本論文探討光波在多層膜中的各向異性 (anisotropic) 傳播特性。我們以晶體光學與光子晶體理論模擬多層介質膜的等效光學參數，並闡釋其物理意義。本論文嘗試結合幾項現有等效理論的優點，分析並比較各等效理論的應用與侷限，並從模擬結果中總結出本論文等效理論的「適用條件」：即單一週期光學厚度，不得超過0.4個入射波長(Nd<0.4λ)，並發現在該條件之下，等效晶體理論具有不錯的預測性。文中引入傳統EMA (effective medium approximation) 作為對照，與本文引入等頻率曲線 (iso-frequency curve) 的等效晶體理論相比較。兩者最大的差異，在於等效介電常數的計算方式。我們從模擬數據中分析造成結果差異的物理成因，同時臚列兩者的優劣之處。
文內前三章，主要介紹現有理論與相關細節的推導，以便在後面章節使用。第四章則為本文等效介質理論的理論構擬，後面章節接續分析結果數據。文章的最後，總結全文，再試著提出未來工作及可能應用。

In this thesis we discuss the anisotropic propagation properties of light waves in multilayer films. The effective optical parameters of the multilayer dielectric films are obtained by using crystal optics and photonic crystal theories, and their physical meanings are explained. We analyze and compare the applicability and limitation of each effective medium theory in the literature, and try to combine their advantages in our newly developed theory. Based on a lot number of numerical simulations, we propose the "applicability condition" of our effective crystal theory as: the optical thickness of a single period must not exceed 0.4 wavelength of the incident light (Nd<0.4λ). Under this condition, our effective crystal theory has good predictability. In this thesis, the traditional EMA (effective medium approximation) is used as the reference, and compared in the simulations with our effective crystal theory based on the iso-frequency curve. The essential difference between these two kinds of theory is the calculation method of the effective dielectric constants. We analyze the physical causes for the difference in the simulation results, and list the advantages and disadvantages of both.
The first three chapters focus on the introduction of existing theories and the related derivation details which will be used later. In the fourth chapter we construct the effective crystal theory in detail, and analyze the simulation results according to this theory. In the last chapter we propose some future works and possible applications.

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