中文摘要

本研究論文是用高斯光束的行進傳輸方式，針對由兩個曲率半徑相同的球面鏡所組成的(Herriott-type multi-pass cell)共振腔，所做的理論分析。由於此非共平面共振腔是一種非正交且非近軸的共振腔，無法用ABCD矩陣的方法來分析，嚴格的分析方法應該考慮高斯光束的行進傳輸方式。今由考慮到高斯光束由於斜角入射的像散性與球面像差以及光束每經一次鏡面反射後須做一個座標變換。當光束在共振腔中走完一整圈時，必須滿足自我協調的條件之下，得到此共振腔的精確解。於其中可發現球面像差的修正是一個很重要的一項，因為如果沒有考慮到此項修正，那麼共振腔是無法得到一個穩定的解。

再入射環形共振腔對於腔長是很敏感的，特別的是當共平面與非共平面的結構具有相同的輸出光點時，因此，精確的分析此共振腔內雷射光束的傳輸極為重要。當考慮到光束經過一次鏡子的反射時需做一次座標變換，由此可發現非共平面立體8字形環形共振腔是可以用類似正交共振腔的做法來分析。以簡單像散性高斯光束的形式在共振腔內行進，可用來分析此非共平面立體8字形環形共振腔，由此並可獲得一個精確的解析解。對於一般情況再入射環形共振腔，則可由設計一個以一般像散性高斯光束在共振腔內行進的程式，來分析此問題。經鏡子反射所產生的相位移動亦使用較為廣泛的形式，由此可得到兩項主要的差別，不同於用ABCD矩陣的做法。其一為腔內光點的形狀一般而言是橢圓形狀，而不一定是圓形，其二為共振腔會產生第二穩定區，其帶寬相較於第一穩定區為窄。

Abstract


In this dissertation a rigorous analysis is performed on the reentrant non-planar ring laser cavity constructed by the Herriott-type multi-pass cell. Since the non-planar ring cavity is a non-orthogonal cavity, so the ABCD matrix method used to analyze the beam propagation is not valid. A rigorous method using Gaussian beam propagation is needed. The beam rotation, astigmatism, and spherical aberration are considered to obtain a self-consistent solution of the Gaussian beam. It turns out that spherical aberration is a very important issue for this non-planar resonator. Without taking into account the spherical aberration, a stable resonator would be difficult to realize. By using a self-consistent Gaussian beam propagation method, the characteristic of laser beam was analyzed and compared with that of the ABCD approximation method.

The reentrant ring cavity is very sensitive to cavity length, especially when the planar and non-planar configurations have the same output beams; therefore, it is very important to consider a rigorous method using Gaussian beam propagation. By considering the coordinate transformation of the beam after mirror reflection, a non-planar figure-8 ring cavity can be treated as an orthogonal cavity except for an exchange of tangential and Sagittal planes after each reflection. A simple astigmatic Gaussian beam approach is used to analyze the non-planar figure-8 ring cavity, and an analytic solution is obtained. For the general case of the multi-pass non-planar ring cavity, a general astigmatic Gaussian beam approach is used to treat the problem. The general form of mirror phase shift is used, and two important differences compared to the ABCD method were found. Firstly, the spot size is always elliptical while the spot size is circular using the ABCD approximation. Secondly, a second stable region is found in the cavity, the width of the second stable region is smaller than the first stable regi

目錄

中文摘要 Ι

英文摘要 II

目錄 III

圖目錄 V

表目錄 IX

第一章 緒論 1
1.1 前言 1
1.2 研究動機 3
1.3 本研究論文的貢獻 5
1.4 本研究論文的架構 7

第二章 環形共振腔的介紹 8
2.1 文獻回顧 8
2.2 環形共振腔的優點 12
2.3 環形共振腔的應用 14
2.4 環形共振腔的設計 16

第三章 再入射環形共振腔的腔長公式與近似解 19
3.1 再入射環形共振腔的腔長公式 19
3.2 再入射環形共振腔的近似解 26
3.3 再入射環形共振腔近似解的穩定性分析 33

第四章 立體8字形再入射環形共振腔的分析 39
4.1 非共平面雷射光束的轉動 39
4.2 像散性以及球面像差 48
4.3 格林(J. M. Greene)殘數方法 50
4.4 立體8字形再入射環形共振腔的解析解 56
4.5 立體8字形再入射環形共振腔的穩定度分析 63
4.6 增益介質側移量趨近於零的情況 69

第五章 一般情況的再入射環形共振腔的分析 71
5.1 再入射環形共振腔的分析觀點 71
5.2 再入射環形共振腔的一般情形 72

第六章 再入射環形共振腔的實驗與分析 85
6.1 再入射環形共振腔四能階紅外光雷射 85
6.2 再入射環形共振腔綠光雷射 88
6.3 再入射環形共振腔的腔長驗證 91
6.4 再入射環形共振腔準三能階紅外光雷射 94

第七章 結論 95

附錄A 再入射環形共振腔雷射光束轉動角度的證明 97
附錄B 模態腔長的證明
100
附錄C 共振腔的模擬程式 103

參考文獻 109
中英文對照表 115

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