When performing time-domain simulations to obtain frequency spectrum data on devices that exhibit narrow spectral features, it is necessary to have adequate spectral resolution to be able to properly resolve them. The spectral resolution of the data produced by the simulation is the inverse of the time window. For a fixed sample rate, the time window increases with the number of samples.
In this example, the spectrum of a double bus ring is simulated in the time domain with both a short and long-time window and compared with a reference spectrum produced by a highly spectrally sampled frequency domain simulation.
The INTERCONNECT project file Time_Window.icp contains three circuits, each comprised of an Optical Network Analyzer (ONA) connected to a double bus ring resonator modeled using a pair of couplers linked by two waveguides such that they form a loop, as shown in Figure 1. The circumference of the ring is given by the sum of the waveguide lengths, and the coupling to the external ports is determined by the coupling coefficient in the couplers. The ring is assumed to have negligible loss in the present example and hence the waveguides are set to be lossless. In this case, the coupling coefficients determine the quality factor, and hence the width of the spectral features displayed. Referring to Figure 1, the highly spectrally sampled frequency-domain simulation is performed by the ONA_1/C_1/WGD_1/C_2/WGD_2 circuit. The ONA_2/C_3/WGD_3/C_4/WGD_4 and ONA_3/C_5/WGD_5/C_6/WGD_6 perform the time-domain simulations with short and long time-windows, respectively.
- Open INTERCONNECT, load the file Time_Window.icp and run the simulation.
- Load and run the script, plotResults.lsf.
Results and Discussion
Figure 2 depicts the power transmission spectrum from the drop port in the ring for the reference (highly spectrally sampled frequency domain simulation), as well as the short- and long- time window time-domain simulations, over a narrow band near the center of the simulation bandwidth. From the figure it is evident that the short-time window simulation produces a spectrum that is not sufficiently resolved to be able to obtain accurate estimates of the widths and free-spectral ranges of the transmission, whereas the long-time domain simulation is able to faithfully reproduce the salient features observed in the reference spectrum.