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.

How to read this gallery

“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 for the boundary.

Browse by topic#

Foundations: fields, time signals, and grids

Start here for the Yee update, propagation, power flow, ring-up/ringdown, and numerical-grid behavior.

5 examples

index.html#foundations-fields-time-signals-and-grids
Materials, interfaces, and dispersion

Fresnel physics, multilayers, metals, tensor media, birefringence, and dispersive constitutive models.

14 examples

index.html#materials-interfaces-and-dispersion
Sources, boundaries, and scattering

Plane waves, beams, dipoles, TFSF injection, broadband correction, and canonical scattering problems.

9 examples

index.html#sources-boundaries-and-scattering
Integrated photonics: waveguides, ports, and routing

Mode launch and readout followed by complete PIC devices: bends, splitters, crossings, and couplers.

10 examples

index.html#integrated-photonics-waveguides-ports-and-routing
Resonators, cavities, and spectral filters

Frequency-selective devices, including a ring, Bragg stopband, and ringdown-extracted nanobeam Q.

2 examples

index.html#resonators-cavities-and-spectral-filters
Free-space and periodic optics

Periodic absorption and wavefront shaping with field and focal-plane observables.

2 examples

index.html#free-space-and-periodic-optics
Inverse design and automatic differentiation

Gradient plumbing and multi-port objectives that are not cavity-design campaigns.

2 examples

index.html#inverse-design-and-automatic-differentiation
Inverse-designed cavities and atom interfaces

High-Q nanobeams, remote-atom cavities, curved mirrors, atom-gap designs, and their validation records.

3 examples

index.html#inverse-designed-cavities-and-atom-interfaces
Explore validated devices and the inverse-design audit →

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.

Real-world device reproductions and inverse-design audit
Frozen remote-atom silicon optimization →

An executed research notebook with literal curved-mirror geometry, complete optimization history, paired Ey field, and a clearly scoped 40 nm result.

Shape optimization of a remote-atom silicon cavity

Foundations: fields, time signals, and grids#

Start here for the Yee update, propagation, power flow, ring-up/ringdown, and numerical-grid behavior.

Vacuum dipole — finite energy + PML decay

PASS · benchmark page · analytical · fields_finite

Vacuum dipole — finite energy + PML decay
Pulsed vs CW multilayer transmission consistency

PASS · benchmark page · analytical · max_rel_err

Pulsed vs CW multilayer transmission consistency
Plane-wave phase velocity + impedance (vacuum & dielectric)

PASS · benchmark page · analytical · pytest_exit

Plane-wave phase velocity + impedance (vacuum & dielectric)
Phasor vs time-domain Poynting flux consistency

PASS · benchmark page · analytical · pytest_exit

Phasor vs time-domain Poynting flux consistency
Mildly stretched grid vs uniform

PASS · benchmark page · analytical · pytest_exit

Mildly stretched grid vs uniform

Materials, interfaces, and dispersion#

Fresnel physics, multilayers, metals, tensor media, birefringence, and dispersive constitutive models.

Dielectric interface Fresnel R/T (upstream method)

PASS · benchmark page · analytical · reflectance_R

Dielectric interface Fresnel R/T (upstream method)
Skin-depth attenuation in lossy conductor

PASS · benchmark page · analytical · pytest_exit

Skin-depth attenuation in lossy conductor
Dispersive Lorentz/Drude/CCPR Fresnel + impedance

PASS · benchmark page · analytical · pytest_exit

Dispersive Lorentz/Drude/CCPR Fresnel + impedance
Fresnel R/T vs Tidy3D golden (tiny 2D-like slab interface)

PASS · benchmark page · forward · reflectance_R

Fresnel R/T vs Tidy3D golden (tiny 2D-like slab interface)
Anisotropic dispersion Fresnel per polarization

PASS · benchmark page · analytical · pytest_exit

Anisotropic dispersion Fresnel per polarization
Birefringence / uniaxial media

PASS · benchmark page · analytical · pytest_exit

Birefringence / uniaxial media
3-layer stack transmission spectrum vs Tidy3D

PASS · benchmark page · forward · T_rel_l2

3-layer stack transmission spectrum vs Tidy3D
Fresnel ε=4 (n=2) upstream gold standard

PASS · benchmark page · analytical · pytest_exit

Fresnel ε=4 (n=2) upstream gold standard
Oriented / tilted crystal dispersion

PASS · benchmark page · analytical · pytest_exit

Oriented / tilted crystal dispersion
Rotated lossy uniaxial tensor

PASS · benchmark page · analytical · pytest_exit

Rotated lossy uniaxial tensor
3-layer stack T vs transfer-matrix theory

PASS · benchmark page · analytical · T_max_abs

3-layer stack T vs transfer-matrix theory
Lossy-metal half-space reflectance vs Tidy3D

PASS · benchmark page · forward · reflectance_R

Lossy-metal half-space reflectance vs Tidy3D
4-pair Bragg stack R/T spectrum vs Tidy3D

PASS · benchmark page · forward · R_rel_l2

4-pair Bragg stack R/T spectrum vs Tidy3D
Lossy slab attenuation ratio vs analytical TMM

PASS · benchmark page · forward · ratio_rel

Lossy slab attenuation ratio vs analytical TMM

Sources, boundaries, and scattering#

Plane waves, beams, dipoles, TFSF injection, broadband correction, and canonical scattering problems.

