廣義倫柏格透鏡之設計

Abstract

此論文應用週期性結構於廣義的倫柏格透鏡，使用的週期性方形金屬貼片屬於一種表面超材料，其特性容易製造而且不會佔據太多體積，可以用來合成此倫柏格透鏡，使其在表面傳導的表面電漿子達到應有的表現。 論文中提出利用單位晶格的色散關係式，進而求出在特定頻率下所對應到的折射率，此為用來作為合成倫柏格透鏡的關鍵因素。 最後提出幾種改進透鏡表現的方式，包括增加離散化的取樣數與改變廣義倫柏格透鏡的交界進而增加特定區域的能量，以及利用完整的二維色散關係式分析在不同位置的單位晶格所造成的折射率變動，這也為改善透鏡效率和表現多了個參考依據。

This thesis, concerns the analysis and applications of periodic structure in the generalized Luneburg lens. The periodic structure in the shape of square patch we use is a kind of metasurface. The metasurface is easy to manufacture and compact that is suitable for the synthesis of Luneburg lens. Thus, it makes the SPPs propagate on the surface and has the performance we expect. We propose using the dispersion diagram of the unit cell and then retrieve the corresponding refractive index in the specific frequency. This is the key point for the synthesis of the gradient lens. Finally, we propose several methods that can improve the performance of the gradient lens including increasing the samples when we discretize the diagram of the refractive index, changing the interface of the generalized Luneburg lens that can enhance the power in the specific location and using the complete 2D dispersion diagram to analyze the variation of the refractive index when the unit cell is in the different location. Theses method construct the basement for the improving the performance and the efficiency of the lens.