地毯式週期斗篷隱形效果與側向位移之探討

Abstract

轉換光學理論的發展，設計出想要的光學路徑，將虛擬空間轉換成物理空間，進而得到材料參數，光就可以在我們所設計出的光學路徑中進行。利用此方法可以設計出許多光學應用，隱形就是其中的一種。 超常材料是藉由人工結構的設計或是發明不同的材料，達到巨觀等效的行為，以取得自然界中不存在之特性。而超常材料的概念，也已經從早期的經驗法則，慢慢地被科學家們所掌握，從理論發展到應用面走進日常生活中；運用轉換光學的方法結合超常材料便可以做出隱形斗篷的效果。 然而，超常材料會有頻寬限制，隨著頻率上升，共振單元對電磁波的吸收增大，工作頻率難以進一步升高，所以，就目前的製造技術而言，難以實現可見光頻率的隱形斗篷。於是在2008年Pendry小组提出地毯式斗篷，把需要隱藏的空間壓縮成一個平面而不是一個點或是一個線，通過選擇的座標轉換，得到適當的光學參數，雖然地毯式斗篷要求隱形目標必須位於平面上，但是可使超常材料的工作頻率範圍變寬，實現起來比較簡單，能夠工作在可見光的頻率範圍。 而本論文中我們提出一個新的保角轉換函數做出二維地毯式週期隱形斗篷，其地毯式斗篷具有極佳的隱形效果，其函數特性是當座標在無窮遠時，物理空間與虛擬空間相似，只有產生局部座標變化，且地毯不會因為座標變化而陷入地面，其斗篷最小高寬比為 。隨著地毯高度增加時反射光束的中心角度只會有極小的變化，偏離角度範圍為0~4.63度，且測向位移效果相當於地毯抬升-0.46到0.69個波長。

Because of the development of transformation optics, optical paths can be designed and it can turn virtual system into physical system to get material parameters. Therefore, light can travel through my designed optical path. Lots of optical devices had been developed by transformation optics. Cloaking is one of them. Metamaterials are artificial materials created to have properties that may not be found in nature. Furthermore, humans usually obtain some special properties from designing artificial structure rather than composition, using small inhomogeneities to achieve effective macroscopic behavior. However, broadband is confined in metamaterials. Under the circumstances, cloaking cannot be achieved in visible frequencies. Because resonance structures absorb electromagnetic radiation when increasing frequencies. In 2008, Pendry developed carpet cloaking which compressed cloaking region into a plane, instead of a point or a line. By coordinate transformations, appropriate material parameters can be obtained. Though carpet cloaking must lie in the plane, the broadband is wider. It can conduct in visible frequencies easily. This thesis we present a function to design two-dimensional isotropic grating cloaks using conformal mappings. It has a good cloaking effect. There are two main characteristics that physical system is similar to virtual system when we take limit and the maximum of the bump in the metal carpet develops into a sharp tip and the refractive index becomes singular at the maximum ratio of height to width .When increasing height of the carpet, angular central gaussian distribution will be changed and ranges from 0 to 4.63o. The lateral beam displacements are similar to lifting carpets which ranges from -0.46 to 0.69 wavelengths.