Multi-Physics

FEM

Calculate the waveguide modes with the full-vector finite-element method. Requires a ‘3D’ license. The cross-section is meshed with triangles that follow every material interface, and the mesh is refined where the modes are under-resolved, as set by the fem_* settings in settings(). The saved fields, effective indices, losses and TE fractions are the same quantities, with the same normalization, as described under FDM(), so get(), get_fields(), report(), plot() and EME() work the same way. Calling FEM() sets the profile’s solver setting to ‘FEM’.

All boundary_condition values, PMLs, expansion regions, bends, transformation-optics sections (bends, the ring and general couplers, and simulation-space transforms), lossy and anisotropic materials (including crystals tilted out of the cross-section with theta), and heat() and electrostatic() perturbations are supported. A symmetric or antisymmetric boundary on an axis whose mirror a crystal’s orientation breaks raises an error, since it would describe a different structure. Field plots sample the FEM solution at x_resolution and y_resolution, and plot(mesh_display=True) shows the triangle mesh.

Parameters:

  • profile (str or int) – profile name to save the solved profile under, default: ‘_default’

  • section (str) – name of an EME section to solve a slice from, instead of the profile’s own settings/shapes, default: None

  • propagation_distance (float) – [nm] where along section to take the cross-section, default: None

  • include_heat (bool) – whether to include the temperature change from the most recent heat() solve, default: True

  • include_static (bool) – whether to apply the electro-optic (Pockels) permittivity perturbation from the most recent electrostatic() solve, default: True

  • verbose (bool) – print progress, default: True

  • simulation_name (str) – simulation name, default: ‘emode’

Returns:

a dict with field (a Field object), n_eff_tilde, TE_fraction, TE_indices, TM_indices, PML_indices, mesh (vertices, triangles and region, the triangle mesh solved on), and refinement (n_eff_history, num_dofs and num_elements per refinement level, and stopped_by, the rule that ended refinement).

heat

Run a steady-state thermal simulation of a waveguide cross-section. Requires a ‘3D’ license.

Warning

This function is only available under beta release. Please report any issues or bugs.

Note

Each shape() now accepts an input parameter called heat_only (default: False), which can be used to set additional shapes on top or bottom of the photonic layer stack. For example, common heat_only shapes are the substrate and metal heater layers.

Each shape() also now accepts an input parameter called fem_resolution (default: 500), which is used to refine the triangular mesh within certain shapes.

Every material carries thermal_conductivity (W/m·K), resistivity (Ohm·nm), dn_dT (1/K), and eps_r_dc; the defaults are 1e-10, infinity, 0, and 1.0 where no reliable published value has been entered. See the Material Database page for values and sources.

Parameters:

  • min_angle (float) – Minimum angle for triangular mesh. Smaller values result in a finer mesh, but can prevent the meshing algorithm from converging. Default: 30.

  • boundary_temperature (float) – Fixed temperature boundary condition in ‘K’ set along each perimeter indicated by boundaries. Default: 298.

  • boundaries (list[str]) – ‘top’, ‘bottom’, ‘left’, or ‘right’; Indicates which boundaries are set to the fixed temperature boundary_temperature. Default: [‘bottom’].

  • verbose (bool) – Control the display of the progress bar. Default: True.

  • simulation_name (str) – Simulation name. Default: ‘emode’.

Returns:

A dictionary/struct with the mesh points (p), mesh triangles (t), temperature, thermal_conductivity, and heat_generation arrays. It also includes the boundary_temperature and boundaries settings.

electrostatic

Run a steady-state electrostatic simulation of a waveguide cross-section. Requires a ‘3D’ license.

Warning

This function is only available under beta release. Please report any issues or bugs.

Note

Each shape() also now accepts an input parameter called voltage (default: None), which is set to create electric field sources. Shapes with voltage left as None do not get a voltage boundary condition applied.

Each shape() also now accepts an input parameter called fem_resolution (default: 500), which is used to refine the triangular mesh within certain shapes.

Each material in the EMode material database now has eps_r_dc (relative permittivity at ~1 kHz).

The DC field derived here perturbs the permittivity through each material’s linear electro-optic (Pockels) tensor r (get('<material>')['r'], m/V): \(\Delta(1/n^2)_{ij} = \sum_k r_{ijk} E_k\), then \(\Delta\varepsilon = -\varepsilon \cdot \Delta(1/n^2) \cdot \varepsilon\). FDM() applies this automatically on the next solve (include_static=False to skip it), the same way heat()’s temperature field perturbs the permittivity through dn_dT.

Parameters:

  • min_angle (float) – Minimum angle for triangular mesh. Smaller values result in a finer mesh, but can prevent the meshing algorithm from converging. Default: 30.

  • verbose (bool) – Control the display of the progress bar. Default: True.

  • simulation_name (str) – Simulation name. Default: ‘emode’.

Returns:

A dictionary/struct with the mesh points (p), mesh triangles (t), voltage, eps_dc_grid, the per-element electric field (Ex, Ey, in V/nm), and centroids (element centers, in the optical window’s frame).

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