在本研究中，我們用三維單層螺旋奈米結構提出了一種新的策略，使原本只能夠在高折射率條件下被激發的掌性依賴電磁誘發透明效應，也能夠重現於低折射率材料中。在本研究的前半段，我們探討了單層螺旋在不同折射率與結構參數的改變下對應的光學特性。並發現當折射率降低時，結構中的共振明顯的被弱化，且電磁誘發透明效應無法被激發。但是藉由幾何參數的調整與優化，許多光學特性，包括法諾共振與電磁誘發透明能夠再次被此低折射率結構所展現。在第二部分的討論中，我們進行了許多不同分析來探討法諾共振的機制與成因。我們利用時域截取分析法驗證了法諾共振所具有的亮暗模態特性。我們也進一步利用法諾共振的力學類比模型：雙振子模型，來理解共振模態間的耦合。另外，我們針對了共振模態的電磁場進行了分析，探討其在不同結構參數下的特性，並歸納其共振模態所表現出的變化，更系統性的了解其機制。目前，法諾共振與電磁誘發透明效已大量地被應用於感測元件與非線性光學領域，並且，在此研究中所提出的低折射率介電質材料能夠被應用於高分子材料的製程平台。因此，此研究結果能夠擴展其在感測與光電元件的應用。

In this study, we present a new strategy that enables handedness-dependent electromagnetic induced transparency (EIT) in a lower refractive index (n~1.5) dielectric 3D single-layer helical nanostructure. In the first part of the study, we numerically present different characteristics of a single layer helical structure while varying the refractive index and geometrical parameters. It is revealed that when decreasing the refractive index of the dielectrics, the resonances of the structures are less pronounced and the EIT behavior cannot be maintained. By properly tailoring the geometrical parameters, we show that diverse optical properties, including Fano resonance and EIT effect, may emerge and can still be implemented in a helical structure with a lower refractive index. In the second part of the study, we implement various analyses to understand the formation of Fano resonance in helix. We carry out time apodization analysis, which examines the information in the time-domain. We show that the resonances in the system exhibit bright and dark mode characteristics. We further adopt a two-oscillator model to get a better understanding of the mode coupling in helix. We also inspect the electric and magnetic field profiles of the resonance modes, and examine the fundamental nature of the resonance modes. Depending on the resonance nature, different operation regimes are recognized and categorized. As EIT-based devices and Fano resonance are widely used for sensors and nonlinear optics, our design based on lower refractive index dielectrics can be readily implemented in polymer-based fabrication platforms, which can broaden the horizon of applications in sensors and optoelectronics devices.

Bibliography
[1] V. M. Shalaev and et al., "Optical negative-index metamaterials," Nature Photon. 1, pp. 41-48, 2007.
[2] A. N. Grigorenko and et al., "Nanofabricated media with negative permeability at visible frequencies," Nature 438, pp. 335-338, 2005.
[3] Y. Liu and X. Zhang, "Metamaterials: a new frontier of science and technology," Chem. Soc. Rev. 40, pp. 2494-2507, 2011.
[4] S. Zhang, Y. S. Park, J. Li. and et al., "Negative Refractive Index in Chiral Metamaterials," Phys. Rev. Lett. 102, p. 023901, 2009.
[5] M. Decker et al,, "Circular dichroism of planar chiral magnetic metamaterials," Opt. Lett. 32, pp. 856-857, 2007.
[6] B. Wang, J. F. Zhou, T. Koschny and et al, "Chiral metamaterials: simulations and experiments," J. Opt. A: Pure Appl. Opt. 11, p. 114003, 2009.
[7] V. A. Fedotov, M. Rose, S. L. Prosvirnin and N. Papas, "Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry," Phys. Rev. Lett. 99, p. 147401, 2007.
[8] A. B. Khanikaev et al., "Experimental demonstration of the microscopic origin of circular dichroism in two-dimensional metamaterials," Nat. commun. 7, p. 12045, 2016.
[9] B. Luk’yanchuk et al., "the Fano resonance in plasmonic nanostructures and metamaterials," Nat. Mater. 9, p. 707, 2010.
