超材料是藉由次波長的人造單位結構，模仿自然界原子規則堆疊建構而成具 獨特性質的電磁物質。超材料擁有自然界鮮少甚至不存在的電磁響應，亦可藉由 調控人造的單位結構達到進一步控制並調整光學響應。超材料亦在微波波段具有 許多新奇之應用。因此，在此論文中，我們將設計兩種獨特的微波超材料，將其 應用於隱形斗篷以及主動式反射/吸收體之領域中。
在隱形斗篷的研究中，我們結合了內置型隱形斗篷(internal cloak)以及外置 型隱形斗篷(external cloak)兩者之優點，欲設計出倒置型隱形斗篷(reciprocal cloak)，此斗篷可在不須客製化斗篷的前提下，隱藏任意形狀及材料甚至在移動 中的物體，同時可以為被隱藏物提供視野。為達成此特性，我們利用轉移光學的 概念調控光學路徑，計算出了達成倒置型隱形斗篷所需要之材料參數條件。在模 擬中，我們利用了有限元素分析法模擬出完美斗篷之表現，同時離散化斗蓬並將 其切割至十二層。為實際設計出斗篷，我們利用有限積分法的方式設計超材料所 需之結構參數，並將所得介電質超材料組合成離散化斗篷並利用有限積分法驗證 斗篷之效果。完成斗篷製作後，我們利用了網路分析儀量測出斗篷之場型分佈， 證明了我們所設計之倒置型隱形斗篷的確可有效的隱藏任意形狀及材料參數之 物體，亦能為隱藏物提供視野。
另一方面，在主動式反射/吸收體中，我們利用了材料選擇表面設計出相較 於傳統吸收體更薄之金屬-介電質-金屬的三明治結構。我們利用二極體調控超 材料吸收體之共振頻率及吸收值，進而控制其在反射及吸收態之轉換。在模擬中， 我們改變材料尺寸來在 X 頻段中找出最佳的反射及吸收值。最佳化的超材料吸 收體當操作於反向電流之二極體中表現為斷路態，呈現出接近 100%之吸收值; 反之，當操作於順向電流之二極體中則表現為短路態，呈現出接近於 0 dB 之反 射值。為了驗證模擬結果，我們製作了電路板樣品並且焊上二極體，利用網路分 析儀量測出其表現。量測結果證明了我們所設計之主動式反射/吸收體可經由外 接電壓調控表現。
最後，在此論文中，我們量測出倒置型隱形斗篷雖可隱藏物體，但斗篷本身 卻產生些微的散射;另一方面，主動式反射/吸收體雖然可經由二極體之導通調 控，量測表現卻不如模擬之預期。為解釋兩元件在量測表現與模擬中之落差，我 們亦在最後考慮了製程因素並利用模擬預測其造成的影響。藉由這些分析，相信 日後若能在模擬中完善考慮這些變異因子，即可量測出最為接近模擬的結果。

