# Validated example atlas
These are **all 47 passing cases** in the current catalog. Each page explains the physical claim, shows the exact recorded metric, identifies its source files, and gives the one-command reproduction path. The gallery is generated from `benchmarks/cases/*/case.yaml` and `progress.json` so it cannot silently drift from the suite. Failed inverse-design fidelity audits remain visible on the separate real-world audit page, but are not counted here.
```{admonition} How to read this gallery
:class: note
“Analytical” means an independent formula or invariant. “Forward” means comparison against a frozen Tidy3D golden. “Invdes” means objective-performance parity. Passing does not imply that every Tidy3D feature is implemented; see [validation status](../project/validation.md) for the boundary.
```
## Browse by topic
::::{grid} 1 2 2 3
:gutter: 3
:::{grid-item-card} Foundations: fields, time signals, and grids
:link: index.html#foundations-fields-time-signals-and-grids
:link-type: url
Start here for the Yee update, propagation, power flow, ring-up/ringdown, and numerical-grid behavior.
**5 examples**
:::
:::{grid-item-card} Materials, interfaces, and dispersion
:link: index.html#materials-interfaces-and-dispersion
:link-type: url
Fresnel physics, multilayers, metals, tensor media, birefringence, and dispersive constitutive models.
**14 examples**
:::
:::{grid-item-card} Sources, boundaries, and scattering
:link: index.html#sources-boundaries-and-scattering
:link-type: url
Plane waves, beams, dipoles, TFSF injection, broadband correction, and canonical scattering problems.
**9 examples**
:::
:::{grid-item-card} Integrated photonics: waveguides, ports, and routing
:link: index.html#integrated-photonics-waveguides-ports-and-routing
:link-type: url
Mode launch and readout followed by complete PIC devices: bends, splitters, crossings, and couplers.
**10 examples**
:::
:::{grid-item-card} Resonators, cavities, and spectral filters
:link: index.html#resonators-cavities-and-spectral-filters
:link-type: url
Frequency-selective devices, including a ring, Bragg stopband, and ringdown-extracted nanobeam Q.
**2 examples**
:::
:::{grid-item-card} Free-space and periodic optics
:link: index.html#free-space-and-periodic-optics
:link-type: url
Periodic absorption and wavefront shaping with field and focal-plane observables.
**2 examples**
:::
:::{grid-item-card} Inverse design and automatic differentiation
:link: index.html#inverse-design-and-automatic-differentiation
:link-type: url
Gradient plumbing and multi-port objectives that are not cavity-design campaigns.
**2 examples**
:::
:::{grid-item-card} Inverse-designed cavities and atom interfaces
:link: index.html#inverse-designed-cavities-and-atom-interfaces
:link-type: url
High-Q nanobeams, remote-atom cavities, curved mirrors, atom-gap designs, and their validation records.
**3 examples**
:::
::::
::::{grid} 1
:gutter: 3
:::{grid-item-card} Explore validated devices and the inverse-design audit →
:link: real_world_devices
:link-type: doc
:class-card: device-ladder-card
Ten validated forward notebooks, a fully executed high-Q fitted-ringdown optimization, independently cross-validated inverse-design audits, complete failed-device notebooks for the digital splitter and compact grating coupler, and explicit records for unsupported or invalid inverse adapters.
:::
::::
::::{grid} 1
:gutter: 3
:::{grid-item-card} Frozen remote-atom silicon optimization →
:link: notebooks/remote_atom_shifted_ldos_optimization
:link-type: doc
:class-card: device-ladder-card
An executed research notebook with literal curved-mirror geometry, complete
optimization history, paired Ey field, and a clearly scoped 40 nm result.
:::
::::
## Foundations: fields, time signals, and grids
Start here for the Yee update, propagation, power flow, ring-up/ringdown, and numerical-grid behavior.
::::{grid} 1 2 2 2
:gutter: 2
:::{grid-item-card} Vacuum dipole — finite energy + PML decay
:link: cases/analytical_vacuum_energy
:link-type: doc
PASS · benchmark page · analytical · fields_finite
:::
:::{grid-item-card} Pulsed vs CW multilayer transmission consistency
:link: cases/analytical_pulsed_vs_cw
:link-type: doc
PASS · benchmark page · analytical · max_rel_err
:::
:::{grid-item-card} Plane-wave phase velocity + impedance (vacuum & dielectric)
:link: cases/analytical_plane_wave
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} Phasor vs time-domain Poynting flux consistency
:link: cases/analytical_phasor_poynting
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} Mildly stretched grid vs uniform
:link: cases/analytical_nonuniform_grid
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
::::
## Materials, interfaces, and dispersion
Fresnel physics, multilayers, metals, tensor media, birefringence, and dispersive constitutive models.
