# Cold-start SiN atom-slot beta optimizer

```{admonition} Live research campaign — qualified_success_plateau
:class: important

This page is regenerated only from atomic optimizer checkpoints. Geometry,
field, beta, and pole metrics are paired to the same evaluated binary mask.
The campaign began from neutral gray density; the shifted phase starts only
from its independently retained clean pole.
```

<div class="optimizer-dashboard-meta">
  <span class="validation-badge metric-pass">two symmetries · 4× reduction</span>
  <span class="validation-badge metric-pass">one-sided right guide</span>
  <span class="validation-badge metric-pass">500 nm atom clearance</span>
  <span class="validation-badge metric-pass">beta_escape</span>
  <span class="validation-badge metric-pass">LBFGS_PARETO_ESCAPE</span>
  <span class="validation-badge">qualified_success_plateau</span>
</div>
<div class="optimizer-metrics">
  <div class="optimizer-metric"><span>latest β</span><strong>79.86%</strong><small>bounded common outer ledger</small></div>
  <div class="optimizer-metric"><span>best β</span><strong>81.33%</strong><small>physically accepted masks</small></div>
  <div class="optimizer-metric"><span>robust β</span><strong>pending</strong><small>minimum across η=0.45 / 0.50 / 0.55</small></div>
  <div class="optimizer-metric"><span>tracked pole</span><strong>Q=206.98 at 782.50 nm</strong><small>field / energy conservative fit</small></div>
  <div class="optimizer-metric"><span>spectral conservation</span><strong>1.37%</strong><small>inner / outer mismatch</small></div>
  <div class="optimizer-metric"><span>connected material</span><strong>99.6%</strong><small>solid reaching right guide</small></div>
</div>

## Literal device contract

The 780.24 nm z-oriented atom sits at the end of a 1 µm-wide air access slot.
No SiN is permitted within 500 nm of it. A 400 nm-wide, 500 nm-thick SiN
waveguide is fixed only on the right. Everything between the slot/clearance
boundary and the terminal guide is a free 2-D topology mask extruded through
one film. The right guide breaks x symmetry; only y and z are reduced, with
parity `(0, +1, -1)`.

The ordinary acquisition used a vacuum-normalized LDOS floor, a 50 nm-radius
conic filter, robust projection, and differentiable material reachability. The
literal Maxwell mask is never silently amputated. The final and shifted solves
use an exactly binary forward mask at projection beta 96.

![Latest literal geometry](../_static/generated/sin_slot_atom_beta_geometry.png)

## Pole-tracked beta continuation

![Beta, LDOS, and pole history](../_static/generated/sin_slot_atom_beta_progress.png)

The clean handoff pole is Q=162.14 at 781.47 nm. The shifted phase runs a
1.55 ps broadband pulse on every adjoint evaluation. Differentiable field and
stored-energy fits follow the complex pole, and the real-frequency pulse DFT
is recentered when the pole drifts. This is the time-domain pole-following
counterpart of [Shaker et al.'s eigenfrequency-shifted method](https://arxiv.org/abs/2511.16643),
not a claim that FDTD contains their FDFD shift-invert eigensolver.

Beta uses one conserved channel decomposition: guided TM power plus `-x`,
residual `+x`, `±y`, and `±z` power on the same outer box. It is bounded by
construction. The shifted score is `log(beta)` and deliberately has no LDOS
or atom-power retention floor; emission, Purcell, and guided Purcell remain
visible diagnostics. A mode overlap exceeding the complete +x face, inner/outer
mismatch above 12%, an unhealthy field/energy fit, or Q below 75% of the
retained seed rejects the proposal and rolls back. The service continues
indefinitely after accepted and rejected steps.

![Current Ez field](../_static/generated/sin_slot_atom_beta_field.png)

![Directional residual loss](../_static/generated/sin_slot_atom_beta_losses.png)

## Pareto escape controller

![Robust beta, Q, and guided-Purcell archive](../_static/generated/sin_slot_atom_beta_pareto.png)

The production controller keeps separate beta, Q, and guided-Purcell islands
on the one GPU. An adjoint supplies a direction, while exact-binary
forward-only candidates at controlled topology churn decide whether the
L-BFGS curvature history is committed. Erosion, nominal, and dilation pole
fits gate promotion into the robust shared archive. Migrated or exploratory
masks that pass only one threshold are visibly marked provisional and cannot
unlock the 90% beta constrained second stage. Structured, spatially correlated
mutations are screened only when the archive stagnates; the best-beta mask is
never overwritten by exploration.

## Current checks

| check | value |
| --- | ---: |
| optimizer status | `qualified_success_plateau` |
| optimizer algorithm | `lbfgs_pareto_escape` |
| completed adjoint updates | 165 ordinary + 23 accepted shifted, including 6 Pareto escape updates (11 new adjoints / 173 validation forwards) |
| active objective | beta_escape |
| robust / provisional archive entries | 0 / 10 |
| full / reduced grid | (360, 208, 80) / 4 |
| guided port effective index | 1.77701 |
| latest gray fraction | 0.00% |
| left slot clear | True |
| right guide present | True |
| disconnected solid pixels | 51 |
| latest dominant residual loss | ±z |
| retained pole source update | 163 |
| last ordinary LDOS / vacuum | 0.594 |
| shifted pulse fit interval | 0.200--1.420 ps |

Last checkpoint update: 2026-08-23T00:15:35.530770+00:00.