Metamaterials, composed of subwavelength artificial atoms, are arranged in the way of nature atoms to achieve highly unique electromagnetic properties beyond nature materials. Electromagnetic responses of metamaterials are rarely observed in nature and possess abilities to further control optical pathway by manipulating artificial unit cells. Therefore, in this thesis, we will design two unique microwave metamaterials devices, i.e., invisibility cloaks and active reflection/absorbers, respectively.
For invisibility cloaks, we combine virtues of internal and external cloaks to design a reciprocal cloak which can hide objects with arbitrary shapes and material properties without custom-made design while providing the vision for hidden objects. To achieve these features, we utilize transformation optics and calculate the required constitutive parameters of the reciprocal cloak. Next, we utilize finite element method to simulate the exact reciprocal cloak and then discretize the cloak into twelve-layered annuli. To demonstrate the reciprocal cloak in experiments, we utilize finite integration method to search for 12 dielectric annuli with required constitutive parameters and then examine performances of the integrated dielectric annulus cloak by finite integration method. As for measurement, we applied the network analyzer to measure the field distributions to validate our simulation; finally, we prove that the proposed reciprocal cloak can hide objects of arbitrary shapes and material properties while providing visions for the hidden objects.
As for the active reflector/absorber, we utilize frequency selective surface based metamaterials to design a metal-dielectric-metal sandwiched structure that is thinner than the traditional absorbers. At the same time, we introduce diodes as an active component to manipulate the reflection and the absorption state of the perfect absorber under the condition of “diode on” and “diode off” denoting “short state” and “open state” of the entire metamaterial perfect absorber, respectively. In the simulation, we modify different dimensions of a unit cell to obtain the optimal reflection and absorption at X band. At the open state, the absorbance could reach almost 100% as the absorption state. On the contrary, the reflectance is quite close to 0 dB at the short state. To verify the performance, we measure S-parameter of the designed printed circuit board with diodes by the vector network analyzer. Finally, we have proved that the active reflector/absorber can be controlled by applied voltages.
Finally, the measured reciprocal cloak can hide hidden objects with arbitrary shapes and material properties. Yet, the outside observer can still perceive small scattering fields from the cloak itself. On the other hand, an active device can be manipulated by diodes; however, the measurement result did not agree with the simulated results pretty well. Although both of the two applications reveal a slight deviation from the simulation, we provide possible reasons to explain these deviations. As long as we can fully take these issues and solve the difficulties in the future, we can approach to ideal devices.

摘要 ----------------------------------------------------------------------------------- I
Abstract ---------------------------------------------------------------------------------- II
Acknowledgements---------------------------------------------------------------------------- IV
Contents ---------------------------------------------------------------------------------- V
List of Figures -------------------------------------------------------------------------------- VII
List of Tables -------------------------------------------------------------------------------- XV
Chapter 1: Introduction---------------------------------------------------------------------1
1.1 Introduction of metamaterials: ----------------------------------------------------- 1 1.1 Thesis organization: -----------------------------------------------------------------4
Chapter 2: Literature Review--------------------------------------------------------------5
2.1 Invisible cloak ----------------------------------------------------------------------------5 2.1.1 Transformation optics --------------------------------------------------------------5 2.1.2 Internal cloak ------------------------------------------------------------------------7 2.1.3 External cloak --------------------------------------------------------------------- 11 2.1.4 Reciprocal cloak ------------------------------------------------------------------ 15 2.1.5 Summary --------------------------------------------------------------------------- 18
2.2 Active tunable absorber/reflector ---------------------------------------------------- 19 2.2.1 Perfect absorber ------------------------------------------------------------------- 19 2.2.2 Active metamaterial device ------------------------------------------------------ 24 2.2.3 Summary --------------------------------------------------------------------------- 26
Chapter 3: Invisible Cloak --------------------------------------------------------------- 27
3.1 Design and simulation ----------------------------------------------------------------- 27 3.1.1 Theoretical analysis and simulations of the proposed cloak ---------------- 27 3.1.2 The cloak based on dielectric annulus metamaterials ------------------------ 34
3.2 Sample construction and fabrication------------------------------------------------- 39 3.3 Measurement setup and result discussion------------------------------------------- 43
3.3.1 Measurement setup --------------------------------------------------------------- 43 3.3.2 Measurement result and field distribution for different cases--------------- 45 3.3.3 Discussion of fabrication tolerance and misalignment----------------------- 50
3.4 Summary -------------------------------------------------------------------------------- 53 Chapter 4: Active Tunable Reflector/Absorber --------------------------------------- 54
4.1 Design and simulation ----------------------------------------------------------------- 54 4.1.1 Theoretical analysis of the active device--------------------------------------- 54 4.1.2 Simulation result of active metamaterial reflector/absorber ---------------- 56
4.2 Sample construction and fabrication------------------------------------------------- 61 4.3 Measurement setup and result discussion------------------------------------------- 67 4.3.1 Measurement set up--------------------------------------------------------------- 67 4.3.2 Measurement results-------------------------------------------------------------- 69 4.3.2 Discussion of diodes error ------------------------------------------------------- 72 4.4 Summary -------------------------------------------------------------------------------- 75
Chapter 5: Conclusions------------------------------------------------------------------- 77 Chapter 6: References -------------------------------------------------------------------- 79

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