EME Control Panel #

This section introduces the simulation control panel for the Eigenmode Expansion (EME) solver.

The functions of its control panel buttons are shown in the figure below:

	Name	Description
Design	To design	Switch back to the design view.
Graphics	Translucent	Set the transparency of objects; 1 for opaque, 0 for completely transparent.
	Hide material	Hide the material structure in the view; check to enable.
	Hide fields	Hide the field distribution in the view; check to enable.
Progress	Status	Display the current simulation status and progress.
	Run EME	Run the EME simulation to obtain monitor data and eigenmode results for each cell and port.
	Tool	Control the opening and clearing of simulation data files.
EME propagate	As source port	Select the port to be used as the light source input.
	Incident mode ID #	Specify the mode ID number of the input light (e.g., 1, 2, ...).
	EME propagate	Click this button to calculate and output the S-parameter matrix for each port based on the user-specified input mode.

EME Ribbon #

The ribbon of the EME solver provides three main functions: EME Port, Monitor, and Mesh.

• EME Port: Used to add a port group; its settings are essentially the same as regular ports.
• Monitor: Used to add a field profile monitor (EME Profile) and a refractive index monitor (Index).
• Mesh: Used to add a custom mesh within the EME simulation region.

EME Port #

Clicking EME Port adds an EME Port Group, which contains two ports by default. The detailed settings for this port group are described below.

Geometry #

The EME Port Group geometry by default coincides exactly with the EME solver region. The user can manually choose to place the input port on the left or right side of the EME solver region. Additionally, the port width can be adjusted by setting the Geometry parameters for each port within the group.

Source Properties #

The Source Properties in the EME Port Group are used to define how the light source is injected.

Name	Description
As source port	Select from the dropdown list which port in the current group will act as the light source injection port.
Incident mode ID #	Specify the mode ID number for the injected light. This number corresponds to the eigenmode number (starting from 1) calculated for that port.

Monitor Properties #

Monitor properties are used to set the recording attributes when the port acts as a monitor.

Name	Description
Data type	The type of data recorded; here it is Frequency-domain, a read-only parameter.
Spatial sampling	Spatial sampling. Sets the spatial sampling resolution.
Spatial resolution	Sets the resolution in the propagation direction. The default value is 100.

Port Settings #

Right-click on an individual port within the EME Port Group to access and configure its detailed properties. Most of the settings are the same as those for regular ports; for details, please refer to Port Settings.

Monitors #

The EME solver currently includes two monitors: the field profile monitor (EME Profile) for recording the field distribution along the propagation direction, and the refractive index monitor (Index) for recording the refractive index distribution of the waveguide structure. In addition, the transmission and reflection characteristics at the device ports can be obtained from the S-parameter matrices in the "EME Results" section below; these matrices reflect the transmission, reflection, and mode conversion information between different modes at each port.

EME Profile #

This monitor is used to view the electromagnetic field distribution along the propagation direction within the simulation region. Its basic settings are the same as those of the FDFP monitor; for details, see FDFP Monitor. For MMI devices, this monitor can intuitively show the propagation of the electromagnetic field within the device, as shown in the figure below:

Index #

This monitor is used to view the relative refractive index distribution within a specified region. Its basic settings are the same as those of the Index monitor in the FDTD solver. For details, please refer to Refractive Index Monitor Settings.

Mesh #

This option allows users to add a custom mesh. Its basic settings are the same as those of the custom mesh in the FDTD solver. For details, please refer to Custom Mesh Settings.

EME Results #

After the EME solver simulation is completed, the results mainly consist of the following three parts:

• S-parameter results: Stored in the EME solver, providing two sets of S matrices: Internal S Matrix and User S Matrix.
• Monitor data: Including the field distribution recorded by the field profile monitor (EME Profile) and the refractive index distribution recorded by the refractive index monitor.
• Cell and port mode information: Eigenmode information obtained from each cell (such as effective index, mode field distribution, etc.), and mode field data recorded at the ports acting as monitors.

The various types of results from the EME solver are described in detail below.

Internal S Matrix #

The Internal S Matrix is the eigenmode scattering matrix calculated based on all cell interfaces in the EME algorithm. During simulation, the EME solver divides the device into multiple cells along the propagation direction and calculates the transmission and reflection coefficients between all possible modes at each cell interface. By cascading the S matrices of these cell interfaces, the Internal S Matrix of the entire device is finally obtained. This matrix contains the complete response between all possible modes at the input and output ports and is a generalized scattering matrix reflecting the intrinsic characteristics of the device.

User S Matrix #

The User S Matrix is the S-parameter result calculated based on the specific modes selected by the user at the ports. Users can specify the modes of interest (e.g., TE0, TM0, etc.) at the input and output ports of the device, and the simulation results will provide the S matrix only for these selected port modes. The dimension of the User S Matrix depends on the number of ports and the number of modes selected at each port. For example, for a three-port device, if one mode is selected at each port, a $3\times 3$ S matrix is obtained, which includes reflection coefficients (e.g., $S_{11}$) and transmission coefficients (e.g., $S_{21}$).

Furthermore, taking a two-port device as an example, if two modes are selected at each port for calculation, a $4 \times 4$ S matrix is obtained. The result is shown in the software as illustrated below:

The indexing of this $4 \times 4$ S matrix follows the rules shown in the figure below. Each element $S_{mn}$ of the matrix represents the transmission coefficient from the input port/mode combination n to the output port/mode combination m.

Name	Description
$S_{11}$	Reflection coefficient for output Port1, Mode1 from input Port1, Mode1.
$S_{12}$	Reflection coefficient for output Port1, Mode1 from input Port1, Mode2.
$S_{13}$	Transmission coefficient for output Port1, Mode1 from input Port2, Mode1.
$S_{14}$	Transmission coefficient for output Port1, Mode1 from input Port2, Mode2.
$S_{21}$	Reflection coefficient for output Port1, Mode2 from input Port1, Mode1.
...	...
$S_{33}$	Reflection coefficient for output Port2, Mode1 from input Port2, Mode1.
...	...
$S_{44}$	Reflection coefficient for output Port2, Mode2 from input Port2, Mode2.

Cell and Port Results #

In the EME simulation, each cell independently solves for eigenmodes; this mode information is the basis for constructing the S parameters. Users can view the result data for a single cell:

Name	Description
neff	The effective index of each mode.
neff_TE	The TE polarization similarity of the mode.
neff_TM	The TM polarization similarity of the mode.
index	The refractive index distribution data of the current cell (function of spatial coordinates).
Mode Fields	The field profile of each mode on the cell cross-section, used to visualize the mode shape and energy distribution.
TE Fraction	The TE polarization fraction of each mode (0 to 1), indicating the proportion of TE component in the mode energy.
mode selection	The mode number selected by the user at this cell.
overlap	The overlap integral between modes of the current cell and adjacent cell, used to analyze mode coupling in different cells.
S	The S-parameter matrix describing the coupling between different modes of the current cell and the next cell.

Ports are typically located at the boundaries of the EME simulation region, and mode information at these locations can also be obtained. Therefore, the data types for port results are essentially the same as those for cell results.