自西元2000年以來，平板透鏡被廣泛研究。由特殊介質構成的平板透鏡能匯聚消散波，並達到次波長聚焦，因而可有效提升成像效率。到目前為止的平板透鏡研究偏重在提升成像效率，以及增加像距與物距的距離，對於像距與物距之關係的探討則較少涉及。本論文研究以週期排列的金屬層與介電質層所構成的平板透鏡的成像特性；其中金屬層設定為銀，介電質層則設定為四氮化三矽。本論文除了探討改變金屬層與介電質層對成像寬度的影響外，也探討物距與像距的關係。利用傳遞矩陣法，可計算出在週期結構中電磁波的傳播模態與頻帶結構，以及在給定入射波之下於各層介質中的電磁場。我們首先根據頻帶結構所得到的等頻曲線，對來自光源的光線是否聚焦做初步的預測，然後再與實際的數值模擬結果做比較。光源波長選定為363.6奈米，光源型式為正向入射之高斯光束，半高寬為1/10波長。平板透鏡為五層銀與四層四氮化三矽所構成。在一個週期中，一層銀與一層四氮化三矽總厚度為80奈米，兩種材料厚度比為1:9~9:1。光源位置與成像位置都在一倍波長內。模擬發現，在有次波長聚焦的組合中，有以下兩個特性。1. 移動光源位置，有次波長成像的最遠距離與光源等量平移。2. 若等量平移光源位置與成像截面位置，則經過歸一化後的成像圖形不變。本論文結果提供了將來以實驗驗證平板透鏡成像行為的理論依據。

The research of slab lens attracts tremendous attention since 2000. Specially designed slab lens made of appropriate materials can gather evanescent waves and focus light to form subwavelength images, thus the imaging efficiency can be improved substantially. Up to now, most researches concerning slab lens are about improving the imaging efficiency and increasing the object-image distance, and the discussions about the relations between the object distance and image distance are rare or lacking. In this thesis, we study the imaging properties of slab lens consisting of periodically arranged metal and dielectric layers. The metal and dielectric are chosen as Ag and Si3N4, respectively. We explore the influences of varying the thickness ratio between the metal layer and dielectric layer as well as the relations between the object distance and image distance. Using transfer matrix method (TMM), the band structures and the field patterns of the propagating modes can be obtained, and the electromagnetic fields in every layer under the illumination of incident light can be calculated. We first predict the propagating direction of the energy flow according to the constant frequency curve of the band structure, and then we compare the prediction with the numerical result of the simulation for electromagnetic waves. The wavelength of the light source is chosen as 363.6 nm, and the source pattern is a normally incident Gaussian beam, having a full width at half maximum (FWHM) of 1/10 wavelengths. The slab lens consists of 5 silver layers and 4 Si3N4 layers. In one period, the total thickness of one sliver layer and one Si3N4 layer is 80nm, with thickness ratio from 1:9 to 9:1. The source is located from the input edge of the slab lens at a distance smaller than one wavelength. Our numerical simulations reveal that: 1. continually varying the object distance, the maximum distance for forming subwavelength image changes following the same direction as the object moves, and the image distance increment is the same as the moving distance of the object. 2. Shifting both the object and the imaging plane towards the same direction and distance, the normalized image profile keeps unchanged. The results obtained in this thesis can provide the theoretical bases for experimental tests of the imaging behaviors of the slab lens.

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