.. currentmodule:: tidy3d
In numerical simulations, the simulation domain is necessarily truncated compared to physical reality due to computational limits. Boundary conditions specify the constraints on the field solution along the external boundaries of the simulation domain. In order to achieve good agreement with the physical scenario, it is important that the user specifies the appropriate boundary type for their application.
The Boundary Specification section discusses how to set up simulation boundaries in a Tidy3D simulation.
Each boundary type is discussed in their respective section. The currently supported types are:
- PEC/PMC: Simulates a perfect electric or magnetic conductor
- Periodic: Simulates periodic boundary conditions in 1, 2, or 3-dimensions
- Absorbing: Simulates an open boundary for outgoing radiation
.. autosummary:: :toctree: _autosummary/ :template: module.rst tidy3d.BoundarySpec tidy3d.Boundary
The BoundarySpec object contains information on the boundary conditions on all six sides of the simulation domain. The Boundary object specifies the boundary conditions along a single axis, i.e. x, y, or z. Typically, the Simulation object contains a BoundarySpec instance, which in turn contains three Boundary instances.
There are several ways to specify boundaries with BoundarySpec. To quickly specify a single boundary type for all six sides, use the BoundarySpec.all_sides() method.
my_boundary_spec = BoundarySpec.all_sides(boundary=PML())
To specify boundaries along each of the three axes:
my_boundary_spec = BoundarySpec(
x = Boundary.periodic(),
y = Boundary.pec(),
z = Boundary.pml(),
)
In the above example, built-in convenience methods such as pec(), pml(), and periodic() in the Boundary object were used to specify boundaries for both sides of each axis.
Finally, for full control of each of the six sides:
my_boundary_spec = BoundarySpec(
x = Boundary(plus=PECBoundary(), minus=PMCBoundary()),
y = Boundary(plus=Periodic(), minus=Periodic()),
z = Boundary(plus=PML(), minus=PECBoundary()),
)
In the above example, individual boundary instances were created and passed into the plus and minus attributes of each Boundary instance.
.. seealso:: For more details and examples, please see the following article: + `Setting up boundary conditions <../notebooks/BoundaryConditions.html>`_
.. autosummary:: :toctree: _autosummary/ :template: module.rst tidy3d.PECBoundary tidy3d.PMCBoundary tidy3d.Boundary.pec tidy3d.Boundary.pmc
These boundary conditions simulate a perfect electric or magnetic conductor by placing constraints on the normal and tangential components of the electric/magnetic fields.
\mathbf{E} \times \mathbf{n} &= 0 \quad \text{(PEC)},\\
\mathbf{H} \times \mathbf{n} &= 0 \quad \text{(PMC)}.
where \mathbf{n} is the boundary normal vector.
Note
To simulate a PEC structure, use the PECMedium class instead. Please refer to the EM Mediums page for details.
.. autosummary:: :toctree: _autosummary/ :template: module.rst tidy3d.Periodic tidy3d.BlochBoundary tidy3d.Boundary.periodic tidy3d.Boundary.bloch tidy3d.Boundary.bloch_from_source
Periodic boundary conditions are commonly used in unit cell simulations. The Periodic boundary type enforces field continuity, i.e.
\mathbf{E}(\mathbf{r}_a) = \mathbf{E}(\mathbf{r}_b)
where \mathbf{r}_a and \mathbf{r}_b are matching positions on the respective pair of periodic boundaries. This is commonly used in conjunction with a normal incidence plane wave excitation.
The BlochBoundary boundary type implements Bloch periodicity, i.e.
\mathbf{E}(\mathbf{r}_a) = e^{i \mathbf{k}_b \cdot (\mathbf{r}_a - \mathbf{r}_b)} \mathbf{E}(\mathbf{r}_b)
where \mathbf{k}_b is the Bloch periodicity vector. This is typically used together with an off-normal incidence plane wave excitation, where the Bloch vector corresponds to the lateral phase difference due to the off-normal plane wave. For user convenience, the Boundary.bloch_from_source() method automatically creates a BlochBoundary object from a given excitation.
.. seealso:: For more details and examples, please see the following notebooks: + `Multilevel blazed diffraction grating <../notebooks/GratingEfficiency.html>`_ + `Defining a total-field scattered-field (TFSF) plane wave source <../notebooks/TFSF.html>`_
.. autosummary:: :toctree: _autosummary/ :template: module.rst tidy3d.PML tidy3d.PMLParams tidy3d.Boundary.pml tidy3d.StablePML tidy3d.Boundary.stable_pml tidy3d.Absorber tidy3d.Boundary.absorber tidy3d.AbsorberParams
For simulations with radiative modes, it is recommended to surround the simulation domain with absorbing boundary conditions, i.e. either the Perfectly Matched Layer PML type, or the Absorber type.
The PML boundary type uses coordinate stretching to rapidly attenuate any outgoing radiation, and is the default boundary condition for all simulations in Tidy3D.
The Absorber boundary type uses a fictitious lossy medium with ramped conductivity to attenuate outgoing waves. In comparison to the PML, there can be greater reflection at the boundary. The Absorber boundary is more numerically stable when structures with dispersive mediums extend into the boundary.
.. seealso:: For more details and examples, please see the following article: + `Suppressing artificial reflections with absorber and PML boundaries <../notebooks/AbsorbingBoundaryReflection.html>`_ For a general introduction to PMLs, please see the following FDTD101 resource: + `Introduction to perfectly matched layer (PML) <https://www.flexcompute.com/fdtd101/Lecture-6-Introduction-to-perfectly-matched-layer/>`_