一維光子晶體(1-D photonic crystal)非均向性介質是金屬與介電質在某個方向上的週期排列。藉著調整金屬和介電質層的厚度比以及選用適當的介質參數，便可操縱光線的傳播行為。當構成此平板的單層厚度遠小於入射光波長時，一維光子晶體可近似成一塊均勻、介質參數為各向異性的單層平板；這便是長波極限下的近似。 論文第一章為光子晶體的發展歷史。第二章包括了相關的電磁概念如傳遞矩陣法、色散關係等。在第三章中分別利用一維光子晶體作為全反射型偏振光分波器、雙折射型偏振光分波器、次波長聚焦平板透鏡的實例，去探討當波長/厚度比改變時，其相關特性改變的行為。經由第四章對資料的分析，得到了第五章的結論為：1.隨著波長/厚度比的增加，平板的特性會趨向均勻的等效單層平板；但表現出的變化行為並不相同。2.若把10%的誤差當作可容忍的，則波長/厚度比須大於18方可稱為長波極限。A 1-D photonic-crystal anisotropic medium is a structure consisting of an alternating arrangement of metallic and dielectric layers. By adjusting the thickness ratio of the two kinds of layers and choosing proper medium parameters, the propagating behavior of rays can be controlled. When the thickness of the medium layers is much smaller than the wavelength of incident light, the 1-D photonic crystal can be treated as a uniform anisotropic slab. Such kind of condition is defined as the long-wavelength limit. The first chapter is a brief review of the development of photonic crystals. We then introduce important electromagnetic concepts in the second chapter, like transfer matrix, dispersion relation…, etc. In the third chapter, examples of 1-D photonic-crystal anisotropic media including the polarizing beam splitters (PBS) based on total reflection and birefringence and a subwavelength imaging slab lens are investigated, and the modifications on their optical characteristics under the influence of changing the wavelength/thickness ratio are discussed. The conclusion of this thesis is obtained through analyzing the data in chapter four. They are: 1. With the increment of wavelength/thickness ratio, some special characteristics of the 1-D photonic crystal will approach that of the uniform anisotropic slab, but the changing tendencies of these optical properties are not the same for all cases. 2. If we neglect a discrepancy smaller than 10%, only when the wavelength/thickness ratio is larger than 18 can we define it as the long-wavelength limit.
