# Frozen shifted-LDOS optimization · remote atom
Status: frozen_example Phase: stopped_by_request Latest evaluation: 48 refresh in 60 s
Last published: **2026-08-22 10:34:52 UTC**. Geometry fingerprint: `e6da737c3f981b3f`. This completed research example starts from the unloaded semi-2D photonic-crystal cavity of [Zhang *et al.*, Scientific Reports 6, 26038 (2016)](https://www.nature.com/articles/srep26038). The coupling waveguide is absent. A physical Ey-oriented atom is fixed at `(0, -1.75, 0) µm`; the nearest allowed silicon point is pinned exactly 0.500 µm away. The design remains a single 220 nm extrusion throughout. The solver uses the valid x and z mirror symmetries, retaining one quarter of the full spatial domain; y is not a symmetry axis for this offset atom/cavity system. The GPU campaign was stopped by request after its best accepted geometry was replayed and frozen. The full parameter → geometry → simulation → field → analysis workflow is available as an [executed notebook](../examples/notebooks/remote_atom_shifted_ldos_optimization.ipynb). ## Current evaluated geometry ```{figure} ../_static/generated/paper_semi2d_ldos_geometry.png :alt: Current optimized Zhang cavity and atom clearance All 235 holes in the selected 7-row mirror are shown. Optimization stores 119 x-mirror representatives and varies every representative's radius and allowed in-plane position. Twenty-five smooth bulge controls give **379 total degrees of freedom**. Matched forward screens retained seven of the published ten rows and reduced the symmetry-reduced grid from `205 × 188 × 32` to `205 × 124 × 32`. At zero controls this compact domain increased shifted LDOS from 1.860 to 1.978 and conservative Q from 10,114 to 11,456, so the crop did not trade away the tracked atom-coupled pole. ``` | Literal fabrication check | Current value | |---|---:| | Atom-to-silicon minimum | 0.500000 µm | | Minimum hole ligament | 126.096 nm | | Minimum hole diameter | 249.597 nm | | Physical / independent holes | 235 / 119 | | x mirror / single etch | True / True | | FDTD symmetry / spatial saving | x + z / 4× | | Full / simulated grid | 410 × 124 × 64 / 205 × 124 × 32 | | Reverse checkpoints | 64 | ## LDOS optimization history ```{figure} ../_static/generated/paper_semi2d_ldos_progress.png :alt: Shifted LDOS, quality factor, mode volume, and fit health by iteration Geometry and fitted metrics are checkpointed atomically after every expensive FDTD evaluation. Green circles are accepted geometries; red crosses are rejected trust-region trials and do not replace the device. The former Q=44,667 / 26,965 alternation was an exact leader/proposal rollback cycle, not pole-fit noise. Half-step backtracking now evaluates a new interior candidate after rejection instead of regenerating the same Adam proposal. ``` | Fitted quantity | Latest trial | Trusted geometry | |---|---:|---:| | Shifted peak LDOS / vacuum | 17.253 | 18.166 | | Resonant Purcell contribution | 16.253 | 17.166 | | Conservative Q | 43705 | 44667 | | Atom-oriented mode volume | 738.88 µm³ | 715.89 µm³ | | Pole wavelength | 1.5349 µm | 1.5355 µm | | Atom detuning | 0.7911% | 0.7478% | | Pole-fit residual / consistency | 1.0855e-05 / 0.0007691 | 1.2359e-05 / 0.0010612 | “Shifted peak LDOS” is the differentiable fitted-pole estimate $$1 + \frac{3}{4\pi^2}\frac{\lambda_*^3 Q_*}{V_\mathrm{atom}},$$ evaluated at the real part of the tracked pole. It is not silently labeled as fixed-frequency atomic LDOS; the pole detuning is displayed separately. The implementation is the time-domain analogue of the frequency-shifting strategy of [Shaker *et al.*](https://arxiv.org/abs/2511.16643), with a 3% branch window, fit-health gates, and automatic fallback to coherent pole acquisition. ## Latest electric field ```{figure} ../_static/generated/paper_semi2d_ldos_field.png :alt: Latest Ey field of the optimized semi-2D cavity Post-pulse Ey snapshot from evaluation 26; refreshed every 5 evaluations. ``` The live field is diagnostic. Final claims require a fresh 20 nm, 8 ps ringdown plus independent energy/flux-Q agreement and matched-vacuum LDOS. The optimizer grid is 40 nm because the reverse solve is automatically kept inside the 12 GiB GPU; analytic subpixel boundaries still move continuously.