---
title: Unqualified success — component-aware Yee atom-strip Q/V cavity
---

# Unqualified success — component-aware Yee atom-strip Q/V cavity

**Worker:** not active · **stage:** `spline_boundary_q_over_v` ·
**status:** `unqualified_success_stopped_resumable_tidy3d_validated` · **checkpoint age:** 3021.7 min

This completed campaign starts from density 0.5 in the
same 100 nm SiN / 300 nm-per-side SiO2 geometry and immutable one-micron atom
access strip as the successful predecessor, but every forward and adjoint solve
uses the upgraded fixed component-aware Yee material operator from the first
step.

Stage A uses raw Adam against the exact absolute atom-field temporal trace of
the Q=10,000, V=0.1 µm³ ideal pole. After the temporal objective plateaus with trustworthy Q≥100, direct Q/V begins. Stage B then
uses adaptive-trust L-BFGS-B to maximize only
`log(Q_harmonic)-log(V_atom/(lambda_pole/n_air)^3)`. Direct density pixels
train while both stack thicknesses remain frozen until pixel-only Q/V plateaus.
Stage C then enables both thickness coordinates, analytically preserves the
physical density at beta=1, and starts gradual unfiltered tanh continuation.
Each fixed-beta Q/V subproblem reaches either strict convergence or less than
1% gain over a settled full L-BFGS memory before beta rises by 1. Binary bulk is
replayed as a topology-free smooth cubic-spline phase field only when binary
readiness and a fixed-beta Q/V plateau coincide. Its controls may fuse or erase
islands while retaining subpixel cut cells. The current rollback-safe boundary
fork optimizes log Q / normalized atom volume; Q, atom volume, and Q/V remain measured
on every trusted replay. No spatial filter is used.

```{admonition} Unqualified success · frozen at accepted update 2562
:class: important

The exact stopped geometry is independently replayed in Tidy3D: **Q=3894.36**, **V=5.99346 (lambda/n_air)^3**, **Q/V=649.767**, **Purcell=49.3764**, and **wavelength=826.213 nm**. The complete optimizer state and smooth-boundary geometry are preserved for later continuation.
```


| quantity | current |
|---|---:|
| temporal Adam updates | 285 · plateau not detected (0/0 trend samples) |
| pixel-only Q/V accepted / transition | 0 / objective plateau |
| pole accepted updates / trials | 2277 / 14 |
| Q | **5779.2** |
| best recorded Q (trust gate shown above) | 5807.83 |
| field / energy Q | 5835.29 / 5779.2 |
| Q-estimator ratio | 1.00971 |
| pole wavelength | 838.603 nm |
| source-center wavelength | 835.887 nm |
| field-monitor wavelength | **838.757 nm** |
| design-region slab thickness | **0.3 µm** |
| Stage-B thickness coordinate / range | **True** / 0.050–0.500 µm |
| SiO2 thickness per side | **0.35846 µm** |
| Stage-B SiO2 coordinate / maximum | **True** / 1.000 µm |
| stack-thickness constraint | t_SiO2 − t_SiN ≥ 0.050 µm |
| SiO2 full width | **2 µm** |
| joint-stage SiO2 width coordinate / range | **False** / 2.000–2.000 µm |
| physical mode volume | 2.72015 µm³ |
| normalized mode volume | 4.61236 (λ_pole/n_air)³ |
| Q / normalized atom volume | **1259.03** |
| Purcell from Q/V | 95.6749 |
| fitted atom-pole amplitude at source clear | **0.010666** |
| absolute atom-trace peak / handoff | 0.248671 |
| source spectral power at pole / actual carrier | 0.99402 |
| reciprocal guided-Purcell proxy | **4.50459e-05** |
| guided-Purcell proxy / handoff | **5.76308** |
| Stage-B volume treatment | **none — log Q / normalized atom volume is optimized** |
| three-window V span | 0.00598368 |
| active Q/V run time / window | 2.75 / 0.8 ps |
| gradient backend / storage | **`checkpointed`** / 221 lean checkpoints |
| structural backend decision | `device memory capacity is unavailable; conservative checkpointed fallback` |
| exact reversible PML tape size | 11.1157 GB |
| frozen measured value+gradient speedup | 5.25199x |
| Q/V fit start / nominal lifetime per window | 0.35 ps / 0.125 τ_amplitude |
| precision-triggered tape growths | 0 |
| final ringdown field-power / energy fraction | 0.540161 / 0.536943 |
| finite-step adjoint direction verified | **False** |
| ideal temporal fidelity | 0.487369 |
| active objective / value | **log Q / normalized atom volume** / 7.1381 |
| stage plateau / reason | **False** / `collecting_optimizer_memory` |
| plateau samples / evidence window | 0 / 0 |
| objective slope / detectable slope | — / — |
| trust-floor restarts since progress | 0 / 2 |
| practical fixed-beta Q/V gain over one memory | —% / 1% limit |
| practical plateau samples / required | 0 / 11 |
| practical trust radius still expanding | False |
| healthy / cumulatively pruned curvature pairs | **0 / 846** |
| L-BFGS / current-gradient predicted-ascent ratio | **1** |
| replay-triggered curvature recoveries | 144 |
| maximum last density motion | 1.84178e-05 |
| trust radius | 1.25e-05 |
| binarity score (1 is binary) | **0.990384** |
| trainable gray fraction (0.05<rho<0.95) | **1.49073%** |
| archived tangent-stage Q/V floor | 309.567 |
| projection beta / eta | **32 / 0.5** |
| fixed-beta accepted Q/V updates / transition | 0 / objective plateau |
| material parameterization | `topology_free_absolute_cubic_spline_phase_field_with_cut_cells` |
| hard atom access | **1.000 µm full-y air strip, immutable** |
| pixel / grid | 50 nm / [181, 35, 45] |
| non-PML z span / material-stack-to-PML air gap | 3.50 / 1.24 µm |
| z PML | 0.50 µm per side |
| z-padding convergence audit | `not_run` |
| 1.50→3.40 µm replay: residual / field-Q / energy-Q change | nan% / nan% / nan% |
| binarization / material projection / filter | **True / False / off** |
| physical waveguide escape eta | not part of the active objective |

