介電係數和磁導率是描述物質基本電磁性質的物理量，在自然界中，這些參數都是大於零的，但是藉由人造物質可實現小於零的材料參數。然而對於聲學介質也可以找出相對應電磁超常材料的聲學超常材料，聲學超常材料新穎的特性可為波動工程拓展新的道路。
傳統聲學透鏡的解析度會受到繞射極限的影響，使得近場聲源無法在遠場處成像。本文提及的聲學雙曲透鏡，則是要讓近場次波長圖形可在遠場解析。根據等效介質的理論，可利用聲學超常材料來實現雙曲透鏡。利用有限元素法來模擬雙曲透鏡次波長成像的特性，證實聲學雙曲透鏡的可行性。聲學雙曲透鏡未來可應用在醫療檢測及微生物觀測上。

The permittivity and permeability of matters are the essential physical quantity of electromagnetics. The material properties are positive. The negative material properties can be realized by using artificial structures. Acoustic metamaterials, as a counterpart to electromagnetic metamaterials, can be explored.The novel properties of acoustic metamaterial will offer many opportunities in wave engineering.

Resolution of conventional acoustics is generally constrained by diffraction limit, which prevents imaging of near field pressure source in the far-field zone. In this thesis, We study the imaging properties of hyperlens, which proffer subwavelength pattern originated from near-field sources and form images in the far-field zone with high resolution. According to the theory of effective medium, a hyperlens can be realized by using acoustic metamaterials. The imaging properties of hyperlens are studied numerically using finite element method. Numerical simulations show the acoustic hyperlens is concrete feasibility.

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