簡併型共振腔(degenerate cavity)是一種特殊的共振腔架構，隨著不同的簡併態，簡併型共振腔中的共振腔長與凹面鏡的曲率半徑會具有不同的特定比例上的關係，在許多研究上也有採用簡併型共振腔的架構。已知簡併腔為激光腔中的圖案操縱提供相對簡單的路徑，並且可用於提高激光系統中的功率提取效率。像差不只對於光學成像系統品質有很大的影響，對於共振腔當中光的軌跡，尤其當離軸光成為主導時雷射共振軌跡主要成份時，雷射輸出行為的對像差的反應必須加以考慮。本論文主要研究就對於具有像差影響的簡併型共振腔進行研究，我們以利用光線追跡法分析平-凹簡併型共振腔，發現較強的球面像差有助於在特定的簡併共振腔中形成不同的簡併幾何模態，這個現象在沒有像差的情況下是無法存在的。從以激發角和像差強度為參數的相空間圖中，我們進一步揭示了多個簡併幾何模式的存在對於劃分了在簡併腔中的雷射光束軌跡分布圖案的相空間分布。

Degenerate cavities are known to provide relative simple routes for pattern manipulation in a laser cavity and can be used for improve the power extraction efficiency in a laser system. The aberration not only affects common optical imaging greatly, but also affects the cavity orbitals that laser light retraces itself when off-axis lights become dominant. In this dissertation, we study the pattern formed by ray trajectories in a spherically aberrated degenerate cavity. It is found that strong spherical aberration helps the formation of different degenerate geometry modes to exist in a particular degenerate cavity, which is not possible without aberration. A phase diagram in terms of excitation angle and strength of aberration further reveals that the existence of the multiple degenerate geometry modes contributes to the phase diagram formation scenario in a degenerate cavity.

中文論文審定書 i
摘要 ii
Abstract iii
目錄 iv
圖目錄 vi
表目錄 xi
第一章、緒論 1
1-1 研究原理 1
1-1-1 光線轉換矩陣 1
1-1-2 簡併型共振腔 2
1-1-3 像差 6
1-1-4 Seidel像差 9
1-1-5 Zernike像差 9
1-2 研究動機 11
1-3 論文架構 12
第二章、像差影響的簡併型共振腔 13
2-1 光線追跡法分析簡併型共振腔 13
2-2 散光像差的簡併型共振腔 16
2-3 彗星像差的簡併型共振腔 24
第三章、球面像差的簡併型共振腔分析 30
3-1 球面像差下從低簡併態的簡併型共振腔產生高簡併態 30
3-2 凹-平面鏡架構產生不同光軌跡的簡併態 54
3-3 球面像差下從高簡併態的簡併型共振腔產生低簡併態 58
第四章、實驗提案討論 65
第五章、結論與未來展望 69
5-1 結論 69
5-2 未來展望 69
參考文獻 70

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