Introduction
When performing Transient Sample Mode time-domain simulations, the sample rate must be sufficiently high for the digital filter representing the impulse response of an element to be accurate over the frequency range of interest. When the sample rate is too low, some frequency content in the element's true response is not captured, resulting in an inaccurate complex transmission at frequencies away from the center frequency of the simulation. The digital filter calculated for an element in INTERCONNECT depends on the sample rate, so long as the number of taps is greater than 1 (i.e. "single tap filter" is false).
In this example, the reflectivity spectrum of a waveguide Bragg grating is simulated in the time domain with both a small and large sample rate and compared with a reference spectrum produced by a highly spectrally sampled frequency domain simulation.
Simulation Setup
In this example, the reflectivity spectrum of a waveguide Bragg grating is simulated in the time domain with both a small and large sample rate and compared with a reference spectrum produced by a highly spectrally sampled frequency domain simulation.
The INTERCONNECT project file SampleRate.icp contains three circuits, each comprised of an Optical Network Analyzer (ONA) connected to a waveguide Bragg grating (WBG) so as to measure the reflectivity spectrum, as shown in Figure 1. The highly spectrally sampled frequency-domain simulation is performed by the ONA_1/WBG_1 circuit and serves as a reference. The ONA_2/WBG_2 and ONA_3/WBG_3 circuits perform the Transient Sample Mode time-domain simulations with low (100 GHz) and high sample rate (2 THz), respectively. The Bragg gratings WBG_2 and WBG_3 both employ Finite Impulse Response (FIR) digital filters with the "number of taps estimation" to set fit tolerance.
Results and Discussion
Open INTERCONNECT, load the file SampleRate.icp and run the simulation. Load and run the script, SampleRate_plotResults.lsf. The scripts plots the transmission at input 1 for all three ONAs in the same window as shown in Fig. 2.
Figure 2 depicts power reflectivity spectrum from the waveguide Bragg grating for the reference (highly spectrally sampled frequency domain simulation plotted in blue), as well as the low and high sample rate time-domain simulations. For the low sample rate simulation, the simulation bandwidth (i.e. sample rate) of ONA_2 is only 100 GHz, and is not sufficiently large to capture all of the frequency content of the Bragg grating peak at 200 THz (as seen in the inset where the same plot is shown over a larger frequency range). As a result, the WBG digital filter cannot accurately capture the time-domain impulse response of the element. The resulting spectrum is only accurate only in the central part of the frequency range. For the high sample rate simulation, excellent agreement is obtained throughout the range plotted. Here the sample rate is increased by a factor of 20 to 2THz.
