# 4-pair Bragg stack R/T spectrum vs Tidy3D

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

<div class="case-meta"><span>forward</span><span>resolution 1</span><span>parity</span><span>p2</span><span>multilayer</span><span>tidy3d_golden</span></div>

This case compares a local FDTDX result with pinned reference data generated by Tidy3D. The originating Tidy3D example is [`BraggGratings.ipynb`](https://github.com/flexcompute/tidy3d-notebooks/blob/c37c785d52e9258c9d048a781524b8e8d7c758ca/BraggGratings.ipynb), pinned at commit `c37c785d52e9`.

```{figure} ../../_static/generated/plane_wave_field.png
:alt: Technical schematic associated with 4-pair Bragg stack R/T spectrum vs Tidy3D

Representative field across a layered material geometry.
```

## What is exercised

4-pair quarter-wave Bragg stack, n1=1.5 / n2=2.0, d1=1/(4n1) um, d2=1/(4n2) um, probed at 0.85/1.0/1.15 um. Method: CW Poynting T=S_T/S0 (lossless), R=1-T, transmission-side flux only (avoids vacuum standing-wave E×H bias). Grid spacing r=d2/6 chosen so both layers are exact quarter-wave cells (d1=8r, d2=6r, n1*d1=n2*d2=250 nm).

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



## Recorded result

| Metric | Observed / error | Reference / limit | Error | Effective budget | Result |
|---|---:|---:|---:|---:|---:|
| `R_rel_l2` | 0.0230984 | 0.05 | 0.0230984 | 0.05 | <span class="metric-pass">PASS</span> |
| `R_max_abs` | 0.0160291 | 0.03 | 0.0160291 | 0.03 | <span class="metric-pass">PASS</span> |
| `T_rel_l2` | 0.0274701 | 0.05 | 0.0274701 | 0.05 | <span class="metric-pass">PASS</span> |
| `T_max_abs` | 0.0160291 | 0.03 | 0.0160291 | 0.03 | <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_bragg_stack
```

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

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