傳統光學透鏡受繞射極限的影響，使解析度無法小於二分之一的波長。由於顯微技術在生物、醫學等領域皆有足夠的重要性，因此，許多人試圖找出突破繞射極限的方法，而本文所探討的雙曲透鏡即為可突破此一限制的結構。 根據等效介質的概念，在波長遠大於結構的尺寸時，由兩種不同介電常數的介質排列而成的結構可等效為一個非均向的均勻介質，而雙曲透鏡即根據此種概念設計，將正介電常數介質與負介電常數介質（通常為金屬）週期排列成同心圓柱結構，適當地選擇工作頻率與結構的金屬與介電質的厚度比，可設計出具有相反符號的徑向與切向介電常數的結構。此種結構不僅能突破繞射極限還可在遠場成像。 本論文研究雙曲透鏡的特性。利用COMSOL Multiphysics模擬軟體，探討不同結構參數對雙曲透鏡解析度之影響，探討其可傳播的最遠距離。此外，我們從雙曲透鏡遠場傳播所需要滿足的條件，探討當波無法傳遞到遠場時，將此種結構視為共振腔的可能性。 ;Classical optics is restricted by the diffraction limit, so the resolution can’t distinguish the fine details of scale less than half of the wavelength. Since microscopy plays an important role in the biological and medical research fields, many people tried to find ways to overcome the restrictions of diffraction limit. Hyperlens is the main structure designed for breaking these restrictions. According to the conception of Effective Medium Theory, when the wavelength is much larger than the size of the structure, structure consists of two different materials aligned periodically behaves like an anisotropic-homogeneous medium. Hyperlens is designed with this concept. Hyperlens consists of alternating concentric layers of media which have opposite sign of permittivity along the radial and azimuth direction. This structure as a lens can overcome the diffraction limit and imaging at the far field zone. In this thesis we study the optical properties of hyperlens numerically. All the simulations are implemented with the COMSOL Multiphysics software. We study the influences of various parameters on the resolution of images. We also explored the possibility of using this structure as an optical cavity if the condition for far-field subwavelength imaging cannot be satisfied.
