本論文將研究渦流光束在大氣中傳播受大氣紊流所造成的能量散失，去做分析探討，考慮Kolmogorov修正後的modified atmospheric model紊流譜分別以高斯光束以及具有六個相位差的六個點之渦流光束去做模擬，會發現長距離傳的下會以渦流光束的能量維持的比較好。
之後我們針對這理論去做實驗，利用空間相位調變器去模擬大氣紊流的型態，模擬在長距離傳遞的下高斯光束及渦流光束遇到大氣紊流的光斑變化，進而去分析其中的能量散失現象，不過由於是利用空間光調變器去模擬大氣，其中調變的能力有限，要達到模擬的條件必須要另外針對非線性的現象討論。
針對高斯光束以及渦流光束，討論非線性的現象，使用空間相位調制器去對影像做回授的操作，產生非線性效應，進而去分析雷射光斑的變化，這個系統可以對應到非局域非線性的系統。
因此未來我們將要將以空間相位調制器所模擬出來的大氣紊流以高斯及渦流光束在長距離傳遞系統與影像反饋空間非線性現象組合在同一系統，進而對於理論去做驗證與討論。

This work studies the propagation of vortex beam in atmospheric turbulence and nonlinear thermal blooming by simulation using numerical model and simulated optical system experimentally. Both in computation and optical system simulator, a modified atmospheric model was used to express and construct a phase mask for the atmospheric turbulence. We numerically simulated the propagation of both fundamental gaussian beam and vortex beam made of six phase-modulated beamlets in turbulence of different coherence length in turbulence and nonlinear power and found vortex beamlet is more resistant to turbulence effect and the thermal blooming. By using a SLM based optical simulator, we also confirm the vortex beams were better in transmitting power under atmospheric turbulence even though the thermal blooming effect was not considered due to the capability of our facility.
To understand the thermal blooming effect using an optical simulator system, we considered to use image feedback to SLM to perform nonlinearity, which can be tuned by additional manipulation on the images, to explore power-tunable, local and nonlocal nonlinearity of both self-focusing and self-defocusing types. Under the nonlocal self-focusing nonlinearity, we found stable wave packet formations having a spot size smaller than the propagating Gaussian similar ( but not exact) to spatial solitons under a certain optical power threshold. For higher power, turbulent optical patterns were observed having a wide spatial frequency distribution. Moreover, vortex soliton clusters are also observed when the injecting laser beam is first phase modulated to form optical vortex by an additional spiral phase plate.
This work predicted that optical vortex a better power carrier than a fundamental Gaussian beam under strong atmospheric turbulence and thermal blooming effect. Moreover, the study of image feedback-SLM-based nonlinear optical simulator provide an efficient route to the extensive study of manipulable nonlinear optical effect.

中文審定書 i
英文審定書 ii
摘要 iii
Abstract iv
目錄 v
圖次 vii
表次 ix
第一章 緒論 1
1-1 雷射在傳遞過程中的大氣紊流 1
1-1-1 光學漩渦簡介(Optical vortex) 1
1-1-2 空間光調變器的原理功能以及用途 2
1-1-3 螺旋相位板(Spiral Phase Plate)- 4
1-1-4 熱暈(thermal blooming)現象 4
1-1-5 自適應光學(Adaptive optics) 5
1-2 研究動機 7
1-3 論文架構 8
第二章 大氣紊流模型理論與實驗 9
2-1 設計大氣紊流模型 9
2-1-1 統計大氣結構參數 9
2-1-2 大氣傳播非線性方程式歸一化與縮放 11
2-2 程式模擬 14
2-2-1 渦流光束的產生 14
2-2-2 大氣紊流的產生 14
2-2-3 非線性熱暈傳播效應 15
2-2-4 渦流光束於大氣紊流下之非線性傳播模擬系統 17
2-3 大氣紊流實驗 20
2-3-1 實驗架構 20
2-3-2 實驗操作 22
2-3-3 大氣紊流模擬圖形 23
2-3-4 實驗結果 24
第三章 影像反饋的非線性光學 26
3-1 反饋之空間相位調制器中的非線性光學模擬 26
3-2 反饋之空間相位調制器中的非線性光學實驗 29
3-2-1 測試SLM的自聚散焦特性 29
3-2-2 高斯光束的回授非線性系統 30
3-2-3 使用渦流光束量測非線性回授系統 32
第四章 結論與未來展望 34
4-1 結論 34
4-2 未來展望 34
參考文獻 35

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