## Q, V, objective, and optimizer history

![Q, V, objective, and motion](../_static/generated/atom_strip_cladded_qv_yee_restart_history.png)

The Q axis is linear. A pole is not trusted until the centered
Ey and total
energy decay estimates agree. Mode volume uses the geometric mean of their
three same-pole windows and the
same fitted pole wavelength; the local permittivity is exactly air by the hard
geometry constraint. This is a clean restart and contains no metric history or
optimizer memory from the legacy staircase campaign. The predecessor remains
preserved on its own dashboard for comparison.

## Independent Tidy3D checkpoint trend

The horizontal coordinate is the **global accepted geometry update**, not a
renumbered index into the bounded history buffer. The latest orange marker
validates checkpoint **2562**; the current FDTDX geometry
is update **2562**. The shaded tail therefore contains
**0 accepted updates without an independent Tidy3D replay**.

Orange stars are independent 6 ps Tidy3D replays on one
fixed 25 nm uniform grid. They use each checkpoint's accepted 50 nm smooth-boundary
cut-cell density and optimized vertical stack. This is a controlled trend check,
not a spatial continuum extrapolation. Markers are intentionally not connected:
Tidy3D evaluated only the listed immutable checkpoints.

| checkpoint | FDTDX λ (nm) | Tidy3D λ (nm) | FDTDX Q | Tidy3D Q | FDTDX V/λ³ | Tidy3D V/λ³ | FDTDX Q/V | Tidy3D Q/V | Tidy3D/FDTDX Q/V |
|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|
| 1100 | 800.442 | 785.086 | 1225.92 | 826.67 | 3.11071 | 3.34574 | 394.097 | 247.082 | 0.626956 |
| 1150 | 801.384 | 785.353 | 1230.58 | 902.376 | 3.09284 | 3.35614 | 397.879 | 268.873 | 0.675766 |
| 1200 | 802.182 | 785.639 | 1235.6 | 992.741 | 3.08324 | 3.3739 | 400.748 | 294.241 | 0.73423 |
| 1250 | 806.05 | 787.652 | 1286.43 | 1261.75 | 3.05731 | 3.69109 | 420.772 | 341.837 | 0.812404 |
| 1300 | 808.208 | 788.505 | 1308.11 | 1093.37 | 3.04234 | 4.04394 | 429.968 | 270.372 | 0.628819 |
| 1350 | 810.444 | 788.688 | 1335.99 | 1039.18 | 3.02226 | 4.59962 | 442.051 | 225.928 | 0.51109 |
| 1400 | 812.357 | 797.561 | 1431.55 | 1077.22 | 3.05115 | 3.18546 | 469.182 | 338.167 | 0.720758 |
| 1450 | 814.585 | 799.298 | 1496.72 | 1378.14 | 3.0498 | 3.33001 | 490.762 | 413.854 | 0.843289 |
| 1500 | 815.767 | 800.103 | 1535.29 | 1472.94 | 3.05762 | 3.42809 | 502.118 | 429.668 | 0.855712 |
| 1550 | 816.911 | 800.824 | 1565.05 | 1493.07 | 3.0687 | 3.54953 | 510.003 | 420.639 | 0.824777 |
| 1600 | 817.833 | 801.222 | 1587.01 | 1491.39 | 3.06638 | 3.60404 | 517.552 | 413.811 | 0.799555 |
| 1650 | 819.947 | 801.986 | 1654.75 | 1502.05 | 3.07799 | 3.6958 | 537.609 | 406.422 | 0.75598 |
| 1700 | 820.763 | 801.752 | 1788.53 | 1733.35 | 3.17373 | 3.89096 | 563.541 | 445.482 | 0.790505 |
