# Waveguide S-parameter transmission

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

<div class="case-meta"><span>analytical</span><span>resolution 1</span><span>analytical</span><span>high_yield</span><span>p1</span><span>pic</span><span>sparams</span></div>

This case checks the implementation against an analytical identity, convergence property, or independent physics invariant. The originating Tidy3D example is [`SMatrix.ipynb`](https://github.com/flexcompute/tidy3d-notebooks/blob/c37c785d52e9258c9d048a781524b8e8d7c758ca/SMatrix.ipynb), pinned at commit `c37c785d52e9`.

```{figure} ../../_static/generated/pic_geometry_atlas.svg
:alt: Technical schematic associated with Waveguide S-parameter transmission

Integrated-photonics geometries covered by the benchmark suite.
```

## What is exercised

Upstream solver/tests/simulation/physics/test_sparams.py

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



## Recorded result

| Metric | Observed / error | Reference / limit | Error | Effective budget | Result |
|---|---:|---:|---:|---:|---:|
| `pytest_exit` | 0 | 0 | 0 | — | <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 analytical_waveguide_sparams
```

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

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