傳統光學透鏡的解析度會受到繞射極限的影響，使得近場光源無法在遠場處成像。本論文所探討的雙曲透鏡，則是要讓近場光源可在遠場處成像並有更好的解析度。根據等效介質的觀念，可利用週期性排列的金屬與介電質來實現雙曲透鏡的模型。在數值模擬時，運用傳遞矩陣的方式來做計算，可以完整的算出每一介質中的散射係數，而得到各處的場值。我們藉由改變不同的模型條件，探討其對雙曲透鏡的特性之影響，以找出最好的解析度。相信在未來，可以利用這篇論文中的方法，找到更適當的實際物質，以實現具有更佳解析度的雙曲透鏡。

Resolution of conventional optics is generally constrained by the diffraction limit, which prevents imaging of near field light source in the far-field zone. In this thesis, we study the imaging properties of hyperlens, which can focus the light originated from near field sources and form images in the far-field zone with high resolution. According to the concept of effective medium, a hyperlens can be realized by using periodic arrangement of metallic and dielectric material layers. The properties of the hyperlens are studied numerically using transfer matrix method (TMM). The scattering coefficients in every layer can be calculated and the electromagnetic fields there can be derived. The optimized material and geometric parameters for best resolution can be found by varying these parameters and observing their influences on the imaging characteristics. In the future, we believe, that a practical hyperlens having better resolution can be constructed by finding proper materials and geometric parameters based on the method provided by this thesis.

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