傳統透鏡無法突破繞射極限，但使用超材料製作的超級透鏡卻可以打破繞射極限的障礙，使得”次波長成像”不再是夢想。超級透鏡雖然能藉著重建消逝波的資訊而做到次波長成像，但此種成像只能在近場實現，因此其實用性有限。在突破繞射極限之後，科學家設計出一些新元件，要使消逝波成份轉換成傳導波，以便能於遠場成像，方便其他傳統光學元件做進一步處理。本文所討論的雙曲透鏡，便是以此為目標所設計的結構。雙曲透鏡(hyperlens)的基本設計，是利用兩種異號介電係數的材質(多為金屬與介電質)，週期層狀排列而成的圓柱形結構，在H-polarization的電磁波下，具有如透鏡放大成像的特性。本文係用傳遞矩陣法計算點光源經由雙曲透鏡的成像，同時輔以光線追跡方式，討論透鏡厚度改變下成像行為的變化。利用單光源成像集中度標準差，量化雙曲透鏡成像之side-lobes光場帶來的影響，並研究side-lobes對成像集中度以及各情況下雙光源最小可分辨距離的影響根據數值模擬的結果，我們發現：雙曲透鏡成像相對於厚度變化，具有震盪現象。這一震盪現像顛覆了我們通常對於雙曲透鏡厚度越大越好的印象。此震盪現象對我們在製作雙曲透鏡時所考慮的理想厚度之研究提供了重要資訊。A conventional optical lens cannot be used to break the diffraction limit, but an appropriately designed metamaterial superlens can do the job, and this fact leads to the realization of subwavelength imaging. Although a superlens can indeed form subwavelength image through reconstructing the information carried by the evanescent waves of the source, the image can only be found in the near field zone, which restricts the practicality of this component. After the idea of superlens has been proposed, scientists further developed other novel devices in order to resolve the disadvantage of near field imaging, hoping to transfer evanescent waves to propagating waves and reconstruct image in the far field zone, which will be more convenient for further manipulation by conventional optical devices. The hyperlens structure discussed in this thesis is a kind of design for fulfilling this purpose.The basic structure of hyperlens consists of two kinds of materials having permittivities of different signs (usually they are metals and dielectrics), arranging alternatively as cylindrical multilayer structure. For the H-polarized waves, this structure can form a magnified image outside the hyperlens in the far field zone for a subwavelength object close to the inner surface of this device. We calculate the light fields by using the transfer matrix method. Besides, we have developed a ray-tracing technique for predicting the location of the images according the geometric optics. Based on the results obtained by these two methods, we further discuss the change of imaging characteristics under the influence of changing the layer thickness. By defining the effective width of the single source image via calculating the standard deviation of the field strength distribution, we can quantify the influence of the side-lobes of the image field. We also explore the influence of the side-lobes to the two images of the two sources and the least-distinguishable distance between them.According to our simulation results, oscillating behaviors are observed for imaging characteristics of the hyperlens when we vary the thickness of the layers. This oscillating behavior conflicts to our expectation that a thicker hyperlens is also a better one. This phenomenon provides us useful and important information for designing an ideal hyperlens.
