How do I set the Bloch boundary condition?

Date	Category
2023-12-15 20:23:55	Boundary Conditions

The tidy3d.BlochBoundary boundary condition allows users to obtain the response of large periodic structures by simulating only a unit cell. It is suitable to simulate systems where the source is injected at an angle, so the tidy3d.Periodic boundary fails. The example below illustrates how to set up the Bloch boundary condition in a typical case, where we have a unit cell and a plane wave source injected at an angle.

# Simulation size.
sim_size = (2, 2, 8)

# Plane wave source at an angle.
plane_wave = tidy3d.PlaneWave(
    center=(0, 0, 3),
    size=(tidy3d.inf, tidy3d.inf, 0),
    source_time=source_time,
    direction="-",
    pol_angle=0,
    angle_theta=np.pi / 3.0,
    angle_phi=np.pi / 6.0,
)

# Bloch boundaries.
bloch_x = tidy3d.Boundary.bloch_from_source(
  source=plane_wave,
  domain_size=sim_size[0],
  axis=0,
  medium=medium
)

bloch_y = tidy3d.Boundary.bloch_from_source(
  source=plane_wave,
  domain_size=sim_size[1],
  axis=1,
  medium=medium
)

bspec = tidy3d.BoundarySpec(x=bloch_x, y=bloch_y, z=tidy3d.Boundary.pml())

# Build the simulation.
sim = tidy3d.Simulation(
    center=(0, 0, 0),
    size=sim_size,
    boundary_spec=bspec,
    grid_spec=tidy3d.GridSpec.auto(min_steps_per_wvl=20, wavelength=1.55),
    structures=[unit_cell],
    sources=[plane_wave],
    monitors=[flux_monitor],
    run_time=1e-12,
)

The tidy3d.BlochBoundary is a generalization of the periodic boundary condition to any incidence angle. However, it is computationally more expensive, so use tidy3d.Periodic boundary to normal incidence.

See this notebook for more details on setting up boundary conditions.