轉換光學可視為一種有效的計算方法設計轉換介質，並且理想地控制著電磁波的傳播行為。藉此，我們分別設計了具有圓形截面與矩形截面的直線型波導，以及矩形截面的彎曲型波導。透過適當的轉換函數，我們不僅可以使電磁波在傳遞時，電場於邊界上的強度降為零，更可以使能量大幅地集中於波導的截面中心並且降低損耗。
　　然而，大部轉換光學理論所設計的光學元件，其所需的材料往往具有異向性以及非均質性。倘若要使用一般自然界的材料進行實際製作，具有相當大的難度。在此，我們化簡原本矩形截面之直線型波導的材料參數，並且根據等效介質理論，進一步地利用三種不同的均質材料，以層狀堆疊的結構具體實現了所設計的光學波導。最後，我們再進行數值模擬分析並說明其可行性。
　　另外，我們也設計與分析了各種轉換光學所衍生的相關元件，例如：光分波器、光干涉器以及遠場區與近場區聚焦的平面透鏡。由於平坦等頻線的聲子晶體將使聲波傳遞時，具有準直的特性。所以，我們進一步透過漸層式的聲子晶體，實現了聲學的遠場區與近場區聚焦之平面透鏡。
　　轉換光學是一種嶄新的概念，設計各種新式的光學元件。我們也藉此設計各式的光學波導，使電磁波得以平順地傳播而不產生大量的損耗以及訊號的扭曲。

　　Transformation optics is regarded as an efficient method to control electromagnetic fields through the transformation medium. Accordingly, we design straight waveguide with both circular and rectangular cross sections, and bending waveguide with rectangular section as well. Not only can the electric field be reduced to zero at boundaries but the energy can be concentrated on the center of cross section with less consumption by proper function of coordinate transformation.
　　Unfortunately, most of optical devices designed by transformation optics require anisotropic and inhomogeneous materials. Thus, the realization would be execessively difficult if common materials in nature are adopted. Nevertheless, we simplify the original transformation media of above straight waveguide with rectangular cross section and realize the waveguide concretely by using three kinds of isotropic material in an alternating layered structure based on the effective medium theory. Finally, we perform numerical simulations to illustrate its functionality.
　　On the other hand, we also design and analyze other relative optical devices such as beam splitter, optical interferometer and flat lens for far-zone and near-zone focusing. Moreover, we use graded phononic crystals to accomplish acoustic flat lens for far-zone and near-zone focusing at particular frequency since acoustic wave can transmit in a non-diffracted way in virtue of the flat-shaped dispersion surface.
　　Transformation optics is a new concept used to design a variety of novel optical devices. It is also a mathematical method that we utilize to design different optical waveguides where the electromagnetic wave propagates smoothly without large energy consumption and destruction of signal.

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