本論文主要是利用穩態分析以及四波混頻分析來探討雷射的鬆弛震盪特性以及遭外界微小干擾時的行為。其中四波混頻分析還能用來量測本質參數，進而探討半導體雷射動態行為。藉由量測外界擾動對本質參數的影響，我們能夠更深入地研究雷射動態行為在有外界擾動時的改變。
在這篇論文中，我們將線性穩態分析套用在量子點雷射和量子井雷射上。光注入下以及未受外界擾動的情形也分別加以探討。藉由從內部微擾推導出的特徵方程式，我們可以得知雷射的鬆弛震盪頻率以及衰減係數。從不同偏壓電流、線寬增益係數、光注入強度、以及調頻頻率下的衰減係數可以得知量子點雷射有比量子井雷射更好的穩定性。另外，光回饋下量子點雷射的穩定性及動態行為也有用數值模擬的方式探討。
為了探討在四波混頻分析的過程中雷射對外部微擾的反應，我們推導了光注入下以及未受外界擾動的量子點雷射和量子井雷射模型並得出其解析解。另外，我們也有推導光回饋下的量子點雷射模型的四波混頻分析。這些理論模型都有仔細地和數值模擬的結果作驗證比對。
我們已經將四波混頻分析成功地套用在量子點雷射上，並且同時求出線寬增益係數等本質參數。在不同的調頻頻率下，藉由將實驗得出的再生訊號強度和調幅訊號強度與理論算出的強度作擬合，我們可以同時得到線寬增益係數、量子點內的載子衰減率、微分增益、以及光子衰減率等本質參數。我們也討論了用這個方法所求出的各個本質參數的精準度。另外，我們也研究了各個參數對再生訊號頻譜和調幅訊號頻譜的影響。
另外，我們用一個簡化的速率方程式模型進行光注入下量子點雷射的四波混頻分析。我們討論了不同本質參數和不同注入條件下再生訊號頻譜和調幅訊號頻譜的變化。藉由擬合實驗得出的再生訊號頻譜和調幅訊號頻譜，我們得到不同注入條件下單模量子點雷射的本質參數。我們也展示了光注入下的線寬增益係數能夠降低到原來六成左右。當注入強度增加時，線寬增益係數可以降得更低。這個現象可以用在減緩光通訊的啾頻效應。
為了完整地研究量子點雷射遭外界干擾時的變化，我們建立了光回饋下量子點雷射的四波混頻模型。我們研究了不同回饋條件下再生訊號頻譜和調幅訊號頻譜的變化。另外，我們也討論了本質參數對再生訊號頻譜和調幅訊號頻譜的影響。基於這些理論預測的結果，我們成功地量測出光回饋下量子點雷射的本質參數，其中光回饋下的線寬增益係數會增加。

In the dissertation, stability analysis and four-wave mixing (FWM) analysis are applied to investigate the characteristics of the relaxation oscillation of the quantum dot (QD) and the quantum well (QW) semiconductor lasers and their responses to the weak external perturbation, respectively. The FWM analysis can also be utilized to extract the intrinsic parameters of the semiconductor lasers, which apparently influence the dynamical behaviors. Through the modifications of strong external perturbations on the intrinsic parameters, the dynamical behaviors of the lasers can be investigated thoroughly.
The linear stability analysis has been applied on the solitary and injection-locked lasers of QD and QW structures. By deriving the characteristic equations from the small internal fluctuations, the relaxation frequencies and the damping rate can be obtained. From the damping rates of the lasers with different bias currents, linewidth enhancement factors, injection strengths, and detuning frequencies, the QD lasers show better stability than the QW lasers. Moreover, the stability and excitability of the QD laser subject to optical feedback are also numerically discussed.
To investigate the responses on small external perturbations in the FWM analysis, the rate equations of the solitary and injection-locked lasers of QD and QW structures are derived for the analytical solutions. Moreover, the FWM mixing analysis on the QD lasers subject to optical feedback is also derived. All the analytical models are carefully verified with the numerical simulations.
FWM analysis has been applied on a QD laser to simultaneously obtain the linewidth enhancement factor and other intrinsic laser parameters. By fitting the experimentally obtained regenerative and amplitude modulation spectra at different detuning frequencies with the respective curves analytically calculated from the rate equations, parameters including the linewidth enhancement factor, the carrier decay rate in the dots, the differential
gain, and the photon decay rate can be determined simultaneously under the same operating conditions. The sensitivity and accuracy of the parameter extracted by the FWM analysis are presented. Moreover, how each parameter alters the shapes of the regenerative and amplitude modulation spectra is also discussed.
Moreover, a simplified rate equation model is utilized for the FWM analysis on QD lasers subject to optical injection. The regenerative and amplitude modulation spectra of the QD laser with different intrinsic laser parameters and external injection conditions are investigated. By curve fitting the regenerative and amplitude modulation spectra experimentally, the intrinsic laser parameters of a commercial single-mode QD laser under different injection conditions are extracted. The linewidth enhancement factor at different injection levels and detuning frequencies are shown, where a reduction of about 40% from its free-running value is demonstrated. By increasing the injection strength, the linewidth enhancement factor can be further reduced to minimize the chirp in optical communications.
To comprehensively investigate the characteristics of QD laser subject to external perturbations, the model for the FWM analysis on the QD laser subject to optical feedback is also developed analytically. The modifications with different feedback conditions on the regenerative and amplitude modulation spectra are discussed. Also, how the regenerative and amplitude modulation spectra vary with each intrinsic parameter is discussed. Based on the theoretical prediction, we successfully extract the intrinsic parameters of the QD laser subject to optical feedback experimentally and the linewidth enhancement factor is found to increase with optical feedback.

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