為研究電磁波在多層結構內之傳播特性，經常將其多層結構根據等效介質理論(Effective Medium Theory) 以近似後的均勻介質表示。多層結構可以被設計成具有傳統材料沒有的電磁特性，例如光子晶體的頻帶隙 (bandgaps)，以及雙曲超材料 (hyperbolic metamaterials) 的非正定介電常數 (indefinite permittivity) 等。人工材料提供了更廣的想像空間，及提高實現理論的可行性，等效介質理論則是一種能簡化描述多層週期結構的電磁特性之方法。以等效介質近似多層週期結構須注意有關結構尺寸與入射波長之間比例的條件，當條件有關的參數改變時，近似的結果會有所影響，影響結果為本論文中模擬之重點，結果說明各參數影響不一，且若能依不同介質或情況對參數做調整可以提高等效介質近似多層週期結構的可信度。

In order to study the propagation characteristics of electromagnetic waves in multilayer period structure, we usually approximate the multilayer period structure as an effective homogeneous medium by applying to it the Effective Medium Theory. Multilayer period structures as artificial materials can be designed to acquire the electromagnetic properties that do not appear in natural media, such like the bandgaps of photonic crystals and the indefinite permittivities of hyperbolic metamaterials. The artificial materials inspire human imagination and thus improve the feasibility of the theory. The effective medium theory is a convenient way to describe the propagation characteristics of the multilayer period structure. The ratio between the size of the constituents in the structure and the wavelength of the source wave must be properly chosen when we approximate the multilayer period structure as a homogeneous medium. If the parameters about the ratios are changed, the results of the approximation would be affected, and this fact is the main theme of this thesis. In this thesis we study for various cases all the parameters which influence the accuracy of effective medium theory and provide suggestions for reducing the difference between the effective medium and the real structure.

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