# Real-world device reproductions and inverse-design audit Ten forward examples from the official Tidy3D notebook collection are validated as **executed, downloadable FDTDX notebooks**. The high-Q nanobeam tutorial independently rebuilds literal cylinders and reaches 5.33× the unchanged cavity Q locally; a matched fixed-hole-count Tidy3D pair confirms a 1.741× shape-optimization gain. The other inverse-design pages distinguish local optimizer scores from independent Tidy3D forward validation of the same final geometry: the S-matrix crossing passes the user's 10% trust check but misses the stricter 95% external gate, while WDM, bandpass, the digital splitter, and compact grating coupler remain explicit failures. ```{admonition} What “reproduced” means here :class: important For a validated entry, the benchmark retains the physical device and observable, then compares an executed local result with a frozen reference derived from the notebook or a reviewed one-time Tidy3D run. Each forward link is the actual `.ipynb`: ordinary Python cells followed by retained geometry, material, field, spectrum, ringdown, or analysis outputs. Inverse cases return only after their initialization, parameterization, symmetries, fabrication constraints, normalization, and FOM all match the cited problem. ``` ## Browse by device family - [Integrated photonic circuits](#integrated-photonic-circuits): routing, splitting, bending, coupling, and polarization conversion. - [Resonators and spectral devices](#resonators-and-spectral-devices): Bragg filtering and nanobeam ringdown Q. - [Free-space and periodic optics](#free-space-and-periodic-optics): a THz metasurface and geometric-phase metalens. - [Inverse-designed devices](#inverse-designed-devices): passing results and fully visible failed fidelity audits. ## Integrated photonic circuits Each notebook follows the same practical sequence: parameter setting, geometry setting, geometry/material plotting, local simulation, field plotting, and quantitative analysis. Solid curves/markers are FDTDX values; dashed comparison curves/markers are the pinned Tidy3D reference where applicable. ::::{grid} 1 1 2 2 :gutter: 3 :::{grid-item-card} Directional coupler — broadband through/cross parity :link: notebooks/directional_coupler :link-type: doc headline error **0.0385** · budget 0.2 **Executed notebook** · parameters · geometry · voxelization · field · analysis ::: :::{grid-item-card} Waveguide crossing — O-band through and crosstalk spectra :link: notebooks/waveguide_crossing :link-type: doc headline error **0.0388** · budget 0.1 **Executed notebook** · parameters · geometry · voxelization · field · analysis ::: :::{grid-item-card} Euler-like bend — broadband 90-degree transmission :link: notebooks/euler_bend :link-type: doc headline error **0.0078** · budget 0.05 **Executed notebook** · parameters · geometry · voxelization · field · analysis ::: :::{grid-item-card} Edge coupler — Gaussian beam to inverse taper :link: notebooks/edge_coupler :link-type: doc headline error **0.155** · budget 0.2 **Executed notebook** · parameters · geometry · voxelization · field · analysis ::: :::{grid-item-card} 1x4 MMI — four-port broadband power distribution :link: notebooks/mmi_1x4 :link-type: doc headline error **0.0769** · budget 0.12 **Executed notebook** · parameters · geometry · voxelization · field · analysis ::: :::{grid-item-card} Compact polarization splitter-rotator — TE/TM routing :link: notebooks/polarization_splitter_rotator :link-type: doc headline error **0.00308** · budget 0.08 **Executed notebook** · parameters · geometry · voxelization · field · analysis ::: :::: ## Resonators and spectral devices ::::{grid} 1 1 2 2 :gutter: 3 :::{grid-item-card} Bragg grating — transmission and reflection stopband :link: notebooks/bragg_grating :link-type: doc headline error **0.0791** · budget 0.12 **Executed notebook** · parameters · geometry · voxelization · field · analysis ::: :::{grid-item-card} Nanobeam cavity — resonant wavelength and Q :link: notebooks/nanobeam_cavity :link-type: doc headline error **0.0193** · budget 0.0229 **Executed