ReferenceAlpha
Wave Optics
Fixed-frequency scalar-polarization Helmholtz wave optics for isotropic, lossless, nonmagnetic dielectric media.
Reference
| Field | Value | Description |
|---|---|---|
| constraints | [] | — |
| coupled_runtime | null | — |
| differentiable_runtime | {"certification":"WaveOpticsComplexHelmholtzRuntime","coordinate_expression_gradient":true,"coordinate_gradient":true,"design_properties":["permittivity"],"execution_backend":"telion-v2-shared-execution","expression_objectives":true,"material_expression_gradient":true,"material_gradient":true,"objective_rules":[{"entity_dimensions":["global","domain","boundary","point"],"modes":["frequency-domain"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["ewfd.absE"],"value_kind":"field"},{"entity_dimensions":["global"],"modes":["frequency-domain"],"operators":["value"],"supports_selection":false,"symbols":["ewfd.energy"],"value_kind":"scalar-global"},{"entity_dimensions":["global"],"modes":["frequency-domain"],"operators":["value"],"supports_selection":false,"symbols":["ewfd.compliance"],"value_kind":"scalar-global"}],"residual_owner":"WaveOptics.element_residual","state_fields":["E"],"supported_objective_symbols":{"coordinate":["ewfd.absE","ewfd.energy","ewfd.compliance"],"material":["ewfd.absE","ewfd.energy","ewfd.compliance"],"topology":["ewfd.absE","ewfd.energy","ewfd.compliance"]},"topology_expression_gradient":true} | — |
| dynamic_outputs | [] | — |
| equation_summary | -div(grad(E)) - omega^2*mu0*epsilon*E = i*omega*mu0*J | — |
| frequency_domain_runtime | {"certification":"WaveOpticsComplexHelmholtzRuntime","operator_terms":[{"angular_frequency_power":2,"coefficient":"permittivity","phase":"real"}],"runtime":"scalar-complex-helmholtz","state_fields":["E"],"supports_sweep":false} | — |
| metadata | {"releaseSupport":{"certifiedStudies":[],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"0a819976ac943e9eedf5bc7f9c80880dd9103cb62bb4c5a915b98c452b135a5c","profile":"september-2026-classroom","reason":"Unavailable.","selectable":false}} | — |
| preferred_material | null | — |
| schema_version | 0.1.0 | — |
| stateVariables | [{"adjointDescription":"The real-packed complex Helmholtz adjoint supports exact field, energy, source-work, coordinate, input, frequency, material, and topology derivatives.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":"ewfd.E","complexValued":true,"componentDescriptions":["Complex scalar electric-field phasor"],"componentNames":["E"],"componentSymbols":["ewfd.E"],"components":1,"description":"Complex scalar electric-field phasor for one fixed frequency.","differentiability":"analytic","displayName":"Electric field phasor","finiteElementSpace":"H1-P1","initialValue":"0","location":"node","name":"E","namingPolicy":"fixed","quantityId":"ewfd.E","rank":"scalar","role":"state","runtimeEvidence":{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","provider":"WaveOptics.element_residual"},"symbolPattern":null,"unit":"V/m"}] | — |
| studies | [{"certified":false,"differentiability":"exact-ad","kind":"frequency-domain","reason":"Frequency Domain is unavailable for this physics interface."},{"certified":false,"differentiability":"exact-ad","kind":"sensitivity","reason":"Sensitivity is unavailable for this physics interface."}] | — |
| transient_runtime | null | — |
| weak_contributions | [{"differentiability":"exact-ad","entity_dimension":"domain","expression":"dot(grad(test(ewfd.E)),grad(ewfd.E)) - angularFrequency^2*mu0*permittivity*test(ewfd.E)*ewfd.E - i*angularFrequency*mu0*test(ewfd.E)*electricCurrentSource","name":"ewfd.wave","test_field":"ewfd.E"}] | — |
| category | Wave Optics | — |
| description | Fixed-frequency scalar-polarization Helmholtz wave optics for isotropic, lossless, nonmagnetic dielectric media. | — |
| dimensions | [3] | — |
| display_name | Wave Optics | — |
| kind | Wave Optics | — |
| namespace | ewfd | — |
| status | development | — |
| visible | false | — |
Fixed-frequency scalar-polarization Helmholtz wave optics for isotropic, lossless, nonmagnetic dielectric media.
Contract
| Property | Value |
|---|---|
| constraints | [] |
| coupled_runtime | null |
| differentiable_runtime | {"certification":"WaveOpticsComplexHelmholtzRuntime","coordinate_expression_gradient":true,"coordinate_gradient":true,"design_properties":["permittivity"],"execution_backend":"telion-v2-shared-execution","expression_objectives":true,"material_expression_gradient":true,"material_gradient":true,"objective_rules":[{"entity_dimensions":["global","domain","boundary","point"],"modes":["frequency-domain"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-min... |
| dynamic_outputs | [] |
| equation_summary | -div(grad(E)) - omega^2*mu0*epsilon*E = i*omega*mu0*J |
| frequency_domain_runtime | {"certification":"WaveOpticsComplexHelmholtzRuntime","operator_terms":[{"angular_frequency_power":2,"coefficient":"permittivity","phase":"real"}],"runtime":"scalar-complex-helmholtz","state_fields":["E"],"supports_sweep":false} |
| metadata | {"releaseSupport":{"certifiedStudies":[],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"0a819976ac943e9eedf5bc7f9c80880dd9103cb62bb4c5a915b98c452b135a5c","profile":"september-2026-classroom","reason":"Unavailable.","selectable":false}} |
| preferred_material | null |
| schema_version | 0.1.0 |
| stateVariables | [{"adjointDescription":"The real-packed complex Helmholtz adjoint supports exact field, energy, source-work, coordinate, input, frequency, material, and topology derivatives.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":"ewfd.E","complexValued":true,"componentDescriptions":["Complex scalar electric-field phasor"],"componentNames":["E"],"componentSymbols":["ewfd.E"],"components":1,"description":"Complex scalar electric-field phasor for one fixed frequency.",... |
| studies | [{"certified":false,"differentiability":"exact-ad","kind":"frequency-domain","reason":"Frequency Domain is unavailable for this physics interface."},{"certified":false,"differentiability":"exact-ad","kind":"sensitivity","reason":"Sensitivity is unavailable for this physics interface."}] |
| transient_runtime | null |
| weak_contributions | [{"differentiability":"exact-ad","entity_dimension":"domain","expression":"dot(grad(test(ewfd.E)),grad(ewfd.E)) - angularFrequency^2*mu0*permittivity*test(ewfd.E)*ewfd.E - i*angularFrequency*mu0*test(ewfd.E)*electricCurrentSource","name":"ewfd.wave","test_field":"ewfd.E"}] |
| category | Wave Optics |
| description | Fixed-frequency scalar-polarization Helmholtz wave optics for isotropic, lossless, nonmagnetic dielectric media. |
| dimensions | [3] |
| display_name | Wave Optics |
| kind | Wave Optics |
| namespace | ewfd |
| status | development |
| visible | false |