傳統光學透鏡受限於繞射極限的影響，難以解析小於二分之一個波長的物體，其原因在於高空間頻率的消逝波無法傳遞到遠場，但若使用非等向性超穎材料構成的雙曲透鏡，則可將消逝波轉換成傳遞波並在遠場放大成像。
本文提出螺旋雙曲透鏡的構想，其透鏡是由超穎材料構成，色散曲線為雙曲線，此種特殊的材料性質可將消逝波轉換為傳遞波傳到遠場，具有次波長放大成像的功能。本篇論文設計兩種不同結構的螺旋雙曲透鏡，皆由銀與氧化鋁的薄層堆疊而成，經由本文模擬與分析可得螺旋雙曲透鏡比起圓形雙曲透鏡有更高的成像解析度以及放大倍率。
本文利用有限元素數值模擬軟體COMSOL Multiphysics做分析，探討不同結構、材料堆疊順序和透鏡厚度的雙曲透鏡對次波長解析的影響，經由分析後可得螺旋雙曲透鏡在光源波長為365奈米時，最高解析度可達到100奈米，高於一般常見的圓形雙曲透鏡。

The resolution of conventional optical lens system is restricted by the diffraction limit. The diffraction barrier arises from the fact that high spatial frequency information carried by evanescent waves only exists in the near field. The hyperlens which used anisotropic metamaterial transfers the evanescent waves into propagating waves and produces magnifying images into the far field.
We propose the spiral hyperlenses that are able to image beyond the diffraction limit. The spiral hyperlens is based on a designed metamaterial with hyperbolic dispersion relation, which support wave propagation with high wavevectors. In comparison with cylindrical hyperlens, spiral hyperlens have the advantages of higher images resolution and better images magnification. In this study, we designed two types of spiral hyperlenses composed of silver/alumina multilayers. According to our numerical simulation, far-field imaging resolution is down to 100nm at 365nm working wavelength which is beyond the diffraction limit.

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