| 1750 | 821.178 | 801.82 | 1832.37 | 1732.04 | 3.18356 | 4.00448 | 575.573 | 432.526 | 0.751471 |
| 1800 | 822.196 | 802.201 | 1928.84 | 1659.53 | 3.22293 | 4.18287 | 598.475 | 396.744 | 0.662925 |
| 2350 | 835.771 | 816.442 | 4162.63 | 1839.01 | 4.10013 | 6.15712 | 1015.24 | 298.681 | 0.294197 |
| 2400 | 836.389 | 816.924 | 4403.37 | 1726.55 | 4.18306 | 6.42061 | 1052.67 | 268.907 | 0.255454 |
| 2450 | 836.389 | 816.906 | 4500.53 | 1726.75 | 4.21186 | 6.48931 | 1068.54 | 266.091 | 0.249023 |
| 2500 | 837.506 | 824.921 | 5493.24 | 3575.55 | 4.60441 | 5.81117 | 1193.04 | 615.288 | 0.515731 |
| 2550 | 838.678 | 826.249 | 5784.12 | 3892.22 | 4.60391 | 5.73195 | 1256.35 | 679.039 | 0.540485 |
| 2562 | 838.603 | 826.213 | 5807.11 | 3894.36 | 4.61236 | 5.99346 | 1259.03 | 649.767 | 0.516085 |

## Fixed-geometry source-carrier audit

At accepted update 2379, one forward-only replay held the
geometry, material stack, pole-fit center, and tape fixed while moving the
broadband mode-source carrier from 811.754 nm
to 835.887 nm. The fitted pole changed by
0.0000%, Q by
+0.0364%, normalized V by
-0.0189%, and Q/V by
+0.0554%. The alternate fit
remained valid with field/energy residuals
5.57e-06/0.00207.
No optimizer step was taken. This verifies that source recentering improves
excitation and telemetry without creating the measured cavity eigenmetric.


## Ideal and measured atom response

![Ideal and measured temporal response](../_static/generated/atom_strip_cladded_qv_yee_restart_response.png)

The target has fixed amplitude and phase for Q=10,000, beta one, V=0.1 µm³,
and perfect Ey-polarized overlap. It is not rescaled
to fit the simulation.

## Geometry and fields

![Initial, current, and difference geometry](../_static/generated/atom_strip_cladded_qv_yee_restart_geometry.png)

![Ey field profiles](../_static/generated/atom_strip_cladded_qv_yee_restart_fields.png)

## Downloadable layout

**Layout status:** authoritative smooth-boundary GDS. The ZIP includes the GDS, JSON stack/metric
manifest, and README. Before the spline handoff the GDS is intentionally marked
as a thresholded preview; after handoff it is the fabrication-oriented smooth
boundary representation. GDS is planar, so use the manifest for SiN and SiO2 thicknesses.

{download}`GDS bundle <../_static/downloads/atom_strip_cladded_qv_yee_restart/atom_strip_cladded_qv_yee_restart_gds_bundle.zip>`

{download}`Current GDS <../_static/downloads/atom_strip_cladded_qv_yee_restart/atom_strip_cladded_qv_yee_restart_current.gds>`

{download}`Layout manifest <../_static/downloads/atom_strip_cladded_qv_yee_restart/atom_strip_cladded_qv_yee_restart_manifest.json>`


{download}`Exact campaign methodology <../_static/downloads/atom_hole/METHOD_XYZ_Y_STRIP_CLADDED_YEE_RESTART.md>`