---
title: 2D 20 µm modal-temporal atom-gap optimizer
---

# 2D 20 µm modal-temporal SiN/SiO2 atom-gap optimizer

```{admonition} Live status
:class: note

**paused by user** · phase **q over area** · evaluation **200** · updated **2026-09-04 17:19:54 UTC**
```

<div class="metric-grid">
  <div class="metric-card"><span>Trusted Q</span><strong>1798.6</strong></div>
  <div class="metric-card"><span>Aeff/(λ/nair)²</span><strong>3.829</strong></div>
  <div class="metric-card"><span>Q / normalized Aeff</span><strong>469.74</strong></div>
  <div class="metric-card"><span>Tracked wavelength</span><strong>777.965 nm</strong></div>
  <div class="metric-card"><span>Simulation time</span><strong>2.000 ps</strong></div>
  <div class="metric-card"><span>Latest step time</span><strong>32.6 s</strong></div>
</div>

```{figure} ../_static/generated/atom_gap_2d_q_over_a_progress.png
:alt: Q, mode area, Q over area, and pole diagnostics versus iteration

Q is intentionally plotted on a linear scale. Green points have passed both independent pole-fit checks.
```

```{figure} ../_static/generated/atom_gap_2d_q_over_a_geometry.png
:alt: Full x-z material geometry and longitudinal SiN density

The hard 1 µm air gap crosses the complete 1 µm SiO2 stack. Only the 300 nm SiN core density outside it changes.
```

```{figure} ../_static/generated/atom_gap_2d_q_over_a_field.png
:alt: Full-domain Ey field in the 2D atom-gap cavity

Latest pole-frequency-filtered Ey field, captured at evaluation 200. Its phase is rotated so the atom field is real and positive.
```

```{figure} ../_static/generated/atom_gap_2d_q_over_a_traces.png
:alt: Atom field and energy ringdown traces

The measured atom response and fixed ideal response use one common amplitude scale. Only the source-off portion enters the independent pole fit.
```

## What this test means

This is a true y-invariant Maxwell solve: a short periodic Yee supercell
represents an infinite structure along y. A solved fundamental TE mode is
launched inward from the fixed density-0.5 guide near +x; x symmetry supplies
the coherent launch from -x, while z symmetry retains the correct even Ey
family. The full design is 20 µm long and the atom remains at the center of
the hard 1 µm air gap.

The physical 2D confinement metric is effective **area**, not an assumed 3D
volume. Stage A differentiates one fixed causal target: the complete modal
pulse response at the atom followed by a Q=10,000, fixed-amplitude ringdown.
It does not fit away amplitude or phase. Its exact compact adjoint carries the
linear atom trace; Q, energy, mode area, and field telemetry are audited by a
separate forward solve every five evaluations and are not interpolated on the
plots. Once the atom trace contains a
trustworthy Q>=100 pole and its temporal progress has clearly slowed, Stage B
maximizes the same-pole harmonic Q/Aeff with replay-validated adaptive trust
steps. The source and pole-field monitor then follow the accepted pole.

The field panel is a source-off frequency projection at the tracked pole—not
the final instantaneous field divided by numerical noise. The 2 ps starting
trace grows only when the fitted lifetime would otherwise show less than
roughly 1.5% energy decay. There is no binarization or spatial filter.

Full method: [campaign methodology](https://github.com/hoodlab/fdtdx-hoodlab/blob/main/benchmarks/cases/invdes_atom_gap_2d_q_over_a/METHOD.md).