超穎材料(Metamaterials)是一種人造物質，透過特殊的幾何設計可創造出自然界不存在的材料，由於其組成單位分子小於電磁波波長，提供了人們一種操作電磁波的方法。親手性材料(chirality)是擁有對左手圓偏光(LCP)和右手圓偏光(RCP)有不同光學特性的材料，使其在左右旋光下有不同的穿透吸收率。這種對LCP偏振光和RCP偏振光有不同反應則稱為圓二色性(Circular Dichroism,CD)。而親手性超穎材料(chiral metamaterials)即是結合兩者，利用奈米等級的週期性排列的非鏡像對稱的幾何結構產生圓二色性，當入射電磁波的偏振旋向與左旋或右旋結構發生交互作用，便會和另一相異卻沒有發生產生共振的旋向有了差異，進而造成圓二色性。有許多幾何結構設計都有顯著的CD效應，如雙層卍字型、雙層C型環、扭曲弧線結構(twisted arch)等…
本篇論文以有限差分時域法(Finite-difference Time-Domain ,FDTD)，使用數值模擬的方式研究親手性超穎材料：扭曲弧線金屬結構(Twisted Arch)產生圓二色性的機制。扭曲弧線金屬結構是由兩塊弧線結構組合而成，利用兩塊金屬間彼此耦合作用，在 、 偏振方向上會各自有藍位移和紅位移發生，並產生出高低能階的差異。藉由控制兩塊金屬弧線結構令其間有高度差，使光在入射兩塊弧線結構時有了相位延遲。透過電荷分布圖可觀察到隨著高度差的增加造成的相位延遲加上因兩弧線結構距離增加使彼此耦合力變化，進而對左右旋光有了不同趨勢，展現出較強的圓二色性。但過大的高度差也會使兩弧線結構變得相對獨立，因此需要適當的幾何結構設計才能得到較佳的圓二色性。而左高右低的扭曲弧線結構與右高左低的結構有著相同的圓二色性機制，只是符號方向正好相反，我們可對應所需的親手性增益和圓二色性去決定其左右高低和弧線間水平距離與高度差。

Metamaterials are artificial materials with special geometry design, so that we can create many unique physical properties which do not exist in nature. Due to its size is much smaller than operating wavelength, metamaterials allow the possibility to control electromagnetic wave. Chiral metamaterials are metamaterials with chirality, which means polarizes light of opposite handedness, namely, left-handed and right-handed circularly polarized (LCP and RCP) interact differently with its’ non-mirror symmetry structures. Optical activity stemming from chirality include circular dichroism (CD) which measures the different optical activity of two opposite handedness circularly polarized waves. Twisted arch nanostructures are chiral metamaterials composed by two metal arch with height difference. The coupling between two metal arch and the phase delay caused by height different will trigger circular dichroism. With Finite Difference Time Domain (FDTD) simulations, we can analyze the mechanism of circular dichroism in twisted arch nanostructures. Base on experiment data, we discover that with appropriate design, twisted arch structure can produce enormously strong circular dichroism.

1. Pendry, John B., et al. "Extremely low frequency plasmons in metallic mesostructures." Physical review letters 76.25 (1996): 4773.
2. Pendry, John B., et al. "Magnetism from conductors and enhanced nonlinear phenomena." IEEE transactions on microwave theory and techniques 47.11 (1999): 2075-2084.
3. Shelby, Richard A., David R. Smith, and Seldon Schultz. "Experimental verification of a negative index of refraction." science 292.5514 (2001): 77-79.
4. Liu, Na, and Harald Giessen. "Coupling effects in optical metamaterials." Angewandte Chemie International Edition 49.51 (2010): 9838-9852.
5. Cui, Yonghao, et al. "Giant chiral optical response from a twisted-arc metamaterial." Nano letters 14.2 (2014): 1021-1025.
6. 邱冠語. "使用奈米球鏡微影術製程親手性結構並以有限時域差分法模擬." 成功大學光電科學與工程學系學位論文 (2018): 1-72.
7. Pendry, John Brian. "Negative refraction makes a perfect lens." Physical review letters 85.18 (2000): 3966.
8. Smith, David R., et al. "Composite medium with simultaneously negative permeability and permittivity." Physical review letters 84.18 (2000): 4184.
9. Plum, E., et al. "Metamaterial with negative index due to chirality." Physical Review B 79.3 (2009): 035407.
10. Rose, Alec, Da Huang, and David R. Smith. "Controlling the second harmonic in a phase-matched negative-index metamaterial." Physical review letters 107.6 (2011): 063902.
11. Schurig, David, et al. "Metamaterial electromagnetic cloak at microwave frequencies." Science 314.5801 (2006): 977-980.
12. Liu, Na, et al. "Stereometamaterials." Nature Photonics 3.3 (2009): 157.
13. Condon, E. U. "Theories of optical rotatory power." Reviews of modern physics 9.4 (1937): 432.
14. Zhao, R., et al. "Conjugated gammadion chiral metamaterial with uniaxial optical activity and negative refractive index." Physical Review B 83.3 (2011): 035105.
15. Li, Zhaofeng, et al. "Chiral metamaterials with negative refractive index based on four “U” split ring resonators." Applied Physics Letters 97.8 (2010): 081901.
16. Askarpour, Amir Nader, Yang Zhao, and Andrea Alù. "Optical chirality enhancement in twisted metamaterials." 2014 Third Conference on Millimeter-Wave and Terahertz Technologies (MMWATT). IEEE, 2014.
17. 吳民耀, and 劉威志. "表面電漿子理論與模擬." 物理雙月刊, 二十八卷二期 (2006).
18. 邱國斌, and 蔡定平. "金屬表面電漿簡介." 物理雙月刊 28 (2006): 472-485.
19. Fano, Ugo. "Effects of configuration interaction on intensities and phase shifts." Physical Review 124.6 (1961): 1866.
20. Condon, E. U. "Theories of optical rotatory power." Reviews of modern physics 9.4 (1937): 432.
21. Zhao, Yang, et al. "Chirality detection of enantiomers using twisted optical metamaterials." Nature communications 8 (2017): 14180.
22. Liu, Na, et al. "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit." Nature materials 8.9 (2009): 758.
23. Jones, R. Clark. "A new calculus for the treatment of optical systemsi. description and discussion of the calculus." Josa 31.7 (1941): 488-493.
24. Menzel, Christoph, Carsten Rockstuhl, and Falk Lederer. "Advanced Jones calculus for the classification of periodic metamaterials." Physical Review A 82.5 (2010): 053811.
25. Schäferling, Martin, et al. "Tailoring enhanced optical chirality: design principles for chiral plasmonic nanostructures." Physical Review X 2.3 (2012): 031010.
26. Yee, Kane. "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media." IEEE Transactions on antennas and propagation 14.3 (1966): 302-307.
27. Choroszucho, Agnieszka. "Analysis of the influence of the complex structure of clay hollow bricks on the values of electric field intensity by using the FDTD method." Archives of Electrical Engineering 65.4 (2016): 745-759.
28. Berenger, Jean-Pierre. "A perfectly matched layer for the absorption of electromagnetic waves." Journal of computational physics 114.2 (1994): 185-200.
29. Slaughter, William S. The linearized theory of elasticity. Springer Science & Business Media, 2012.
30. Fukushima, Yuma, Daisuke Sasaki, and Kazuhiro Nakahashi. "Cartesian mesh linearized Euler equations solver for aeroacoustic problems around full aircraft." International Journal of Aerospace Engineering 2015 (2015).
31. Gedney, Stephen D. "An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices." IEEE transactions on Antennas and Propagation 44.12 (1996): 1630-1639.