notebook** · parameters · geometry · voxelization · field · analysis ::: :::: ## Free-space and periodic optics ::::{grid} 1 1 2 2 :gutter: 3 :::{grid-item-card} Dielectric metasurface absorber — periodic THz resonator :link: notebooks/metasurface_absorber :link-type: doc headline error **0.00985** · budget 0.12 **Executed notebook** · parameters · geometry · voxelization · field · analysis ::: :::{grid-item-card} Geometric-phase metalens — focal distance and spot size :link: notebooks/metalens :link-type: doc headline error **0.112** · budget 0.448 **Executed notebook** · parameters · geometry · voxelization · field · analysis ::: :::: ## Inverse-designed devices ::::{grid} 1 :::{grid-item-card} Executed Autograd24 digital-splitter audit → :link: notebooks/digital_splitter :link-type: doc :class-card: device-ladder-card Parameters → exact shallow-hole geometry → uniform start → 150 differentiable FDTD updates → fully binary checkpoint selection → convergence and passivity → fresh five-wavelength fields. The scientifically comparable run reaches **0.4325** (91.6% of Tidy3D), below the repository's stricter **0.4485** gate. ::: :::: ::::{grid} 1 :::{grid-item-card} Executed compact grating-coupler audit → :link: notebooks/grating_coupler :link-type: doc :class-card: device-ladder-card Exact random cold start → 20 nm double-filtered controls → 80 nm erosion/dilation rule → 150 differentiable 3D FDTD updates → fully binary checkpoint → fresh xy/xz fields → independent Tidy3D spectrum. FDTDX reports **0.5773**; Tidy3D gives **0.5339** for that same geometry versus **0.6637** published. **Scientific result: FAIL.** ::: :::: Five former passes or scalar claims remain visible as failures when independent validation, parameterization, or memory requirements do not support equivalence. The high-Q cavity is a separate validated local objective—not a claim of parity with a published Tidy3D inverse-design result. No reduced 16×16 surrogate is presented as equivalence. See the [inverse-design fidelity audit](../project/inverse_design_audit.md) for the exact comparison and memory evidence. ::::{grid} 1 1 2 2 :gutter: 3 :::{grid-item-card} GPU-native inverse design of a high-Q nanobeam cavity :link: notebooks/high_q_nanobeam_optimization :link-type: doc best FOM **187133.234** · target 70250.601 · 1 updates **Executed notebook** · parameters · geometry · voxelization · field · analysis ::: :::{grid-item-card} Inverse-designed waveguide bend — modal-transmission parity :link: ../project/inverse_design_audit :link-type: doc **invalid adapter** · scalar claim withdrawn **Audit record** · initialization · symmetry · constraints · FOM ::: :::{grid-item-card} Inverse-designed four-channel wavelength demultiplexer :link: ../project/inverse_design_audit :link-type: doc **invalid adapter** · scalar claim withdrawn **Audit record** · initialization · symmetry · constraints · FOM ::: :::{grid-item-card} Inverse-designed broadband photonic bandpass filter :link: ../project/inverse_design_audit :link-type: doc **invalid adapter** · scalar claim withdrawn **Audit record** · initialization · symmetry · constraints · FOM ::: :::{grid-item-card} Inverse-designed low-loss waveguide crossing :link: ../project/inverse_design_audit :link-type: doc **invalid adapter** · scalar claim withdrawn **Audit record** · initialization · symmetry · constraints · FOM ::: :::{grid-item-card} Inverse-designed crossing from a four-port S-matrix target :link: notebooks/smatrix_crossing :link-type: doc best FOM **0.969** · target 0.931 · 75 updates **Executed notebook** · parameters · geometry · voxelization · field · analysis ::: :::: ::::{grid} 1 :::{grid-item-card} Frozen remote-atom shifted-LDOS optimization → :link: notebooks/remote_atom_shifted_ldos_optimization :link-type: doc :class-card: device-ladder-card Executed parameter setting → literal seven-row geometry → shifted-pole FDTD configuration → complete accepted/rejected history → paired Ey field → frozen 40 nm analysis. The best accepted silicon geometry reaches LDOS **18.166** and conservative Q **44,667**; it is explicitly