超穎材料(metamaterials)是一種人造介質，在自然界並不存在，利用小於光波長的微結構當作類似材料組成單元的原子分子，導致整體具有異常光學特性，例如：負折射率(negative refraction index)、負磁導率(negative permeability)、強親手性(strong chirality).親手性是一種對左手圓偏振(LCP)光和右手圓偏振(RCP)光有不同光學特性的現象，又稱作圓二色性(circular dichroism)簡稱CD，親手性超穎材料(chiral metamaterial)CMM就是利用缺乏鏡象對稱的結構來分辨左右手旋光差異來造成CD。近年已有些許CD效應顯著的設計；例如：雙層共軛卍字形(conjugated gammadion)[33]
本篇論文使用有限時域差分法(finite difference time domain)FDTD數值模擬方法來研究金屬共軛卍字形CMM，發現雙層共軛卍字形比起單層卍字形和雙層順向卍字形有較強的CD，而其中CD效應強的波長位置，位於頻率選擇表面FSS所造成的反射頻譜中的反射頻帶的帶邊緣(band edge)。然而在使用完美導體PEC共軛卍字形結構的模擬，FSS的慮波效應仍然存在 但CD效應就不見了，由於PEC和金屬之間的差異是表面電漿的有無，表面電漿對親手性的影響仍有待釐清。我們接著使用簡化雙層共軛卍字形的雙層共軛Z字型，來檢驗CD效應是否為表面電漿造成，結果卻發現PEC雙層共軛Z字型卻依舊有CD，表示表面電漿在此系統是非必要。
最後我們使用Lagrange-Jones模型來解釋我們的模擬結果， PEC共軛Z字型不僅符合omega particle模型描述，也藉由Lagrange-Jones模型成功描述共軛Z字型結構的CD性質；推導出它的非對稱且各向異性(anisotropic)複數介電常數張量(complex permittivity tensor)，利用此複數介電常數張量可以求出該系統的Jones矩陣，可顯示RCP與LCP透射後電磁場偏振態的強度差異。利用Lagrange-Jones模型亦可解釋為何PEC共軛卍字形會無CD：共軛卍字形系統的複數介電常數張量是個準對稱形式，若將損耗項取掉則介電常數張量就變成對稱實數矩陣，這樣會使求出透射後的偏振態對LCP和RCP並無差異。再透過將金屬Drude模型改成無損耗，此FDTD模擬實驗證實表面電漿並無CD貢獻；共軛卍字形系統需要有損耗,才能造成透射後與透射前有明顯的相差，才會造成共軛卍字形有CD的主因。

Metamaterial is an artificial material with tailored dielectric or metallic nanostructure at optical sub wavelength size to mimic the nature atoms or molecules. It leads to extraordinary optical property such as negative refraction index, negative permeability, strong chirality, etc. Chirality means different optical response for right-hand circular-polarized (RCP) light and left-hand circular-polarized (LCP) light. This phenomenon of having different optical responses for LCP and RCP is called circular dichroism (CD). The chiral metamaterial CMM, a structure in the absence of mirror-symmetry, can distinguish LCP and RCP. Recently some design of CMM possess observable CD effect, for example, the conjugated gammadion structure.[33]
In this thesis we first numerically analyze the CD properties of conjugated gammadion (CG) CMM by Finite-Difference Time-Domain (FDTD) simulations. Our results indicate that the CD of CG CMM is much stronger than that of a single-layer gammadion and bi-layered gammadion CMM. Significant CD effect is located at reflection band edge of the reflection spectrum caused by frequency selective surface (FSS) effect. But when the metallic part of CG CMM is replaced as perfect electric conductor (PEC), the CD effect is vanished. The main distinguish between PEC and metal is the existence of surface plasma (SP) or not. One might suspect that the CD of CG CMM is caused by SP. Next, we trim down the design of CG structure to conjugated Z (CZ) shape structure to unveil the role of SP in CD. However, PEC CZ did demonstrate CD even without SP. This indicates that SP does not play a critical role in the CD effect for CZ system.
Finally we employ Lagrange-Jones model to explain our previous findings. The permittivity of the PEC CZ obtained via Lagrange-Jones model, is a complex asymmetry anisotropic tensor. The transmission polarized state is then referred by Jones matrix from complex permittivity tensor. The effective permittivity of CG is a quasi-symmetry form. When the damping (loss) component is ignored, the permittivity tensor becomes a real symmetry matrix. In a lossless CG system, the transmission coefficient of incident LCP and RCP light is indistinguishable. And then through the virtual experiment by removing the damping term in the metallic Drude model, SPP provides little effect on CD. The Lagrange-Jones model and our FDTD simulations verify that damping loss is crucial to generate phase retardation in CG system and thus leads to strong CD effect.

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