail to reproduce the implicit gradient after tightening the analytical truncation.
One sign failure automatically halves the trust radius in the autonomous driver. Two sign failures should stop the run for model revision rather than continuing to spend FlexCredits.
Method references¶
The monitor and harmonic-inversion pattern follows Flexcompute's official Cavity FOM example, with ResonanceFinder for the short ringdown and Tidy3D field/permittivity/flux monitors for V and directional loss accounting.