This page provides more information on the Frequency Analysis part of the Eigensolver analysis window.

## Set calculation parameters

With the OPTION PULL-DOWN set to "set calculation parameters", the frequency analysis tab contains parameters for the frequency sweep. Some of the parameters can be set through the List of commands.

The parameters shown include:

- TRACK SELECTED MODE: check this box to track the selected mode in the mode list.
- START, STOP FREQUENCY: the first and last frequency at which the modes are solved for. If a particular mode is being tracked, the start frequency parameter defaults to the value used to initially calculate the modes within the MODAL ANALYSIS tab.
- START, STOP WAVELENGTH: the first and last wavelength at which the modes are solved for. If a particular mode is being tracked, the start wavelength defaults to the value used to initially calculate the modes within the MODAL ANALYSIS tab.
- NUMBER OF POINTS: The number of frequency/wavelength points to include in the sweep.
- NUMBER OF TEST MODES: This parameter sets the maximum number of modes to use for the sweep calculation. To track a single mode, this parameter is best set to approximately 3 in order to keep the computation time to a minimum (unless there are discontinuities in the sweep data, in which case this parameter will need to be increased slightly). If track selected mode is not set, then this parameter determines the maximum number of modes which are to be swept over the frequency/wavelength range of interest.
- EFFECTIVE INDEX: This parameter is used to specify the value of effective index around which the modes are solved for. Only valid when not tracking a selected mode.
- DETAILED DISPERSION CALCULATION: Calculate the mode properties at some additional frequencies to obtain more accurate dispersion data over the frequency/wavelength range of interest. This takes more time but gives a more accurate result.
- STORE MODE PROFILES WHILE TRACKING: This option is used for exporting to INTERCONNECT only. This will store the mode profiles for each frequency.
- BENT WAVEGUIDE: Select this option to sweep a waveguide which has a bend in it.

- Bend radius - the radius of curvature of the waveguide bend
- Bend orientation - the orientation of the bend; refer to Bent waveguide calculation for details.

## Data export

The "export data" option is where the user can export the data for the current frequency sweep.

Standard export:

- TEXT FILE (COLUMN): exports a column table of frequency, real effective index, and imaginary effective index, loss, real beta, imaginary beta, overlap (when tracking a mode), group velocity and dispersion.
- TEXT FILE (STANDARD): exports vectors of the frequency, real and imaginary effective indices, loss, real and imaginary beta, overlap (when tracking a mode),group velocity and dispersion.
- MATLAB: exports the data to a Matlab-compatible file which contains a frequency vector, a complex-valued effective refractive index vector, a loss vector, a complex-valued beta vector, a group velocity vector and a dispersion vector.
- LDF FILE: exports the frequency results into a Lumerical .ldf file.
- Export Frequency Data: exports the frequency sweep results into the selected standard format.

INTERCONNECT export:

Export the frequency sweep results into a format that can be easily loaded into INTERCONNECT. Please see INTERCONNECT - MODE waveguide for details.

## Mode plot and Frequency plot

You can control various options of the frequency sweep plot, or the mode plots (initial plot and current plot) by selecting various options. The mode plot options are the same as in the Modal analysis tab, and the frequency plot options are as follows.

The plot pull down box allows the user to choose which data to visualize. The screenshot below shows the different ways in which the simulation data can be plotted. Data which can be plotted versus wavelength or frequency include:

- EFFECTIVE INDEX: selecting this option will generate a plot of the effective index for each calculated mode, plotted as a function of wavelength or frequency.
- LOSS: selecting this option will generate a plot of the modal loss as a function of frequency. Measured in units of dB/mm of propagation.
- GAIN: selecting this option will generate a plot of the modal gain as a function of frequency. Measured in units of dB/mm of propagation.
- GROUP INDEX: Is the ratio of the speed of light to the group velocity, \(c/\upsilon_g\). Unitless.
- GROUP VELOCITY: Is defined \(\upsilon_g = \partial \omega / \partial \beta\), and can be interpreted as the rate at which the peak of a temporal pulse will propagate in the absence of nonlinearities. Measured in meters per second (m/s).
- GROUP DELAY: Is defined as \(\tau_g = 1/\upsilon_g\). Measured in picoseconds per kilometer.
- DISPERSION: Is defined as the rate of change of the group delay with respect to wavelength (\(D_{\lambda}=\partial \tau_g / \partial \lambda_0\)). Measured in picoseconds per nanometer per kilometer (ps/(nm km)).
- BETA: Defined as \(\beta = 2\pi n_{eff} / \lambda_{0}\), where \(n_{eff}\) is the effective index, and \(\lambda_{0}\) is the free-space wavelength. Measured in units of inverse meters (1/m).

An example running frequency analysis using parameter sweep and script, please see Sweep analysis for dispersion.