EME

Backend lightsmith-eme (method eme, modules lightsmith.backends.eme and lightsmith.backends._eme). Eigenmode expansion for devices whose ports lie on two opposite planes, in 2D and 3D. It is exact for piecewise-uniform devices given enough modes, and well suited to long devices where light travels mostly along one axis.

Method

1. Slicing. The device between its port planes is cut into cells that are uniform along the port-normal axis. Tapers and curves are staircased into many cells, and adjacent identical cells are merged.
2. Cell modes. Each cell's modes come from the FDE solver: full-vector cross-sections in 3D, or slab modes in 2D.
3. Interfaces. S-matrices at each cell interface come from unconjugated mode overlaps, so lossy and evanescent modes stay biorthogonal. The cells and interfaces are cascaded with Redheffer star products (Bienstman & Baets 2001).
4. Ports. Port modes are solved in each port's window and coupled in through symmetrised overlaps.

GDS layouts are resolved through lightsmith.layout. Cell modes are cached across solves, in a process-wide cache limited to 256 MB.

Options

options["eme"] or options["lightsmith-eme"].

Option	Default	Meaning
num_modes	None	Modes per cell. Default 30 in 2D and 10 in 3D.
grid_spacing_nm	None	Cross-section grid step
points_per_wavelength	None	Default 40 in 2D and 15 in 3D
cells_per_feature	6	Used for the default spacing
subpixel	"anisotropic"	Permittivity averaging, as in FDE
subsamples	32	Supersampling in cut cells
boundary	"pec"	Cross-section walls: "pec" or "pml"
pml_cells	10	PML thickness
pml_reflection	1e-6	Target PML reflection
polarization	"auto"	"auto" means "te" (in-plane E) in 2D and "any" in 3D. In 3D, filtering by "te" or "tm" uses te_fraction and makes the mode basis incomplete.
taper_cells	None	Cells per varying segment. Default: enough for the outline to move about 3 grid cells per step, clipped to 10–60.
max_cell_length_nm	None	Also split segments longer than this
max_grid_cells	400000	Refuse larger cross-section grids
cache	True	Reuse cell modes across solves

The solver runs on the CPU. There are no gradients. Multimode ports are labelled name@j.

Validation

All tests are in tests/test_eme.py.

Test	Reference	Tolerance
test_uniform_waveguide_3d_transmits_fully_with_the_fde_phase: 500 × 220 nm, L = 2 µm	|S21| = 1; phase k₀·neff·L from FDE	1e-6; reflection < 1e-8
test_uniform_waveguide_2d	|S21| = 1	1e-5; |S11| < 1e-6
test_width_step_3d_is_reciprocal_and_passive: 500 → 700 nm width step	reciprocity; passivity	|S21 − S12| < 1e-6; 0.97 < |S21|² < 1 (about 0.989 with 48+ modes)
test_linear_taper_approaches_adiabatic_limit: 0.5 → 3 µm taper, 1–30 µm long	adiabatic limit	T rises with length; T(30 µm) > 0.98
test_mmi_1x2_self_imaging_length: W = 3 µm MMI	Soldano & Pennings self-imaging length	50/50 split to 1e-6; best length within 0.9–1.0 × the paraxial estimate; transmission > 0.9

Limits

• Every port must be normal to the same axis and lie on one of exactly two opposite planes. Each port must point into the device: + at the lower plane, - at the upper plane.
• In 2D, ports cannot be normal to z.
• Raises an error when a cross-section grid exceeds max_grid_cells, or when a port supports fewer modes than its num_modes.
• Warns when a cell has fewer modes than requested, and when Σ|S|² > 1.05 for an input. In that case, increase num_modes or refine the grid.