雙光源光子晶體平板成像特性之研究

光子晶體就是週期性排列的介電質材料。從概念的提出開始，它就經歷了許多研究方向與重點的演變與調整；如今它已成為應用潛力非常廣泛的研究領域。本文藉理論分析與數值模擬，探討一個點光源和兩個點光源之光場透過有限寬度的光子晶體平板的次波長成像特性；所採用的數值模擬方法為平面波展開法與多重散射法。首先利用平面波展開法計算二維光子晶體的能帶結構，以找出光線在光子晶體平板中的傳導方向。其次利用多重散射法計算二維光子晶體平板在點光源照射下的光場分布。此平板是由介電質圓柱依正方晶格週期排列所構成。在一個點光源的情況下，探討光源平移的成像穩定性；而在兩個點光源的情況中，探討欲形成可分辨之像時，兩點光源的最小可允許距離，並探討平移此兩個點光源的成像穩定性。

關鍵字

光子晶體；次波長成像；平面波展開法；多重散射法

並列摘要

Photonic crystal is by definition periodically arranged dielectric materials. Since the emerging of the idea, the main research focus related to it has been changed for several times and the research methods have been revolutionized as well. Now it becomes a convincing research area having widespread applications. In this thesis the subwavelength imaging of finite photonic crystal slab for focusing the light either from one point source or two point sources are explored. The numerical calculations are based on the plane wave expansion method and multiple-scattering method. We first use the plane wave expansion method to calculate the band structure of the photonic crystal consisting of a square-lattice array of dielectric cylinders. The band structure provides the information to derive the propagation direction of the transmitted light. We then calculate the field distribution pattern when the photonic crystal slab of finite size is present, under the illumination of one point source or two point sources. In the one source case we study the imaging stabilility under the source displacement, whereas in the two-source case we first find the smallest interval between which the two sources can form distinguishable images. We then study the imaging stability of the two-source system under source displacement.