# Binary atom-gap antenna coupled to a feedthrough waveguide

<span class="validation-badge">validated · 2026-08-28</span>

<div class="case-meta"><span>invdes</span><span>resolution 1</span><span>invdes</span><span>cavity_qed</span><span>beta_factor</span><span>waveguide</span><span>free_form</span><span>symmetry</span><span>binary</span><span>hard_vacuum_gap</span></div>

This case checks optimization performance: the best objective reached, not geometry identity or convergence speed.

```{figure} ../../_static/generated/inverse_design_splitter.png
:alt: Technical schematic associated with Binary atom-gap antenna coupled to a feedthrough waveguide

Differentiable inverse-design result and convergence history.
```

## What is exercised

Stage one is deliberately ordinary density topology optimization. It starts from a generic nearly uniform control field, maximizes the actual waveguide branching ratio, follows a fixed projection schedule, and ends with an exact binary straight-through mask. No cavity or optimized geometry is used as a warm start. Equal left/right emission is imposed by x symmetry, so a total guided beta of 0.90 means 0.45 into each physical propagation direction.

This case runs at its declared full benchmark resolution (resolution factor 1.0).



## Recorded result

| Metric | Observed / error | Reference / limit | Error | Effective budget | Result |
|---|---:|---:|---:|---:|---:|
| `guided_beta` | — | — | — | — | <span class="metric-blocked">CHECK</span> |
| `gap_dielectric_violation` | — | — | — | — | <span class="metric-blocked">CHECK</span> |
| `material_binary_fraction` | — | — | — | — | <span class="metric-blocked">CHECK</span> |

The table is rendered from `progress.json`; it is not a hand-written success claim. For metrics that report an error directly, the “observed” column repeats that error and the reference column is the acceptance threshold.

## Reproduce

```bash
uv run fdtdx-bench run --case invdes_scratch_atom_beta
```

Implementation and provenance: `benchmarks/cases/invdes_scratch_atom_beta/case.yaml`, `benchmarks/cases/invdes_scratch_atom_beta/run.py`.

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