How to define the number of modes for an EME simulation?

Date	Category
2025-05-27 18:52:21	EME

The tidy3d.EMEModeSpec object controls how modes are computed in each EME cell. The most important parameters to tune for accuracy and performance are described below.

num_modes

It is important to use a sufficient number of modes to accurately capture the physics of the device and ensure that the simulation results are converged. The exact number of modes required depends on the characteristics of the device. For example, larger waveguides support more propagating modes and therefore require a greater number of modes to achieve accurate results.

A recommended approach is to perform a convergence sweep, where the simulation is run with increasing numbers of modes to analyze how the results converge. This can be done efficiently using tidy3d.EMEModeSweep, which sweeps over the number of modes without recomputing them. This process is demonstrated at the end of this tutorial.

num_pml

Controls the number of PML (Perfectly Matched Layer) layers added at the edges of the mode solving cross-section. Increasing num_pml is important when the structure supports leaky or radiative modes that extend beyond the simulation boundaries. If you observe that results depend on the simulation domain size, adding PML layers can help absorb those radiative components and improve accuracy.

sort_spec

Primarily used in EME for filtering and pinning modes — for example, to retain only modes of a particular polarization (te_fraction), to exclude unwanted higher-order or spurious modes from the expansion, or to pin the mode whose field energy most overlaps a specific region via the fill_fraction_box sort key combined with ModeSortSpec.bounding_box. The fill_fraction_box option is especially useful for multi-waveguide devices (splitters, couplers, directional couplers) where the supermodes of the full cross-section need to be indexed by which waveguide they primarily live in. Filtering the mode set can also improve both accuracy and performance by focusing computational effort on the modes that contribute meaningfully to device behavior.

interp_spec

Controls how modes are interpolated across frequencies in broadband simulations. This is set via the interp_spec parameter and determines the number of frequency points at which modes are explicitly solved; intermediate frequencies are interpolated. Increasing the number of interpolation points improves broadband accuracy but increases computational cost.

Other useful parameters

• precision: Set to "double" for simulations that require high accuracy, such as bent waveguides with low expected losses.

• bend_radius and bend_axis: Used for simulating bent waveguides. The geometry should be defined as straight; the curvature is applied analytically during mode solving. See this tutorial for details.

Checking convergence

num_modes is only one of four discretization choices that interact; in practice all four should be tested together:

• Number of EME cells along the propagation axis. EME solves modes at the centre of each cell and treats each cell as translation-invariant, so slowly varying sections (tapers, adiabatic bends, graded transitions) are resolved by splitting them into enough cells for each to be approximately uniform. For such structures the number of cells is typically the first convergence knob — increase num_cells on tidy3d.EMEUniformGrid (or add boundaries to tidy3d.EMEExplicitGrid) until the S-matrix stops changing.

• Number of modes per cell (num_modes). tidy3d.EMEModeSweep scans this cheaply without re-solving modes.

• Transverse simulation window plus num_pml. The mode plane must be wide enough that guided modes decay before the edge, and radiation modes have room to resolve.

• Yee grid resolution (grid_spec on tidy3d.EMESimulation). Sets the accuracy of the underlying eigenproblem in each cell.

Tighten them one at a time — many “non-converged” symptoms come from under-resolution on a different axis than the one being tuned.

Diagnostics

Invalid-mode warnings in the simulation log usually mean the transverse window or Yee grid is too coarse to support the requested num_modes, and the extra modes come back as numerical noise. Widen the simulation and/or refine the grid (and consider more num_pml) before lowering num_modes. If a physically relevant mode is filtered out because its imaginary effective index is only slightly negative, relax the filter with increasing_mode_tolerance on EMEModeSpec.

The S-matrix keeps changing even at large num_modes — add an tidy3d.EMECoefficientMonitor to record the forward (A) and backward (B) amplitudes per cell. If a handful of high-index modes carry significant power in some cell, that cell needs more modes, a finer Yee grid, or a boundary placed at a nearby discontinuity. Set EMESimulation.store_coeffs=True to keep the full internal coefficients in EMESimulationData.coeffs.