Mode Expansion Monitors use overlap analysis to calculate the forward/backward propagating components of any mode of a waveguide or fiber at an arbitrary location in the simulation region. The Mode Expansion monitor facilitates the interoperability between FDTD and INTERCONNECT as it returns the S parameters, which can be imported into INTERCONNECT directly. For more information and tips on best practices to get the most accurate results from this monitor, see using the mode expansion monitor.
Note that if performing parameter extraction using FDTD, using ports and the S-parameter sweep tool is preferable since the port objects can act as both sources and monitors and return S-parameters as a result.
Monitor type: The monitor type and orientation, this option will control the available of spatial setting below
- X, Y, Z: The center position of the simulation region
- X MIN, X MAX: X min, X max position
- Y MIN, Y MAX: Y min, Y max position
- Z MIN, Z MAX: Z min, Z max position
- X SPAN, Y SPAN, Z SPAN: X, Y, Z span of the simulation region
The DOWN SAMPLE X, Y, Z option is used to set the spatial downsampling performed by the monitor. A down sample value of N corresponds to sampling (recording) the data every Nth grid points. Setting the down sample value to 1 gives the most detailed spatial information (i.e. information at each grid point).
Mode expansion tab
The Mode Expansion tab contains two main sections. The "Mode calculation" section allows users to select a mode (or a set of modes) to expand the input profile with. The "Monitors for expansion" section allows users to choose a field profile from an arbitrary monitor in the simulation to expand. For more information on this expansion calculation, and the results that are returned, see Using Mode Expansion Monitors.
- MODE SELECTION: Allows users to select the modes to use for the mode expansion calculation. The "user select" option launches the eigenmode solver where the user can calculate and visualize the supported modes (see Mode analysis); use this option to select multiple modes. The eigenmode solver also provides a tool for frequency analysis (see Frequency Analysis - Modal Analysis Tab).
Following the "mode selection" combo box is a frame for choosing the frequencies to calculate the modes for. Note that this does not have to correspond to the frequency points for the monitors in the "Monitors for expansion" table. The mode expansion monitor will automatically perform the necessary interpolation between different frequency points.
- OVERRIDE GLOBAL MONITOR SETTINGS: A toggle to override the global monitor settings. If checked, the user can specify the frequency range and number of points at which the modes will be calculated at (using the options described below). If unchecked, the options below are set from the global monitor settings.
- SAMPLE SPACING: This combo-choice parameter determines how the sample frequency/wavelength will be selected. The three sample options are "uniform", "chebyshev" and "custom".
- USE WAVELENGTH SPACING: By default, data is recorded at certain spaced points with respect to frequency. Selecting this option spaces data at certain spaced points with respect to wavelength.
- USE SOURCE LIMITS: When checked these monitors use the source limits. When unchecked, the frequencies/wavelengths at which to record data can be set using the pull down menus and boxes below them.
- FREQUENCY POINTS: Set to choose the number of frequency points at which to record data.
When sample spacing is selected to be "custom", all the above settings will be disabled and a "custom frequency samples" table will be shown. Properties of the table are:
- ADD: Adds an entry above the selected entry to the "frequency (THz)" table
- REMOVE: Removes the selected entry from the "frequency (THz)" table
- SORT: Sorts the table with frequency from low to high
- SELECT MODE: If the "user selected" option has been chosen, this will bring up the Mode analysis tab for the user select from a calculated list of modes.
- VISUALIZE MODE DATA: This will bring up the Visualizer, showing all the profiles for the selected modes.
- CLEAR MODE DATA: Clears all the mode data.
This frame allows user to apply an arbitrary rotation to the calculate modes.
- THETA: The angle of propagation, measured in degrees, with respect to the normal axis.
- PHI: The angle of propagation, in degrees, rotated about the normal axis in a right-hand context.
- OFFSET: Allows users to set an offset to the plane where the modes are calculated. This is useful for ensuring that monitors at an angle do not intersect with unwanted structures.
Note: For best accuracy, we should place mode expansion monitors with rotations on a mesh cell. A useful approach is to add an override mesh region at the same position of the mode expansion monitor, and this override region can be infinitely thin (i.e., one of the spans can be '0').
- AUTO UPDATE BEFORE ANALYSIS: If checked, the monitor will automatically update the chosen modes when "user select" in MODE SELECTION is selected. The monitor will find the best overlap between the chosen modes and the currently calculated modes, if there are a new set of modes. This allows users to keep track of the same chosen modes even the mode orders are switched, for example, when running a Parameter sweep over the waveguide width. This checkbox can be unselected but it has no effect if "fundamental mode", "fundamental TE mode" or "fundamental TM mode" is chosen in the MODE SELECTION dropdown list.
- ALIGN TO FREQUENCY MONITOR CENTER:
- By default, it is unchecked. In some cases, aligning to the center can lead to incorrect expansion when a monitor is offset. By unchecking this option, it performs the overlap calculation without aligning the center of the mode expansion monitor with the center of the frequency monitor. This feature is useful when a monitor, or both expansion and frequency monitor, is offset. For the best practice, when expanding the fields from a single frequency monitor, it is recommended to leave this unchecked and also to align the mode expansion monitor precisely with the frequency monitor that will be expanded, and with the center of the waveguide.
- If checked, the center of the mode expansion monitor will be laterally shifted to align with the center of the frequency monitor when the expansion is calculated. This makes it possible to use the same mode expansion monitor for the expansion of modes on different waveguides that are laterally offset. For example, using one mode expansion monitor to expand the modes in multiple channels that are laterally offset (e.g., drop and through) in a ring resonator simulation. It is recommended to place all monitors at the centers of the waveguides accordingly to avoid incorrect expansion. This shift does not add additional phase to the expansion.
- NUMBER OF TRIAL MODES: The number of modes specified to look for in order to find a fundamental mode. This will affect the modes that the solver finds. If this number is too small, the desired modes may not be found. Often, setting this number to 100 modes will ensure that no physical modes have been missed. If more than 100 modes exist, then a larger number should be used if one is interested in higher order modes.
Monitors for expansion
After the modes have been selected, the next step is to choose the monitor with the input field profile. The "Add" and "Remove" buttons on the side can be used to add/remove monitors, and users can choose the desired monitor from the monitor drop down list. See the getting Ring resonator getting started example for an example that uses mode expansion monitor.
Notes: Advanced setup tips for best results
- NEFF: Effective index as a function of selected mode and frequency/wavelength is returned.
- MODE PROFILES: Mode profiles (E, H, and index) as a function of position and frequency/wavelength.
- EXPANSION FOR: A set of expansion results are returned for each input monitor specified under "Monitors for expansion". Each set of result contains Ttotal, Tforward,Tbackward, Tnet, a,b, N, and P. Please see the Using Mode Expansion Monitors page for more information.