光子晶體負折射效應與平板成像特性之研究

Abstract

近年來，有關於電磁波在光子晶體裡傳播的負折射效應成了快速成長的研究課題。負折射的觀念逐漸吸引了許多的注意。雖然這個課題跟左手介質有關，但是左手介質跟光子晶體的負折射效應仍有相當的差異。許多的文獻試圖為負折射這個課題提供完備的觀點，但是仍有許多關於光子晶體所形成負折射效應的物理機制的議題仍未被解決。 本論文主要在研究光子晶體所形成的負折射效應，因此在本論 文中裡，將會探討電磁波在光子晶體傳播時所形成的負折射效應機制以及討論光子晶體的平板成像特性。為了研究這個主題，必須具備平面波展開法(PWM)以及有限時域差分法(FDTD)這兩種數值模擬方法的基礎，其中平面波展開法是用來計算能帶結構；而有限時域差分法可以計算電磁波的傳播情形。 然而等頻率曲面法也是分析光子晶體負折射效應的一個重要方 法，因為此方法基本上可以預測電磁波經過介質後折射的行進軌跡。在本論文裡，也將展示不受限制的superlensing雖然不會發生在正方晶格光子晶體裡，但是可以被三角晶格光子晶體實現。 除此之外，我們探討了光子晶體的平板成像特性與頻率有強

烈的相關性，而且也探討成像位置與光子晶體平板結構的相關性。例如，當平板厚度增加或是在特定頻率內，頻率上升時，成像的效率皆會降低。 最後，將探討三維光子晶體所造成的負折射效應。如果三維的負折射效應可以被光子晶體完整地實現，則將可能可以實際應用在三維的立體成像技術上。

Recently, there is a rapidly growing search for the negative refraction effect on the electromagnetic wave propagation in the photonic crystals. This concept of negative refraction has attracted gradually a lot of attention. This topic is related to the materials which are called left-handed materials (metamaterials), but, it appears rather differently from the negative refraction effect in the photonic crystals. Many articles are attributed to study the negative refraction in the left-handed materials and the negative refraction effect in the photonic crystals for providing a satisfactory perspective on the topic of negative refraction. However, there are some arguments for the physical mechanism of the negative refraction effect in the photonic crystals unsolved. The main purpose of this work is to study the negative refraction effect in the photonic crystals, therefore, the mechanism of negative refraction effect of electromagnetic waves propagation in the photonic crystals was described and the slab imaging property was discussed in this study. To address this topic, it is always necessary to provide the simulations background with both the plane-wave expansion (PWM) methods, which is used for calculating the band structure, and the finite-difference time-domain (FDTD) methods, which is applied for calculating the propagation of electromagnetic waves in the finite domain. Moreover, it is very important to introduce the equal frequency surface (EFS) method because the trajectory of the refraction can be predicted basically by this useful method. In addition, it was also demonstrated that the triangular lattice photonic crystals can lead to the unrestricted superlensing but the square lattice ones can not. Besides, we studied that the slab imaging properties of the photonic crystals are strongly frequency dependent and the relation between the configuration of the photonic crystal slab and the position of the slab image. For example, the imaging efficiency diminishes when the thickness of the slab increases or the frequency increases in the certain range. Lastly, the realization of negative refraction effect in the three-dimensional photonic crystals was studied and it might give the possibilities of three-dimensional photographing with the help of the refraction effect in the three-dimensional photonic crystals.