The TWLM model divides the cavity into a number of discretized segments, each with a length of \(\Delta L\).
The segment length in the model is calculated as the product of the group velocity, \(v_g\), and the time step, \(\Delta T\):
$$
\Delta L = \Delta T \cdot v_g
$$
$$
v_g = \frac{c}{n_g}
$$
$$
\Delta T = \frac{1}{\text{sample rate}}
$$
where \(c\) is the speed of light, \(n_g\) is the group index of the mode, and \(\text{sample rate}\) is a parameter set in the Root element in INTERCONNECT. This segment length ensures that the optical fields propagate through one segment in one time step.
TWLM variables, such as the photon density, carrier density, gain, grating chirp and apodization, and others, are calculated in the middle of each section.
Note: The sample rate sets the simulation bandwidth, and it should be wide enough including the consideration of side modes and the gain spectrum width. Another consideration for the sample rate is to ensure sufficiently small segment size for spatial discretization accuracy. The sample rate should also be high enough to ensure adequate fidelity of the gain and spontaneous emission frequency dependencies implemented by a time-domain digital filter if user defined gain is used.
INTERCONNECT will determine the number of segments as a ratio of the defined length, \(L\), and the segment length \(\Delta L\) as calculated above. If the ratio is not an integer, it is rounded to the nearest integer, resulting in a simulated length that may slightly differ from the defined length. This length difference results in round trip phase and group delay difference. The phase difference is automatically compensated, while the group delay difference is not, which may result in a small error in the free spectral range.
You can specify a minimum number of segments in the “minimum number of discretized segments” parameter. However, this parameter only serves as a guideline and does not alter any simulation parameters. A warning message will appear if the number of segments is less than the specified minimum.
See Also
INTERCONNECT as a Laser Design Platform, Laser TW – INTERCONNECT Element