# Lossy slab attenuation ratio vs analytical TMM

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

<div class="case-meta"><span>forward</span><span>resolution 1</span><span>parity</span><span>analytical_reference</span><span>p2</span><span>metal</span></div>

This case compares a local FDTDX result with pinned reference data generated by Tidy3D.

```{figure} ../../_static/generated/material_models.svg
:alt: Technical schematic associated with Lossy slab attenuation ratio vs analytical TMM

Representative dispersive material response.
```

## What is exercised

FDTDX attenuation ratio for 1um and 2um lossy slabs. The comparator uses ratio_theory from the cached artifact, not its Tidy3D ratio, so this is an analytical TMM validation and is intentionally not tagged tidy3d_golden.

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



## Recorded result

| Metric | Observed / error | Reference / limit | Error | Effective budget | Result |
|---|---:|---:|---:|---:|---:|
| `ratio_rel` | 2.16804 | 2.16635 | 0.00168897 | 0.216635 | <span class="metric-pass">PASS</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 parity_skin_depth
```

Implementation and provenance: `benchmarks/cases/parity_skin_depth/case.yaml`, `benchmarks/cases/parity_skin_depth/run.py`, `benchmarks/goldens/parity_skin_depth.npz`.

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