[10] Z. Fuli and et al., "Large group index induced by asymmetric split ring resonator dimer," Appl. Phys. Lett. 103, p. 221904, 2013.
[11] R. Singh, I. A. I. Al-Naib, M. Koch and W. Zhang, "Sharp Fano resonances in THz metamaterials," Opt. Express 19, p. 6312, 2011.
[12] P. Moitra, A. B. Slovick, W. Li and et al., "Large-Scale All-Dielectric Metamaterial Perfect Reflectors," ACS Photonics 2, pp. 692-698, 2015.
[13] P. Moitra, A. B. Slovick, Z. G. Yu and et al., "Experimental demonstration of a broadband all-dielectric metamaterial perfect reflector," Appl. Phys. Lett. 104, p. 171102, 2014.
[14] A. B. Slovick, G. Z. Yu, M. Berding and S. K., "Perfect dielectric-metamaterial reflector," Phys. Rev. B 88, p. 165116, 2013.
[15] S. Jahani and Z. Jacob, "All-dielectric metamaterials," Nature Nanotech 11, pp. 23-36, 2016.
[16] Z. Liu, X. Liu, Y. Wang and P. Pan, "High-index dielectric metamaterials for near-perfect broadband reflectors," J. Phys. D 45, p. 195101, 2016.
[17] J. Z. Hao, Y. Seokho, L. Lan, D. Brocker, D. H. Werner and T. S. Mayer, "Experimental demonstration of an optical artificial perfect magnetic mirror using dielectric resonators," IEEE Antennas and Proapagation Society International Symposium, pp. 1-2, 2012.
[18] S. Liu, M. B. Sinclair, T. S. Mahony, Y. C. Jun, S. Campione, J. Ginn, D. A. Bender, J. R. Wendt, J. F. Ihlefeld, P. G. Clem, J. B. Wright and I. Grener, "Optical magnetic mirrors without metals," Optica 1, pp. 250-256, 2014.
[19] M. Esfandyarpour, E. C. Garnett, Y. Cui, M. D. Mcgehee and Brongersma M. L., "Metamaterial mirrors in optoelectronic devices," Nature Nanotech 9, pp. 542-547, 2014.
[20] A. S. Schwanecke and et al., "Optical magnetic mirrors," J. Opt. Pure appl. Opt. 9, pp. L1-L2, 2007.
[21] V. A. Fedotov, A. V. Rogacheva, N. I. Zheludev, P. L. Mladyonov and S. L. Prosvirnin, "Mirror that does not change the phase of reflected waves," Appl. Phys. Lett. 88, p. 091119, 2006.
[22] M. Silveirinha and N. Engheta, "Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media," Phys. Rev. B 75, p. 075119, 2007.
[23] X. Huang, Y. Lai, Z. H. Hang, H. Zheng and C. T. Chan, "Dirac cones induced by accidental degeneracy in photonic crystals and zero-induced by accidental degeneracy in photonic crystals and zero-refractive-index materials," Nat. Mater. 10, pp. 582-586, 2011.
[24] P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs and J. Valentine, "Realization of an all-dielectric zero-index optical metamaterial," Nat. Photonics 7, pp. 791-795, 2013.
[25] A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang., A. A. Firsov, I. Y. Khrushchev and J. Petrovic, "Nanofabircated media with negative permeability at visible frequencies," Nature 438, pp. 335-338, 2005.
[26] V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, pp. 41-48, 2007.
[27] M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch and Y. S. Kivshar, "High-efficiency dielectric Huygens' surfaces," Adv. Opt. Mater. 3, pp. 813-820, 2015.
[28] C. Pfeiffer and A. Grbic, "Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets.," Phys. Rev. Lett. 110, p. 197401, 2013.
[29] F. Aieta, M. A. Kats, P. Genevet and F. Capasso, "Multiwavelength achromatic metasurfaces by dispersive phase compensation," Science 347, pp. 1342-1345, 2015.
[30] F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro and F. Capasso, "Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces," Nano Lett. 12, pp. 4932-4936, 2012.
