臺灣博碩士論文加值系統

本論文運用光學實驗設置產生干涉平面波的二維準晶格圖案（Quasi-crystal）方法，研究氦氖雷射平行光照射不同孔洞數量及不同半徑的週期圓光柵，並照射渦漩相位板不同位置使相位改變產生不同圖案，從不同平面波疊加中可得知分為三種晶格結構，典型對稱晶格結構、準晶格結構和萬花筒結構，並通過渦漩相位板改變圖的相位角大小觀察到有近似貝塞爾函數（Bessel function）圖案的產生，並研究其圖案的差異。
　　本實驗運用MathCAD驗證實驗架構以及圖型大小精確性與圖案的奇異點，觀察到當奇異點為奇數晶格圖，偶數相位角為0或π與無法呈現，其餘的相位晶格圖的圓心部分或周圍有Donut排列圖案的地方接可觀察到渦漩相位的存在，實驗結果均證實與預測結果和電腦模擬圖案吻合。

In this paper, optical experiments are used to set up a 2D quasicrystal pattern method for generating interfering plane waves. He-Ne laser parallel light illuminates periodic circular gratings with different number of holes and different radii, and irradiates vortex phase plates at different positions the phase change produces different patterns. From the superposition of different plane waves, we can know that it is divided into three crystal structures, crystal structure, quasicrystal structure and kaleidoscope structure, and it is observed that the phase angle of the diagram is changed by the vortex phase plate. There are similar Bessel function patterns generation, and study the pattern difference.
In this experiment, MathCAD was used to verify the experimental structure and the accuracy of the pattern size and the singular points of the pattern. It was observed that when the singular point is an odd crystal diagram, the even phase angle is 0 or π and it cannot be presented. The center of the remaining phase crystal diagram Donut place around or access array pattern can be observed the presence of vortex phase results confirmed the results consistent with the predicted pattern and computer simulations.

摘要 I
ABSTRACT II
目錄 III
圖目錄 V
第一章緒論 1
1-1 研究動機 1
1-2 本文結構 4
參考文獻 5
第二章 二維晶格與準晶格圖騰 6
2-1 礦物中的圖騰 6
2-2 萬花筒圖騰 8
2-3 TILING 圖樣 10
2-4伊斯蘭的圖騰與分子結構 11
2-5克拉得尼圖案(CHLADNI PATTERNS) 13
參考文獻 14
第三章 理論模型產生不同相位結構晶格和準晶格結構光束 15
3-1 繞射與非繞射(DIFFRACTING AND NON-DIFFRACTION) 15
3-2 奇異點(SINGULARITY) 17
3-3 理論模型 19
3-4 結論 22
參考文獻 23
第四章 利用螺旋相位片產生不同相位結構晶格和準晶格結構光束 25
4-1 實驗架構介紹 25
4-2 小型圓半徑光柵實驗結果與討論 27
4-3 中型圓半徑光柵模擬與實驗比較圖 42
4-4 實驗分析與討論 56
第五章總結與未來展望 58
5-1 總結 58
5-2 未來展望 59

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