Eigenmode Expansion (EME) Solver #

The Eigenmode Expansion (EME) solver obtains the complete optical characteristics of a device by dividing a long waveguide structure into multiple computational cells along the direction of propagation. Within each cell, it solves for the eigenmodes of its cross-section, then calculates the coupling of these modes between adjacent cells.
The EME solver is particularly well-suited for analyzing and designing photonic devices whose length is much greater than the wavelength and that have slowly varying or periodic refractive index distributions. Examples include Multimode Interference (MMI) couplers, Fiber Bragg gratings, and adiabatic tapers. Compared to direct three-dimensional Finite-Difference Time-Domain (3D FDTD) simulations, the EME solver achieves extremely fast calculation speeds while maintaining accuracy. It allows for rapid scanning and optimization of key parameters such as device length and wavelength after computing the modes once, significantly enhancing the design efficiency of photonic integrated devices.

EME Solver Settings #

To add an EME solver, select the EME button in the Home tab, then click anywhere in the composite view window to create it. Modify the solver's settings in the automatically opened properties editor window to complete the setup.

The EME solver properties page is shown below and will be explained in detail in the following sections.

General Settings #

The General tab is used to configure the solver's simulation space, which includes the simulation dimension and geometry.

Simulation Dimension #

The Dimension tab is used to set the simulation dimension for the EME solver. Currently, three normal directions are supported: 2D Z normal, 2D X normal, and 2D Y normal.

Geometry #

The Geometry tab is used to set the geometric size of the EME solver region.

Name	Description
X/Y/Z pos	Sets the geometric center of the solver's simulation region.
X/Y/Z span	Sets the extent of the solver's simulation region along the three-dimensional coordinate directions.

EME Settings #

This tab contains the core settings specific to the EME algorithm, used for defining the computational cells.

Central Wavelength #

Name	Description
central wavelength	Sets the central wavelength used for calculating the eigenmodes in all cells.

EME Cell Geometry #

This section allows you to define one or more cell groups, each of which can have independent geometry and mode settings. Key parameters in the table include:

Name	Description
Group span (µm)	The overall width of this cell group (along the propagation direction).
Cells	The number of cells this group is subdivided into. A higher number of cells typically means higher accuracy but also greater computational cost.
Modes	The number of eigenmodes calculated and used for this cell group. Must include all propagating modes to ensure accuracy.
Cell range	The range of cell indices included in this group.
Start/Stop (µm)	The start and stop coordinates of this cell group.

Additionally, key configuration items are:

Name	Description
Min z	The starting coordinate of the entire EME simulation region.
Number of cell groups	Defines the total number of cell groups.
Number of modes	(Global) Sets the number of modes to solve for.
Auto calculate cell groups	Click this option to automatically divide cell groups based on the device geometry.

Periodicity #

If your defined structure is periodic, you can view the number of repetitions of the periodic unit in this section.

Name	Description
Start cell group	The starting cell group index for a periodic unit.
End cell group	The ending cell group index for a periodic unit.
Periods	The number of repetitions of the above periodic unit.

Background Material #

The Background Material tab provides a Background Material dropdown menu for selecting the background material.

Name	Description
Background material	Background materials can be selected from the built-in Optical Materials Library , or you can create custom materials and add them to the library via the Add/Edit button.

Mesh #

The Mesh tab provides the mesh settings for the solver. The EME solver offers both uniform mesh and auto non-uniform mesh settings. For specific parameters, please refer to Mesh Settings.

Boundary Conditions #

The Boundary conditions tab provides the boundary condition settings for the solver. For detailed settings of each parameter, refer to Boundary Conditions.