在探討材料的性質當中，介電係數和磁導率是描述物質基本電磁性質的物理量，然在自然界中，這些參數絕大部分是大於零的，但是藉由人造物質可實現小於零的材料參數或是自然界中不存在的材料特性。而相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，聲學超常材料的特性可為波動工程及研究開創出新的可能性。
以往傳統透鏡的解析度會受到繞射極限的影響，使得近場的波源資訊無法在出透鏡端得到可解析的成像。本文所提及的聲學雙曲透鏡，目的為讓近場次波長圖形可在遠場解析。根據等效介質的理論，可利用層狀堆疊的均質材料來達成聲學異向性材料；藉由推導複數質量密度於波傳關係來探討單層的均質材料中的波傳與衰退距離；而幾何結構的設計可使聲學異向性材料應用於聲學雙曲透鏡，所以提出螺旋型聲學雙曲透鏡，模擬其點波源成像的放大效果優於一般圓柱型雙曲透鏡。數值方法中，本文利用有限元素法來模擬雙曲透鏡次波長成像的特性，並在長波極限下加以探討波傳在不同單層厚度組成的聲學異向性材料中的傳遞情形；以多重散射法計算多層圓柱的等效超常材料參數，實現螺旋型聲學雙曲透鏡。
若經過適當的設計，進而聲學雙曲透鏡未來可應用在非破壞性檢測、海底聲納、醫療檢測及微生物觀測上。

The permittivity and permeability are the basic quantity of electromagnetics in physics. Although almost all of natural material properties are positive, however, negative material properties can be realized by using artificial structures. Thus, what so-called “Metamaterial” is that materials have properties don’t exist in nature. Acoustic metamaterials, as a counterpart to electromagnetic metamaterials, can be explored as well. The novel properties of acoustic metamaterial will develop many possibilities in wave propagation design.
Resolution of conventional lens is generally constrained by diffraction limit. Therefore, we study the imaging properties of spiral acoustic hyperlens which can achieve far-field subwavelength imaging with high resolution. Based on effective medium theory, a hyperlens can be realized by an alternating layered structure of water and negative mass density that has nearly flat eguifrequency contours. To accomplish such an anisotropic medium, we had derived the relation between density and wave vector in a homogeneous material and calculated the effective dynamic mass density in acoustic metamaterial by multiple scattering theory. Simulation results have showed the spiral acoustic hyperlens has better amplification of image which can be used to propagate delicate details of a source for deep-subwavelength imaging. Furthermore, it can be applied to sonar, nondestructive testing, medical and biological examinations through a proper design.

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