利用波的干涉研究超晶格與碎形圖案

Abstract

利用不同方向的平面波疊加，可以產生各式各樣的美麗圖案，而 本論文主要研究的圖案為超晶格及碎形晶格。平行光通過等距分佈在光罩圓環上的孔洞可形成單一晶格或準晶格圖案，在原本的孔洞旁各增加一個夾相同角度的孔洞，形成的圖形即為超晶格。以圓環上原本的孔洞為中心，將孔洞分布在較小半徑的圓環上，讓雷射光照射其上干涉疊加後所產生的圖案即為二層碎形晶格，依此類推出多層的碎形晶格圖案。本論文將利用數學軟體-Mathcad模擬干涉圖形，並設置雷射光學實驗產生干涉圖案，理論與實驗圖形兩廂吻合。

The thesis is focused on exploring the generation of various superlattice and fractal patterns via the superposition of plane waves with different directions. An experimental scheme that is formed with a collimated light to illuminate a mask with multiple apertures regularly distributed on a ring is employed to generate the crystal and quasicrystal patterns. Furthermore, we add a hole next to every original hole on the ring to experimentally generate the superlattice patterns. It is also found that the second floor of the fractal patterns can be generated with laser light to illuminate the mask with multiple apertures distributed on a ring of smaller radius which the original holes as its center. Finally, the same method is exploited to generate the multi-layered fractal patterns.