臺灣博碩士論文加值系統

在此論文中，我們研究半導體雷射泵浦微晶片型固態雷射(包括: Nd:YAG及Nd:YVO4)的複雜動力學行為。在有延遲回饋的半導體雷射泵浦單模微晶片型Nd:YVO4雷射中，我們首次觀察到兩種不穩定現象 (混沌暴漲及正弦暴漲)。這些結果與幾十年來受到廣泛研究的半導體雷射在延遲回饋下的行為所得到的結果截然不同。這兩種不穩定現象的主要性質可以用Lang-Kobayashi模型加上強的相位噪音數值模擬重現。另外，我們在鬆弛振盪態及隨機混沌暴漲態間的轉變點處發現機率相關性的非靜態特性，這也是第一次在實驗上看。這些現象也可以數值模擬重現。在歷史上，類似的特性也在簡單的動力學系統中被發現過。
此外，我們也探討B類雷射在雷射閥值(分歧點)附近的相對噪音行為。我們使用單模雷射速率方程式做數值模擬。我們發現在雷射閥值附近相對噪音強度在某些情況下會變強。此外，我們透過Fokker-Planck方程的方法在雷射閥值附近發現連續的transicritical分歧。另外，我們也有系統地探討單模雷射速率方程式裡的參數對相對噪音強度的影響。在實驗上，我們使用一個半導體雷射及兩個固態雷射(包括: Nd:YAG及Nd:YVO4)來探討相對噪音強度在雷射閥值附近的行為，並發現這兩種雷射的行為明顯不同。內在的參數，也就是反轉分布生命期及光子生命期的比值，被認為是影響結果的最主要的因素。
最後，我們提出一個新穎的耦合雷射系統方案，並且在兩個耦合的微晶片型Nd:YVO4雷射上發現了同步鬆弛振盪及同步混沌。另外，我們採用耦合雷射模型加上外加噪音，很成功的得到我們實驗上所觀察到的現象。

In this dissertation, we study the complex dynamical behaviors in laser-diode(LD)-pumped microchip solid-state lasers (SSLs), including neodymium doped yttrium orthvanadate (Nd:YVO4) and neodymium doped yttrium aluminum garnet (Nd:YAG).
In an LD-pumped single-mode microchip Nd:YVO4 laser with delayed-feedback system, two kinds of instabilities, random chaotic burst (RCB) generations and random sinusoidal burst generations, were observed experimentally for the first time.
These results are totally different form those observed in LDs with delayed-feedback systems, which have been widely studied last decades. Main features were reproduced numerically by utilizing the Lang-Kobayashi equations with strong phase noise, indicating phase-noise driven dynamical instabilities. Furthermore, a non-stationary characteristic of probability association was observed experimentally for the first time
at the transition between noise-driven relaxation oscillation state and RCB state. It was also well reproduced numerically. Before our study, the non-stationary characteristics were reported only by numerical simulations of simple dynamical systems. It was observed in a real physical system for the first time.
The relative intensity noise of class-B lasers around the lasing threshold (bifurcation point) was explored. Using single-mode laser rate equations, a enhancement of relative intensity noise was observed numerically around lasing threshold in some
conditions. Furthermore, the Fokker-Planck equation method was employed and a successive transcritical bifurcation was observed around the lasing threshold. The effects of each parameters in single-mode laser rate equations on the relative intensity fluctuation were explored systematically. One LD and two microchip SSLs, a Nd:YAG and a Nd:YVO4, were employed in the experiment. Significant differences in the characteristics of the LD and the SSLs were observed. The intrinsic parameters
of the lasers, namely, the time ratio between the lifetimes of carrier (population inversion) and photon, was considered to influence fluctuation dynamics dramatically.
Finally, a novel coupled-laser scheme was proposed and synchronized relaxation oscillations and synchronized chaos have been observed in a microchip Nd:YVO4 laser array with constant-power LD pumping. Coupled laser model equations with added noises are adopted to simulate the dynamics and the observed behaviors have been reproduced successfully.

1 Introduction 1
1.1 Complex Dynamics in optics 1
1.2 Typical Characteristics of Microchip Solid-state Lasers 2
1.3 Organization of this Dissertation 9
2 Phase-noise-driven Instability in a Single-mode Microchip Nd:YVO4 Laser with Feedback 13
2.1 Experimental Setup 16
2.2 General Features of Experimental Results 19
2.3 Theoretical Exploration Based on Lang-Kobayashi Model 23
2.4 Summary 31
3 Non-stationary Characteristics of Instability in a Single-mode Microchip Nd:YVO4 Laser with Feedback 48
3.1 Probability Association Analysis 50
3.2 Experimenxal Results 53
3.3 Numerical Results 54
3.4 Summary 55
4 Successive Transcritical Bifurcation and Relative Intensity Fluctuation Enhancement in Single-mode Class-B Lasers 60
4.1 Relative Intensity Noise (RIN) 62
4.2 Rate Equation Description 63
4.3 Analytic Approach Based on the Fokker-Planck Equation 64
4.4 General Features 71
4.5 Experimental Results 74
4.6 Summary 77
5 Synchronized Noise-driven Relaxation Oscillations in Mutually Coupled Nd:YVO4 lasers 85
5.1 Experimental Setup 86
5.2 Experimental Results 88
5.3 Numerical 90
5.4 Summary 91
6 Conclusions and Future Works 98
6.1 Conclusions 98
6.2 Future Works 102
A Numerical Methods for Stochastic Differential Equations 104
A.1 Expansion in the Step Length h 104
A.2 Method for the Estimation of Measurable Quantity 108
B SVD Analysis 112
B.1 Introduction and Background 112
B.2 Practice of Embedding 113
B.3 SVD Test of Determinism: The Formalism 116
C Experimental Setup 118
D Measurement Instruments 120
D.1 Intensity Fluctuation Measurement 120
D.2 Optical Spectrum Measurement 121
Bibliography 126

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