pending fine-grid validation. ::: :::: ## Results at a glance | Device | Mode | Headline result | Status | |---|---|---:|---:| | [Directional coupler — broadband through/cross parity](notebooks/directional_coupler.ipynb) | forward | 0.03851 / 0.2 budget | PASS | | [Waveguide crossing — O-band through and crosstalk spectra](notebooks/waveguide_crossing.ipynb) | forward | 0.03879 / 0.1 budget | PASS | | [Euler-like bend — broadband 90-degree transmission](notebooks/euler_bend.ipynb) | forward | 0.007795 / 0.05 budget | PASS | | [Edge coupler — Gaussian beam to inverse taper](notebooks/edge_coupler.ipynb) | forward | 0.155 / 0.2 budget | PASS | | [1x4 MMI — four-port broadband power distribution](notebooks/mmi_1x4.ipynb) | forward | 0.07692 / 0.12 budget | PASS | | [Bragg grating — transmission and reflection stopband](notebooks/bragg_grating.ipynb) | forward | 0.07908 / 0.12 budget | PASS | | [Nanobeam cavity — resonant wavelength and Q](notebooks/nanobeam_cavity.ipynb) | forward | 0.0193 / 0.02294 budget | PASS | | [GPU-native inverse design of a high-Q nanobeam cavity](notebooks/high_q_nanobeam_optimization.ipynb) | invdes | 187133.2341 / 70250.6014 minimum | PASS | | [Dielectric metasurface absorber — periodic THz resonator](notebooks/metasurface_absorber.ipynb) | forward | 0.009849 / 0.12 budget | PASS | | [Compact polarization splitter-rotator — TE/TM routing](notebooks/polarization_splitter_rotator.ipynb) | forward | 0.003077 / 0.08 budget | PASS | | [Geometric-phase metalens — focal distance and spot size](notebooks/metalens.ipynb) | forward | 0.1125 / 0.448 budget | PASS | | [Inverse-designed waveguide bend — modal-transmission parity](../project/inverse_design_audit.md) | invdes | not scientifically comparable | AUDIT FAIL | | [Inverse-designed four-channel wavelength demultiplexer](../project/inverse_design_audit.md) | invdes | not scientifically comparable | AUDIT FAIL | | [Inverse-designed broadband photonic bandpass filter](../project/inverse_design_audit.md) | invdes | not scientifically comparable | AUDIT FAIL | | [Inverse-designed low-loss waveguide crossing](../project/inverse_design_audit.md) | invdes | not scientifically comparable | AUDIT FAIL | | [Inverse-designed crossing from a four-port S-matrix target](notebooks/smatrix_crossing.ipynb) | invdes | 0.9694 / 0.9314 minimum | PASS | | [Compact inverse-designed grating coupler](notebooks/grating_coupler.ipynb) | invdes | 0.5339 / 0.6637 published | FAIL | | [Remote-atom shifted-LDOS shape optimization](notebooks/remote_atom_shifted_ldos_optimization.ipynb) | invdes research | LDOS 18.166 / Q 44,667 at 40 nm | FROZEN EXAMPLE | ## Automatic setup policy The point of this ladder is broader than making fifteen hand-tuned scenes pass. The reusable policies that emerged are now part of the benchmark infrastructure: - choose grid pitch from the smallest physical feature and material wavelength, with anisotropic spacing for long adiabatic devices; - boolean-union touching material before rasterization so geometry does not acquire artificial seams; - normalize modal and free-space power with an independent incident/reference solve; - stop pulsed simulations from a relative field-energy decay criterion, retaining a hard time-window ceiling; - reproduce the source notebook's filter, projection schedule, initialization, and erosion/dilation constraints exactly; - retain fixed incident calibration and reject non-passive results instead of rescaling powers onto a passive simplex. Those choices are recorded in each case and are visible in the runners. A new device should normally need geometry, materials, ports, and an objective—not a private collection of normalization factors and termination constants. ## Reproduce the ladder Run one case directly: ```bash uv run fdtdx-bench run --case device_directional_coupler uv run fdtdx-bench run --case invdes_power_splitter ``` The exact notebook list, SHA-256 pins, and cloud-spend ceiling live in `benchmarks/device_ladder.yaml`. Frozen-reference provenance lives in `benchmarks/golden_provenance.yaml`; no Tidy3D job is submitted in the benchmark loop.