Abstract
The effect of bandwidth limitation on the pulsing frequency of an optoelectronic feedback semiconductor laser was studied numerically. Linear-phase finite-impulse-response (FIR) filters with various responses characteristics were considered in the thesis for different filtering effects. The design parameters for the filter consist with a filter order and five other parameters, including low frequency roll-off, high frequency roll-off, low stopband rejection, high stopband rejection, and filter delay time, that defines the characteristics of the simulated filter response. Together with the operational parameters of the optoelectronic feedback system, which are the feedback strength and feedback delay time, the filtering effects on the main pulsing frequency and bifurcation diagram under different conditions were studied. To perform the computation efficiently, the overlap-save method was utilized in the simulation. The pulsing frequency and bifurcation diagram of the optoelectronic feedback laser filtered with a high-pass filter was first investigated. For filters with same values of the low frequency roll-off, the main pulsing frequency and bifurcation diagrams with respect to the feedback strength were studied under different low stopband rejections. The relation between the main pulsing frequency and the bifurcation diagram was shown and explained. Moreover, conditions of different low frequency roll-offs with a fixed feedback strength were also considered. The main pulsing frequency and bifurcation diagram with respect to the low frequency roll-off were studied under different low stopband rejections. Two regions, namely I and II, were categorized under different low stopband rejections according to the distinct characteristics in both the main pulsing frequency and the bifurcation diagram. The borderline of the two regions was found influencing by the low stopband rejection where in some cases the main pulsing frequency saturated with the low stopband rejection. Different nonlinear dynamical states were analyzed with their time series, power spectra, and the phase portraits. For band-pass filters, high-pass and low-pass filtering effects were then discussed under the condition of same low stopband rejection and high stopband rejection. To simplify the analysis, a fixed feedback strength was considered for demonstrating the filtering effect. For high-pass filtering effect, the high frequency roll-off of the filter was fixed while the low frequency roll-off varies. Two different regions, I and II, were also found. Similar behaviors were observed when utilizing a high-pass filter as the bandwidth limitation component. However, dynamical states disappeared and the laser becomes stable when the filter bandwidth was too narrow or the low frequency roll-off was far above the relaxation oscillation frequency. For low-pass filtering effect, the low frequency roll-off was fixed while the high frequency roll-off varies. Dynamical states were found to disappear when the filter bandwidth was too narrow or the high frequency roll-off was below a certain frequency. The main pulsing frequency was influenced by the high frequency rolloff and saturated at certain region as the low frequency roll-off becomes small. Otherwise, the main pulsing frequency was independent of the high frequency roll-off. Finally, a map of the main pulsing frequency with respect to both the low frequency roll-off and the high frequency roll-off was plotted, which demonstrated how the bandwidth limitation affects the main pulsing frequency in the optoelectronic feedback laser.