[31] Q. Zhao, J. Zhao, F. Zhang and D. Lippens, "Mie resonance-based dielectric metamaterials," Elsevier materialstoday 12, pp. 60-69, 2009.
[32] Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhao and L. Li, "Experimental Demonstration of Isotropic Negative Permeability," Phys. Rev. Lett. 101, p. 027402, 2008.
[33] C. F. Bohren and D. R. Huffman, "Absorption and Scattering of Light by Small Particles," Wiley-Interscience, 1983.
[34] Z. S. Wu, Q. C. Shang and Z. J. Li, "Calculation of electromagnetic scattering by a large chiral sphere," Appl. Opt. 51, pp. 6661-6668, 2012.
[35] Q. Fu and W. Sun, "Mie theory for light scattering by a spherical particle in an absorbing medium," Appl. Opt. 40, pp. 1354-1361, 2001.
[36] K. Sergey and K. Yuri, "Functional Meta-Optics and Nanophotonics Governed by Mie Resonances," ACS Photonics 4, pp. 2638-2649, 2017.
[37] L. Lewin, "The electrical constants of a material loaded with spherical particles," Proc. Inst Electr. Eng. 94, p. 65, 1947.
[38] C. L. Holloway and et al., "A Double Negative (DNG) Composite Medium Composed of Magnetodielectric Spherical Particles Embedded in a Matrix," IEEE Trans Antennas Propag. 51, p. 2596, 2003.
[39] E. Yablonovitch, "Photonic band-gap structures," J. Opt. Soc. Am. B 10, pp. 283-295, 1993.
[40] J. B. Pendry, "Calculating photonic band structure," Journal of Physics: Condensed Matter 8, p. 9, 1996.
[41] H. T. Tung, Y. K. Chen, P. L. Jheng and Y. C. Hung, "Origin and manipulation of band gaps in three-dimensional dielectric helix structures," Opt. express 25, pp. 17627-17638, 2017.
[42] W. D. St. John, W. J. Fritz, Z. J. Lu and D.-K. Yang, "Bragg reflection from cholesteric liquid crystals," Phys. Rev. E 51, p. 1191, 1995.
[43] J. Park, H. Kim and B. Lee, "High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating," Opt. Express 16, pp. 413-425, 2008.
[44] U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, pp. 1866-1878, 1961.
[45] E. M. Andrey and et al., "Fano resonance in nanoscale structures," Rev. Mod. Phys. 82, p. 2257, 2010.
[46] M. F. Limonov, M. V. Rybin, A. N. Poddubny and Y. S. Kivshar, "Fano resonances in photonics," Nature Photonics 11, pp. 543-554, 2017.
[47] Y. S. Joe and et al., "Classical analogy of Fano resonances," Phys. Script 74, pp. 259-266, 2006.
[48] A. B. Khanikaev and et al., "Fano-resonant metamaterials and their applications," Nanophotonics 2, pp. 247-264, 2013.
[49] M. F. Finch and B. A. Lail, "Multi-coupled resonant splitting with a nano-slot metasurface and PMMA phonons," In Proc. SPIE 9547, p. 954710, 2015.
[50] Y. Yang et al., "All-dielectric metasurface analogue of electromagnetically induced transparency," Nat. Commun.5, p. 5753, 2014.
[51] L. Verslegers et al., "electromagnetically induced transparency to superscattering with a single structure: a coupled-mode theory for doubly resonant structures: a coupled-mode theory for doubly resonant structures," Phys. Rev. Lett. 108, p. 083902, 2012.
[52] T. Ma, Q. Huang, H. He, Y. Zhao, X. Lin and Y. Lu, "All-dielectric metamaterial analogue of electromagnetically induced transparency and its sensing application in terahertz range," Optics Express 27, pp. 16624-16634, 2019.
[53] K. Yee, "Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media," IEEE, pp. 302-307, 1996.
[54] MEEP documentation, "Yee Lattice," [Online]. Available: https://meep.readthedocs.io/en/latest/Yee_Lattice/.
[55] Lumerical official website, "Understanding time apodization in frequency domain monitors," [Online]. Available: https://reurl.cc/Ob8Y2A.