2D Mie scattering dielectric cylinder

PASS · benchmark page · analytical · pytest_exit

2D Mie scattering dielectric cylinder
Gaussian beam Fresnel / power checks

PASS · benchmark page · analytical · pytest_exit

Gaussian beam Fresnel / power checks
Uniform plane source physics

PASS · benchmark page · analytical · pytest_exit

Uniform plane source physics
Dipole radiated power + pattern symmetry

PASS · benchmark page · analytical · pytest_exit

Dipole radiated power + pattern symmetry
TFSF box cancellation + dispersive bg

PASS · benchmark page · analytical · pytest_exit

TFSF box cancellation + dispersive bg
TFSF grid-metric independent injection

PASS · benchmark page · analytical · pytest_exit

TFSF grid-metric independent injection
CW / Gaussian / custom temporal profiles

PASS · benchmark page · analytical · pytest_exit

CW / Gaussian / custom temporal profiles
Broadband dispersive-source correction

PASS · benchmark page · analytical · pytest_exit

Broadband dispersive-source correction
2D dielectric cylinder forward-T vs Tidy3D

PASS · benchmark page · forward · T_through

2D dielectric cylinder forward-T vs Tidy3D

Integrated photonics: waveguides, ports, and routing#

Mode launch and readout followed by complete PIC devices: bends, splitters, crossings, and couplers.

Si slab mode source: neff + confinement

PASS · benchmark page · analytical · pytest_exit

Si slab mode source: neff + confinement
Waveguide S-parameter transmission

PASS · benchmark page · analytical · pytest_exit

Waveguide S-parameter transmission
Si/SiO2 slab TE waveguide transmission vs Tidy3D

PASS · benchmark page · forward · T_far

Si/SiO2 slab TE waveguide transmission vs Tidy3D
Rectangular Y-junction power split vs Tidy3D

PASS · benchmark page · forward · T1

Rectangular Y-junction power split vs Tidy3D
Directional coupler — broadband through/cross parity

PASS · executed notebook · forward · through_spectrum

Directional coupler: through and cross spectra
Waveguide crossing — O-band through and crosstalk spectra

PASS · executed notebook · forward · through

Waveguide crossing: transmission and crosstalk
Euler-like bend — broadband 90-degree transmission

PASS · executed notebook · forward · out

Euler-like waveguide bend: broadband bend loss
Edge coupler — Gaussian beam to inverse taper

PASS · executed notebook · forward · out

Edge coupler: Gaussian beam to inverse taper
1x4 MMI — four-port broadband power distribution

PASS · executed notebook · forward · out1

1×4 MMI: broadband four-port splitting
Compact polarization splitter-rotator — TE/TM routing

PASS · executed notebook · forward · te_wide

Polarization splitter-rotator: TE/TM routing

Resonators, cavities, and spectral filters#

Frequency-selective devices, including a ring, Bragg stopband, and ringdown-extracted nanobeam Q.

Bus + ring transmission spectrum vs Tidy3D

PASS · benchmark page · forward · T_rel_l2

Bus + ring transmission spectrum vs Tidy3D
Bragg grating — transmission and reflection stopband

PASS · executed notebook · forward · transmitted

Bragg grating: transmission and reflection stopband

Free-space and periodic optics#

Periodic absorption and wavefront shaping with field and focal-plane observables.

Dielectric metasurface absorber — periodic THz resonator

PASS · executed notebook · forward · R

Dielectric metasurface absorber: R, T, and A
Geometric-phase metalens — focal distance and spot size

PASS · executed notebook · forward · focal_distance_um

Geometric-phase metalens: focal distance and spot size

Inverse design and automatic differentiation#

Gradient plumbing and multi-port objectives that are not cavity-design campaigns.

Invdes smoke: transmission FOM improves under gradient steps

PASS · benchmark page · invdes · best_fom_gain

Invdes smoke: transmission FOM improves under gradient steps
Inverse-designed crossing from a four-port S-matrix target

PASS · executed notebook · invdes · best_fom_parity

S-matrix crossing: four-port inverse design

Inverse-designed cavities and atom interfaces#

High-Q nanobeams, remote-atom cavities, curved mirrors, atom-gap designs, and their validation records.

Nanobeam cavity — resonant wavelength and Q

PASS · executed notebook · forward · wavelength_um

Nanobeam cavity: resonant wavelength and quality factor
GPU-native inverse design of a high-Q nanobeam cavity

PASS · executed notebook · invdes · validated_q_ratio

Inverse design of a high-Q nanobeam cavity
Binary atom-gap antenna coupled to a feedthrough waveguide

PASS · benchmark page · invdes · guided_beta

Binary atom-gap antenna coupled to a feedthrough waveguide