由於半導體幫浦的固態雷射同時具有半導體雷射體積小、輕巧的特性和固態雷射高峰值功率以及高品質的輸出模態優點，近年來此種雷射廣泛地應用於電子、通信和醫療各業。本研究的目的是研發出一兼具小型與實用的環形共振腔雷射系統，目標是利用兩片球面鏡及一個增益介質達到多次再入射的雷射系統，打破傳統環型共振腔需至少使用三片面鏡的之設計。我們採用兩片球面鏡實現多次再入射雷射的技術，其成本低廉、結構簡單、且光學元件少、光學元件校準容易，較傳統環型共振腔更符合簡單化、輕巧的時代潮流。此環型共振腔可用於有效產生單縱模的近紅外光及藍、綠光雷射，並可應用於航空、微量檢測、研製皮秒(picosecond)量級的小型固態鎖模雷射。

我們的研究從理論和實驗上來討論及驗證多次再入射雷射的可行性，並由一些基本雷射原理，推導出腔長與輸出點數、腔內迴圈數及增益介質中心與光軸的距離的關係式，並得到一個精確解析解，同時實驗結果與理論模擬相當吻合。本論文並對多次再入射之精確解析解與近軸近似做比較。針對不同的多次之再入射共振腔，分析光束路徑的端視圖、側視圖及俯視圖，同時分析空腔與加入增益介質的雷射共振腔穩定性，更以實驗加以驗證其準確性。本論文亦比較TEM01 mode 及雙鏡式立體八字形的共振腔設計，並分析此兩者的差異。

Diode laser pumped solid state laser is compact, and can generate high peak power laser with good output mode. It has been applied extensively in electronics, communication, and medical treatment in recent years. The purpose of this study is to develop a compact and practical ring laser system. The multi-reentrant ring laser system developed in this work composes of two spherical mirrors and a gain medium where the conventional ring laser systems have at least three mirrors to construct the laser cavity. The laser system is more compact and simple than conventional ring laser systems. It can be used for producing single frequency green and blue lasers. The laser system can also be applied in aviation, trace detection as well as compact picosecond mode-locked laser.

We not only prove that the multi-reentrant laser system is feasible theoretically and experimentally, but also use the fundamental laser theory to find the relation among cavity length, number of points, number of circulation, and the distance between center of gain medium and optical axis. The exact solution we obtained is experimentally verified with good agreement. A comparison between exact solution and paraxial approximation is also performed. The beam paths observing from the top, side, and end view are analyzed for various multi-reentrant laser cavities. The stability of the cavity is numerically analyzed and experimentally verified with good agreement, too. Finally, the differences in cavity configuration between TEM01 mode and the figure-8 mode are compared in this thesis.

中文摘要 Ι

英文摘要 II

目錄 III

圖目錄 IV

表目錄 VII

第一章 緒論 1

第二章 多次再入射之雙鏡式環形共振腔 4
2.1 文獻回顧 4
2.2 多次再入射之雙鏡式環形共振腔的應用 7

第三章 多次再入射之精確解析解 10
3.1 近軸近似法 10
3.2 多次再入射之精確解析解 16
3.3 近軸近似法與多次再入射之精確解析解的比較 34
3.4 比較TEM01 與立體八字形的差異 38

第四章 共振腔的設計與穩定性分析 40
4.1 共振腔的設計 40
4.2 雷射共振腔穩定性分析-空腔 44
4.3 雷射共振腔穩定性分析-加入增益介質 52

第五章 結論 58

參考文獻 60

附錄A 63
附錄B 66
附錄C 67
附錄D 共振腔的穩定性模擬(for Fortran) 69
中英文對照表 73

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