::::{grid} 1 2 2 2
:gutter: 2
:::{grid-item-card} Dielectric interface Fresnel R/T (upstream method)
:link: cases/analytical_dielectric_slab
:link-type: doc
PASS · benchmark page · analytical · reflectance_R
:::
:::{grid-item-card} Skin-depth attenuation in lossy conductor
:link: cases/analytical_skin_depth
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} Dispersive Lorentz/Drude/CCPR Fresnel + impedance
:link: cases/analytical_dispersion
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} Fresnel R/T vs Tidy3D golden (tiny 2D-like slab interface)
:link: cases/parity_fresnel_interface
:link-type: doc
PASS · benchmark page · forward · reflectance_R
:::
:::{grid-item-card} Anisotropic dispersion Fresnel per polarization
:link: cases/analytical_anisotropic
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} Birefringence / uniaxial media
:link: cases/analytical_birefringence
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} 3-layer stack transmission spectrum vs Tidy3D
:link: cases/parity_multilayer_T
:link-type: doc
PASS · benchmark page · forward · T_rel_l2
:::
:::{grid-item-card} Fresnel ε=4 (n=2) upstream gold standard
:link: cases/analytical_fresnel_n2
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} Oriented / tilted crystal dispersion
:link: cases/analytical_oriented_dispersion
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} Rotated lossy uniaxial tensor
:link: cases/analytical_complex_tensor
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} 3-layer stack T vs transfer-matrix theory
:link: cases/analytical_multilayer_tmm
:link-type: doc
PASS · benchmark page · analytical · T_max_abs
:::
:::{grid-item-card} Lossy-metal half-space reflectance vs Tidy3D
:link: cases/parity_metal_reflect
:link-type: doc
PASS · benchmark page · forward · reflectance_R
:::
:::{grid-item-card} 4-pair Bragg stack R/T spectrum vs Tidy3D
:link: cases/parity_bragg_stack
:link-type: doc
PASS · benchmark page · forward · R_rel_l2
:::
:::{grid-item-card} Lossy slab attenuation ratio vs analytical TMM
:link: cases/parity_skin_depth
:link-type: doc
PASS · benchmark page · forward · ratio_rel
:::
::::
## Sources, boundaries, and scattering
Plane waves, beams, dipoles, TFSF injection, broadband correction, and canonical scattering problems.
::::{grid} 1 2 2 2
:gutter: 2
:::{grid-item-card} 2D Mie scattering dielectric cylinder
:link: cases/analytical_mie_cylinder
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} Gaussian beam Fresnel / power checks
:link: cases/analytical_gaussian_source
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} Uniform plane source physics
:link: cases/analytical_plane_source
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} Dipole radiated power + pattern symmetry
:link: cases/analytical_dipole_radiation
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} TFSF box cancellation + dispersive bg
:link: cases/analytical_tfsf_region
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} TFSF grid-metric independent injection
:link: cases/analytical_tfsf_grid
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} CW / Gaussian / custom temporal profiles
:link: cases/analytical_temporal_profiles
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} Broadband dispersive-source correction
:link: cases/analytical_dispersive_source
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} 2D dielectric cylinder forward-T vs Tidy3D
:link: cases/parity_mie2d_cylinder
:link-type: doc
PASS · benchmark page · forward · T_through
:::
::::
## Integrated photonics: waveguides, ports, and routing
Mode launch and readout followed by complete PIC devices: bends, splitters, crossings, and couplers.
