When performing time-domain simulations in Transient Block Mode (TBM), it is important for the time window to be broader than both the input and output waveforms. If this is not the case then, incorrect results may be produced due to the effects of time-domain aliasing.
In this example, the broadening of a Gaussian pulse as it travels through a length of fiber with normal dispersion is simulated using the Linear Optical Fiber Element in INTERCONNECT.
The INTERCONNECT project file BlockModeTimeWindowEffects.icp, contains a circuit comprised of a Pseudo-Random Bit Sequence Generator (PRBS) driving a Gaussian Pulse Generator (GAUSS) which launches a pulse into a dispersive Linear Optical Fiber (FIBER). The input and output pulses are recorded by Optical Oscilloscopes (OOSC). The circuit schematic is depicted in Figure 1.
Gaussian Pulse broadening effect circuit
In order to run the example all that is needed is to run the script file runBlockModeTimeWindow.lsf. This script file runs three different time-domain simulations in Block Mode, each with a different time-window and bit rate. However, the sample rate and number of samples (as well as the number of samples per bit) are the same in the three simulations.
- Place the files, BlockModeTimeWindowEffects.icp, runBlockModeTimeWindow.lsf, calculateParameters.lsf and plotResultsBlockMode.lsf in the same directory.
- Open INTERCONNECT, load and run the script file runBlockModeTimeWindow.lsf.
Results and Discussion
When a Gaussian pulse travels through a length of fibre with normal dispersion in the linear regime, the pulse retains its Gaussian shape, but its width increases with the distance traveled. Figure 2 shows the shape of the optical intensity as a function of the retarded time normalized by the full-width-at-half-max (FWHM), \(T_0\), of the input pulse, for the input pulse as well as those for the output pulses for three simulations with different time-windows. The retarded time, \(t'\), is given by \(t'=t-z/v_g\), where \(t\) is time, \(v_g\) is the group velocity in the fiber, and \(z\) is the distance traveled through the fiber.
The length of the fibre, \(L\), in the current example is approximately 564 m. As can be seen in the figure, the simulations with the larger time windows relative to the input and output pulse width produce the expected behavior (pulse shape retention), whereas the shorter time-window simulation results in a distorted and incorrect output pulse.