The MODE ANALYSIS window is shown in the screenshot below. The upper portion of the window contains the MODE LIST where the mode number, effective index, propagation loss, and polarization are shown. The lower left-hand corner shows the calculation parameters; upon launch, the lower left-hand portion of the window shows the default calculation parameters to be used to simulate the structure. The right-hand portion of the window contains the PLOT AREA where the simulation data is plotted, and the two drop-down boxes at the top of the plot area are used to specify which data to plot in the plot window, while the region at the bottom right can be used to modify the current mode plot options. Upon launch, the plot area shows the refractive index profile of the structure being analyzed.

## Modal analysis tab

The modal analysis portion of the window displays simulation data relevant to the different modes calculated for the structure of interest. This portion of the window shows the modes, arranged from top to bottom in terms of the highest effective index and numbered sequentially. For each mode, this portion of the window shows the effective index of the mode, the calculated loss (measured in dB per millimeter of propagation; only valid for lossy materials), and the polarization fraction (please see Mode List and Deck for the full definition).

## Boundary conditions tab

The boundary conditions that are supported by FDTD and MODE are listed below.

Perfectly matched layer (PML)1 boundaries absorb electromagnetic waves incident upon them. They essentially model open (or reflectionless) boundaries. In FDTD and varFDTD simulation regions, the user can directly specify all the parameters that control their absorption properties including the number of layers. To facilitate the selection of PML parameters, a number of profiles (or predefined sets of parameters) are available under the boundary conditions tab. In most simulation scenarios, the user only needs to choose one of the predefined profiles and fine tune the number of layers. PML boundaries perform best when the surrounding structures extend completely through the boundary condition region. This will be the default behavior of structures whether or not they were drawn to end inside or outside the PML region.

1 J. P. Berenger, Perfectly Matched Layer (PML) for Computational Electromagnetics. Morgan & Claypool Publishers, 2007.

Metal boundary conditions are used to specify boundaries that behave as a Perfect Electric Conductor (PEC). The component of the electric field parallel to a metal (PEC) boundary is zero; the component of the magnetic field H perpendicular to a metal (PEC) boundary is also zero. Metal boundaries are perfectly reflecting, allowing no energy to escape the simulation volume along that boundary. In the FDE solver, metal BC is the default setting.

### PMC

Perfect Magnetic Conductor (PMC) boundary conditions are the magnetic equivalent of the metal (PEC) boundaries. The component of the magnetic field H parallel to a PMC boundary is zero; the component of the electric field perpendicular to a PMC boundary is also zero.

Periodic BC should be used when both the structures and EM fields are periodic. Periodic boundary conditions can be used in one or more directions (i.e. only in the x direction) to simulate a structure which is periodic in one direction but not necessarily other directions.

Bloch BC should be used when the structures and the EM fields are periodic, but a phase shift exists between each period. Bloch boundary conditions are used in FDTD and propagator simulations predominantly for the following two simulations:

- Launching a plane wave at an angle to a periodic structure – in this situation, accurate reflection and transmission data can be measured at a single frequency point for a given simulation.
- Calculating the bandstructure of a periodic object – in this situation, a broadband pulse is injected via a dipole source into a periodic structure.

Note: if you choose BFAST plane wave source, the Bloch BCs will be automatically overridden and use its built_in boundary conditions. |

### Symmetric / Anti-Symmetric

Symmetric/anti-symmetric boundary conditions are used when the user is interested in a problem that exhibits one or more planes of symmetry; both the structure and source must be symmetric. Symmetric boundaries are mirrors for the electric field, and anti-mirrors for the magnetic field. On the other hand, antisymmetric boundaries are anti-mirrors for the electric field, and mirrors for the magnetic field. Careful consideration must be given to whether symmetric or anti-symmetric boundary conditions are required, given the vector symmetry of the desired solution. For meaningful results, the sources used must have the same symmetry as the boundary conditions. Further information about symmetric and anti-symmetric boundary conditions can be found in Choosing between symmetric and anti-symmetric BCs.

ALLOW SYMMETRY ON ALL BOUNDARIES: Allows symmetric boundary conditions with periodic structures (this option is not available in the boundary condition tab of mode sources and mode expansion monitors).

## Select Mode

Pressing this button (located on the lower right corner of the window) will initialize the mode source with the current mode selected within the mode table in the upper left-hand portion of the window.

## Advanced Options

The ADVANCED OPTIONS button (located on the lower left corner of the window) brings up the "Mode Advanced Options" window with the following parameters:

- CONVERGENCE TOLERANCE: the convergence tolerance used for the calculations. The default value corresponds to 1e-12 but can be increased by the user to speed convergence or decreased to improve accuracy.
- MAXIMUM NUMBER OF MODES TO STORE: When searching for modes in a range of effective indices from n1 to n2, it is possible to fill your available memory if too many modes are found. For this reason, the maximum number of modes is limited and the calculation will stop when this number of modes is exceeded.
- USE SINGLE PRECISION: this can be used to save some memory during the calculation of the modes but the results are less accurate.

Note: Default boundary conditions (BC) in Mode solver By default, the integrated mode solver uses Metal BC's, except in the following situations. - Symmetry - If the solver uses symmetry BC's, the integrated mode solver will use the same symmetry option.
- Periodic - If the solver uses periodic BC's, and if the mode source span is large enough to cover the entire simulation region span, the integrated mode solver will use periodic BC's on that axis.
In the Boundary conditions tab you can override these default settings to select PML or PMC boundary conditions. |