以體積布拉格光柵作為雷射共振腔反射鏡之橫模行為研究

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研究生：	廖啟村 Chi-Chun Liao
論文名稱：	以體積布拉格光柵作為雷射共振腔反射鏡之橫模行為研究 Study of the transverse mode of lasers using volume Bragg grating as a cavity mirror
指導教授：	鍾德元 Te-Yuan Chung
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 光電科學與工程學系 Department of Optics and Photonics
畢業學年度：	100
語文別：	中文
論文頁數：	100
中文關鍵詞：	橫模、體積布拉格光柵、共振腔反射鏡
外文關鍵詞：	transverse mode, cavity mirror, volume Bragg grating
相關次數：	點閱：11 下載：0
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將體積布拉格光柵用於雷射系統中，可以有效窄化雷射的輸出光譜，以及改善雷射輸出的空間模態M2，而體積布拉格光柵的角度選擇性與一般的共振腔反射鏡有極大的差別。本論文以數值模擬的方式，計算以體積布拉格光柵為共振腔反射鏡的雷射系統輸出橫模。並由數值模擬結果，預測以體積布拉格光柵為共振腔反射鏡的雷射系統將有機會輸出環形模態，並成功架設固態雷射系統，驗證環形模態的存在。
且由模擬結果發現，在以體積布拉格光柵為共振腔反射鏡的雷射系統中，若雷射波長小於體積布拉格光柵的繞射中心波長，系統將會發生不同於傳統的模態輸出。

Volume Bragg grating for the laser systems can be effectively narrowing the laser output spectrum, and to improve the spatial beam quality M2 of the laser output. There has the great difference in the angular selectivity between the volume Bragg grating and the general cavity mirror. In this thesis, uses the numerical simulation to calculate the output transverse mode of lasers using volume Bragg grating as a cavity mirror. By the numerical simulation results, predicts that lasers using volume Bragg grating as a cavity mirror, will have the opportunity to output the ring-shaped mode, and successfully set up a solid-state laser system, verify the existence of the ring-shaped mode.
From the simulation results, lasers using volume Bragg grating as a cavity mirror, when the laser wavelength is less than the diffraction central wavelength of volume Bragg grating, the system will output the mode that is different from the traditional Gaussian mode.

中文摘要 .................................................................................................. i
Abstract .................................................................................................. ii
致謝 ....................................................................................................... iii
目錄 ......................................................................................................... v
圖目錄 ................................................................................................... vii
表目錄 .................................................................................................... xi
第一章 緒論 ........................................................................................... 1
1 前言 ............................................................................................................ 1
2 研究動機 .................................................................................................... 3
第二章 基本原理 ................................................................................... 4
1 雷射基本原理 ............................................................................................ 4
1.1 增益介質 ......................................................................................... 4
1.2 雷射輸出與有效反射率 .................................................................. 7
2 體積布拉格光柵 (volume Bragg grating, VBG) ...................................... 12
2.1 VBG的構造與工作原理 ................................................................ 12
2.2 VBG的材料與製作原理 ................................................................ 14
2.3 VBG的光學特性 ........................................................................... 16
3 光的傳播原理 .......................................................................................... 18
3.1 傅立葉轉換 ................................................................................... 18
3.2 平面光波的波向量與空間頻率之關係 ......................................... 19
3.3 光的傳遞 ....................................................................................... 20
4 雷射之橫向模態特性 ............................................................................... 22
4.1 雷射橫模簡介 ................................................................................ 22
4.2共振腔對橫模的影響 ..................................................................... 26
第三章 模擬原理與分析 ...................................................................... 30
1 計算VBG之繞射光譜與其原理 ............................................................. 30
1.1 光在分層介質中的傳播推導......................................................... 30
1.2 週期性分層介質 ............................................................................ 37
1.3 計算VBG的繞射光譜 .................................................................. 39
2 以線性代數方法求解雷射共振腔之橫向eigenmode .............................. 42
2.1 一般共振腔模擬 ............................................................................ 42
2.2 以VBG為反射鏡之線型共振腔模擬 ........................................... 48
2.3 高度聚焦於VBG表面之短共振腔模擬 ....................................... 53
3 不同波長對VBG線型共振腔橫模輸出的影響 ...................................... 62
第四章 實驗與結果討論 ...................................................................... 66
1 以VBG為反射鏡之線形共振腔 ............................................................. 66
1.1 實驗架設 ....................................................................................... 66
1.2 實驗結果 ....................................................................................... 67
2 高度聚焦於VBG表面之短共振腔實驗 ................................................. 69
2.1 實驗架設 ....................................................................................... 69
2.2 雷射橫模特性 ................................................................................ 70
2.3 雷射輸出功率特性 ........................................................................ 73
2.4 輸出模態分布不均勻之討論......................................................... 75
第五章 結論 ......................................................................................... 78
1 結論 .......................................................................................................... 78
2 未來展望 .................................................................................................. 79
附錄一 V型共振腔模擬 ...................................................................... 80
附錄二 加入增益介質的響應與二維包含極化模擬 ........................... 81
參考文獻 ............................................................................................... 82
附件 ....................................................................................................... 85

                                

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