本論文以數值模擬的方式討論頻寬限制對於延遲電濾波光電回授半導體雷射系統的影響。我們以不同的振幅響應的線性相位有限脈衝響應濾波器作為頻寬限制的元件。針對濾波器的頻率響應特性，定義了五個濾波器參數，分別為：低頻響應衰減頻率(low frequency roll-off)、高頻響應衰減頻率(high frequency roll-off)、低頻截止帶衰減率(low stopband rejection)、高頻截止帶衰減率(high stopband rejection)以及濾波延遲時間(filter delay time)。加上光電回授半導體雷射系統的兩個操作參數：回授強度(feedback strength)以及回授延遲時間(feedback delay time)，我們討論了頻寬限制在光電回授半導體雷射系統中對於主要脈衝頻率以及分支圖的影響。為了計算上的效率，在數值模擬中應用了數位訊號處理裡常用的重疊儲存法(overlap-save method)。

首先，為了討論高通濾波的特性，我們在光電回授半導體雷射系統中加入高通濾波器，並分析脈衝頻率與分支圖對於不同操作參數的關係。在使用相同的低頻響應下降頻率、不同低頻響應衰減率的高通濾波器時，我們發現並解釋了回授強度對於主要脈衝頻率以及分支圖的密切關係。此外，我們也討論在使用相同回授強度、不同低頻響應衰減率的高通濾波器時，低頻響應下降頻率對於主要脈衝頻率以及分支圖的關係。根據主要脈衝頻率以及分支圖對於不同低頻響應下降頻率的特性，可以分成兩個區域。這兩個區域的分界隨著不同的低頻響應衰減率而改變，而且在某些情形下，主要脈衝頻率對於低頻響應衰減率有著飽和關係。再者，我們也採用了時間序列、功率頻譜，以及相位圖來分析在不同操作條件下所觀察到的非線性動態，而且也發現了在低頻響應下降頻率遠高於雷射鬆弛震盪頻率時，非線性動態會消失。

在相同的低頻截止帶衰減率以及高頻截止帶衰減率下，論文中也考量採用帶通濾波器的濾波效應。為了清楚地展現頻寬限制的特性，我們固定了回授強度，並且分別以高通濾波以及低通濾波的觀點來分析。考量帶通濾波器的高通濾波效應，我們固定住高頻響應下降頻率，改變低頻響應下降頻率來觀察主要脈衝頻率與分支圖的變化。這兩張圖同樣地可區分成兩區，跟使用高通濾波器作為頻寬限制的元件相比，我們也發現了類似的現象。然而略有不同的是，除了低頻響應下降頻率遠高於雷射鬆弛震盪頻率外，當濾波器頻寬太窄，非線性動態也會消失。另一方面，考量帶通濾波器的低通濾波效應，我們固定住低頻響應下降頻率，改變高頻響應下降頻率來觀察主要脈衝頻率與分支圖的變化，當帶通濾波器頻寬太窄或是高頻響應下降頻率低於特定的頻率時，非線性動態也會消失。此外，我們也發現主要脈衝頻率會受到高頻響應下降頻率影響，而當低頻響應下降頻率夠小的情形下，主要脈衝頻率對於高頻響應下降頻率在特定頻段有著飽和現象。最後，為了完整表露頻寬效應對於主要脈衝頻率的影響，我們以主要脈衝頻率對於高頻響應下降頻率與低頻響應下降頻率的圖作為總結，並列出一張總表歸納本論文考量的情形以及物理上的解釋。

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.

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