::::{grid} 1 2 2 2
:gutter: 2
:::{grid-item-card} Si slab mode source: neff + confinement
:link: cases/analytical_mode_waveguide
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} Waveguide S-parameter transmission
:link: cases/analytical_waveguide_sparams
:link-type: doc
PASS · benchmark page · analytical · pytest_exit
:::
:::{grid-item-card} Si/SiO2 slab TE waveguide transmission vs Tidy3D
:link: cases/parity_waveguide_TE
:link-type: doc
PASS · benchmark page · forward · T_far
:::
:::{grid-item-card} Rectangular Y-junction power split vs Tidy3D
:link: cases/parity_y_junction
:link-type: doc
PASS · benchmark page · forward · T1
:::
:::{grid-item-card} Directional coupler — broadband through/cross parity
:link: notebooks/directional_coupler
:link-type: doc
PASS · executed notebook · forward · through_spectrum
:::
:::{grid-item-card} Waveguide crossing — O-band through and crosstalk spectra
:link: notebooks/waveguide_crossing
:link-type: doc
PASS · executed notebook · forward · through
:::
:::{grid-item-card} Euler-like bend — broadband 90-degree transmission
:link: notebooks/euler_bend
:link-type: doc
PASS · executed notebook · forward · out
:::
:::{grid-item-card} Edge coupler — Gaussian beam to inverse taper
:link: notebooks/edge_coupler
:link-type: doc
PASS · executed notebook · forward · out
:::
:::{grid-item-card} 1x4 MMI — four-port broadband power distribution
:link: notebooks/mmi_1x4
:link-type: doc
PASS · executed notebook · forward · out1
:::
:::{grid-item-card} Compact polarization splitter-rotator — TE/TM routing
:link: notebooks/polarization_splitter_rotator
:link-type: doc
PASS · executed notebook · forward · te_wide
:::
::::
## Resonators, cavities, and spectral filters
Frequency-selective devices, including a ring, Bragg stopband, and ringdown-extracted nanobeam Q.
::::{grid} 1 2 2 2
:gutter: 2
:::{grid-item-card} Bus + ring transmission spectrum vs Tidy3D
:link: cases/parity_ring_bus
:link-type: doc
PASS · benchmark page · forward · T_rel_l2
:::
:::{grid-item-card} Bragg grating — transmission and reflection stopband
:link: notebooks/bragg_grating
:link-type: doc
PASS · executed notebook · forward · transmitted
:::
::::
## Free-space and periodic optics
Periodic absorption and wavefront shaping with field and focal-plane observables.
::::{grid} 1 2 2 2
:gutter: 2
:::{grid-item-card} Dielectric metasurface absorber — periodic THz resonator
:link: notebooks/metasurface_absorber
:link-type: doc
PASS · executed notebook · forward · R
:::
:::{grid-item-card} Geometric-phase metalens — focal distance and spot size
:link: notebooks/metalens
:link-type: doc
PASS · executed notebook · forward · focal_distance_um
:::
::::
## Inverse design and automatic differentiation
Gradient plumbing and multi-port objectives that are not cavity-design campaigns.
::::{grid} 1 2 2 2
:gutter: 2
:::{grid-item-card} Invdes smoke: transmission FOM improves under gradient steps
:link: cases/invdes_fom_improve
:link-type: doc
PASS · benchmark page · invdes · best_fom_gain
:::
:::{grid-item-card} Inverse-designed crossing from a four-port S-matrix target
:link: notebooks/smatrix_crossing
:link-type: doc
PASS · executed notebook · invdes · best_fom_parity
:::
::::
## Inverse-designed cavities and atom interfaces
High-Q nanobeams, remote-atom cavities, curved mirrors, atom-gap designs, and their validation records.
::::{grid} 1 2 2 2
:gutter: 2
:::{grid-item-card} Nanobeam cavity — resonant wavelength and Q
:link: notebooks/nanobeam_cavity
:link-type: doc
PASS · executed notebook · forward · wavelength_um
:::
:::{grid-item-card} GPU-native inverse design of a high-Q nanobeam cavity
:link: notebooks/high_q_nanobeam_optimization
:link-type: doc
PASS · executed notebook · invdes · validated_q_ratio
:::
:::{grid-item-card} Binary atom-gap antenna coupled to a feedthrough waveguide
:link: cases/invdes_scratch_atom_beta
:link-type: doc
PASS · benchmark page · invdes · guided_beta
:::
::::
```{toctree}
:hidden:
:maxdepth: 1
categories/foundations
categories/materials
categories/sources-boundaries-scattering
categories/integrated-photonics
categories/resonators-cavities-filters
categories/free-space-periodic-optics
categories/inverse-design
categories/inverse-designed-cavities
categories/research-and-fidelity-audits
```