Grid Specification

Bent Medium Frames

For bent EME cells, EMEModeSpec provides a bend_medium_frame field to choose how media are interpreted:

• "global" keeps the material axes fixed in physical space. This matches the global-frame convention used in FDTD and is appropriate for chip-defined anisotropy that should not rotate with the local bend frame.

• "co_rotating" keeps the material profile attached to the local waveguide cross-section. This is appropriate for cases such as a bent fiber, or a CustomMedium sampled directly on the straight EME coordinates.

The choice affects both accuracy and validation. With bend_medium_frame="global", orientation-sensitive anisotropic bends often need multiple EME cells because the local mode basis can change with absolute bend angle, so repeating a single bent cell with num_reps is generally only exact when the medium is rotation-invariant about the bend axis. Check convergence with respect to the number of EME cells when refining such bends. This applies to both AnisotropicMedium and reciprocal FullyAnisotropicMedium. Bent custom media, including CustomAnisotropicMedium, are currently supported only with bend_medium_frame="co_rotating", because remapping custom-medium data into bent physical space is not implemented for the global-frame interpretation.

Rule of thumb: use "global" for chip-fixed anisotropy and "co_rotating" when the material profile is intended to stay attached to the bent cross-section.

The snippet below shows two distinct modeling choices for the same three-cell bend:

import tidy3d as td

straight = td.EMEModeSpec(num_modes=6)
chip_bend = td.EMEModeSpec(
    num_modes=6,
    bend_radius=40.0,
    bend_axis=1,
    bend_medium_frame="global",
)
fiber_bend = chip_bend.updated_copy(bend_medium_frame="co_rotating")

# Example 1: a patterned birefringent waveguide on a chip.
# Keep the material axes fixed in the global frame.
eme_grid_chip = td.EMEExplicitGrid(
    boundaries=[2.0, 6.0],
    mode_specs=[straight, chip_bend, straight],
)

# Example 2: a bent fiber or a pixelated custom profile.
# Let the material profile bend with the local section.
eme_grid_fiber = td.EMEExplicitGrid(
    boundaries=[2.0, 6.0],
    mode_specs=[straight, fiber_bend, straight],
)

Weakly Increasing Modes

By default, EME drops modes whose effective index has a negative imaginary part because they grow exponentially along the propagation direction. In practice, a physically useful mode can sometimes pick up a tiny negative Im(n_eff) from numerical noise, especially in weakly confined or bent problems.

Use EMEModeSpec increasing_mode_tolerance to relax that filter slightly:

• 0.0 preserves the historical behavior.

• A mode is dropped only if Im(n_eff) < -increasing_mode_tolerance.

• Start with a very small value such as 1e-6 and increase it only when a relevant mode is being spuriously removed.

This tolerance only affects EME’s post-solve propagation-basis filtering; it does not change the underlying mode solve itself.

import tidy3d as td

robust_bend = td.EMEModeSpec(
    num_modes=8,
    bend_radius=30.0,
    bend_axis=1,
    increasing_mode_tolerance=1e-6,
)

tidy3d.EMEUniformGrid	Specification for a uniform EME grid.
tidy3d.EMECompositeGrid	EME grid made out of multiple subgrids.
tidy3d.EMEExplicitGrid	EME grid with explicitly defined internal boundaries.
tidy3d.EMEGrid	EME grid.
tidy3d.EMEModeSpec	Mode specification for EME cells.