# Geometric-phase metalens — focal distance and spot size

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

<div class="case-meta"><span>forward</span><span>resolution 1</span><span>device</span><span>real_world</span><span>metalens</span><span>free_space</span><span>circular_polarization</span><span>tidy3d_golden</span><span>official_notebook</span></div>

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

::::{grid} 1

:::{grid-item-card} Open the complete executed tutorial →
:link: ../notebooks/metalens
:link-type: doc
:class-card: device-ladder-card

Parameters → exact geometry → voxelized material → local FDTDX run → simulated field → quantitative analysis. Every code cell and retained output is visible, and the `.ipynb` source is downloadable.
:::

::::

This page is the compact benchmark record. The linked notebook is the primary scientific documentation and contains the actual simulation evidence.


## What is exercised

A compact 7x7 version retains the official 600 nm, NA=0.5 phase law, 410x85x600 nm TiO2 pillars, silica substrate, and circular input. A pulsed phasor monitor records the x-z intensity map; the propagating focal maximum, transverse FWHM, and focal-core contrast over the same 1 um aperture are compared.

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

## Reconstruction choices

The official device dimensions, material stack, excitations, and measured observable are retained where they determine the physics. The local scene uses **145 × 145 × 254 cells** and the common port/source normalization machinery. Geometry is rasterized as connected material before placement when touching polygons would otherwise introduce grid-snapping seams.

The field panel above is explicitly a schematic of the device and propagation path. The curves and scalar values in the result panel are executed benchmark outputs: solid circles are FDTDX; dashed crosses are the frozen Tidy3D reference.


## Recorded result

| Metric | Observed / error | Reference / limit | Error | Effective budget | Result |
|---|---:|---:|---:|---:|---:|
| `focal_distance_um` | 1.9625 | 1.85 | 0.1125 | 0.448 | <span class="metric-pass">PASS</span> |
| `fwhm_um` | 0.502048 | 0.497904 | 0.00414467 | 0.224686 | <span class="metric-pass">PASS</span> |
| `focal_core_contrast` | 1.92435 | 1.87628 | 0.0480716 | 0.437628 | <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 device_metalens
```

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

[Return to the example atlas](../index.md)