超材料（Metamaterial）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獨具特殊性的電磁物質。超材料擁有自然界鮮少甚至不存在的電磁響應，例如高頻磁響應、超低頻電漿頻率和負折射係數等。更重要的是，超材料具有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的能力。因此，在此論文中，我們將設計三種獨特的超材料，並將之應用於包括超寬頻濾波器、慢光裝置以及隱形斗篷等不同領域中。
首先，不論是在電子或光子元件中，濾波器皆是不可或缺的元件之一。然而，視不同頻段製作相對應的濾波器，尤其當頻率趨向高頻時，將是一大挑戰。此處，為了應用於60 GHz 免執照頻段，我們利用超物質特有的左手電磁響應並結合傳統材料的右手電磁響應形成左右手複合型濾波器，使其具有20 GHz的有效頻寬、250 dB/10 GHz 以上的邊帶轉換效率及高於-1 dB 穿透效率的濾波表現，更重要的是能同時滿足了好的品質因子及超大頻寬這兩項互斥的要素。
再者，由於電磁波與物質較弱的交互作用，使得我們難以讀取藉由光子所攜帶的訊號。因此，我們發展了利用多角度入射皆能引發負折射係數的超材料建構左手性波導，進而利用在負折射係數波導中引發之負的古斯−漢欣效應，使光子在波導特定位置中來回盤旋，降低光子的等效速度，大幅增加光子與物質的作用時間，甚至能將光子完全儲存於負折射係數波導中，形成慢光裝置。
最後，在光學中，設計光的傳遞路徑亦是一大重點。在傳統光纖傳遞訊號時，可能因為光纖扭曲造成訊號損耗或失真。為了解決這種不必要的損耗，研究學者藉由光學轉換（transformation optics）的理論，去扭曲光在空間的行進路線，使得光訊號不受光纖曲度產生損耗而完美地傳至接收段。在此，我們將使用光學轉換的概念並以隱形斗篷為例，同時引入互補媒介（complementary medium）的概念，使隱形斗篷能夠隱藏移動並帶有視野的任意物體。

Metamaterials are a new class of artificial electromagnetic materials in which
the building elements are smaller than the wavelength of illuminating light and
arranged in the orders of natural atoms. They possess unprecedented electromagnetic responses such as high frequency magnetic responses, an ultra-low plasmonic frequency and negative refraction index, which are all rare or even not existing in nature. Moreover, metamaterials can further manipulate and control light by designing their unit cells instead of their constitutive materials. In this dissertation, we would design three remarkable metamaterials to approach applications such as an ultrabroad filter, slowing light devices and the innovative cloak.
First of all, no matter in electronic or photonic devices, a filter is a crucial
component to select signals from noises. However, it becomes a challenge to design filters especially for much higher frequency ranges. As an example, to design a filter in the unlicensed 60 GHz frequency range, we combine the right-handed response from nature materials and the left-handed response from metamaterials to form a composite right/ left-handed filter. The filter possesses the effective bandwidth of 20 GHz, the band-edge transitions of 250 dB/10 GHz, and the transmission efficiency above -1 dB, which accomplish the high quality factor and large effective bandwidth simultaneously.
Next, due to much weaker interaction between electromagnetic waves and
materials compared to the one between electrons and materials, it is difficult to
manipulate information carried by photons. Thus, we employ negative Goos-
Hänchen effect to detour photons around the critical thickness of the negative
refractive waveguide composed of a multiple incidence metamaterial and slow down the speed of photons effectively to enhance the interaction time between photons and materials. Further, we can even store energy of photons in the waveguide completely as a light storage medium.
Finally, to design the optical path is also an important issue in optics. For
example, an optical fiber might lose its signals when the fiber is bent or twisted. To avoid unnecessary losses, researchers employ transformation optics to distort the coordinate systems to render that optical signals transmitting through a bent fiber insusceptibly. Here, we will demonstrate an innovative cloak of invisibility as an example to validate the robustness of transformation optics and also we bring in the concept of complementary medium in the design procedure to enable the cloak to conceal arbitrary multi-objects with movements and visions.

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