# Dielectric interface Fresnel R/T (upstream method)

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

<div class="case-meta"><span>analytical</span><span>resolution 1</span><span>analytical</span><span>p0</span><span>fresnel</span><span>materials</span><span>high_yield</span></div>

This case checks the implementation against an analytical identity, convergence property, or independent physics invariant.

```{figure} ../../_static/generated/plane_wave_field.png
:alt: Technical schematic associated with Dielectric interface Fresnel R/T (upstream method)

Representative field across a layered material geometry.
```

## What is exercised

Matches solver/tests/simulation/physics/test_fresnel.py: T = S_T/S0 from transmission-side Poynting only; R = 1 - T. n2=1.5. Do not use vacuum-side flux (standing-wave bias).

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



## Recorded result

| Metric | Observed / error | Reference / limit | Error | Effective budget | Result |
|---|---:|---:|---:|---:|---:|
| `reflectance_R` | 0.0407569 | 0.04 | 7.569e-04 | 0.007 | <span class="metric-pass">PASS</span> |
| `transmittance_T` | 0.959243 | 0.96 | 7.569e-04 | 0.053 | <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_dielectric_slab
```

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

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