我們通常以等效介質理論(effect medium theory)預測一維雙曲超材料的光學反應，然而，等效介質理論在入射光波長與結構的晶胞尺寸相近的情形下，會產生顯著的偏差。因此，近來電漿子能帶理論(plasmonic band sturcture theory)被引入用以分析一維雙曲超材料，並且預測了表面態的存在。表面態存在與否決定於導納匹配條件(admittance matching condition)。此外，可藉由導納的引入顯現位於能隙的表面態與電漿子能帶性質的特定關係，是為塊材-表面連動(bulk-interface correspondence)。在此篇論文中，我們已透過克雷奇曼(Kretschmann)和奧圖(Otto)模組證實了一維雙曲超材料表面態的存在。藉由調控一維雙曲超材料的金屬層比例，我們展示了表面態的消失與再現，也證實了一維雙曲超材料的光學拓樸相轉換行為。

The optical responses of one dimensional hyperbolic metamaterials (1DHMMs) are usually determined by effective medium theory based on the long wavelength approximation. However, the long wavelength approximation shows significant deviation when the wavelength of the incident light is comparable with the unit cell of HMMs. Therefore, plasmonic band theory have been suggested to analyze the 1DHMMs recently and the existence of the interface state has been proposed. The requirement for the existence of the interface state is determined by the admittance matching condition. Furthermore, the interface state formation in the plasmonic band gap can be related to the properties of the plasmonic band in terms of the wave admittance, so called “bulk-interface correspondence”. In this work, we experimentally identify the existence of the interface state of 1DHMM by the Kretschmann and the Otto configurations. By varying the metallic filling ratio in the 1DHMMs, we successfully demonstrate the disappearance and reappearance of the interface state which indicates the optical topological phase transition of 1DHMMs.

摘要.....................................................................................................II
ABSTRACT.......................................................................................III
誌謝...................................................................................................IV
CONTENTS........................................................................................V
LIST OF FIGURES...........................................................................VI
CHAPTER 1 INTRODUCTION.........................................................1
1.1 HYPERBOLIC METAMATERIALS......................................1
CHAPTER 2 LITERAURE REVIEW................................................6
2.1 SURFACE PLASMON POLARITON....................................6
2.1.1 Surface Plasmon Polariton Dispersion Relation..................6
2.1.2 Thin Film Surface Plasmon Polariton Dispersion Relation.9
2.1.3 Otto and Kretschmann Configuration................................13
2.2 ONE DIMENSIONAL HYPERBOLIC METAMATERIALS....14
2.2.1 Effective Medium Theory..................................................14
2.2.2 Band Structure Theory.......................................................15
2.2.3 Band Crossing Behavior....................................................17
2.2.4 Surface State Formation.....................................................18
2.2.5 Analogy to the Multiple Oscillators Model.......................20
2.2.6 Topological Phase Transition.............................................24
CHAPTER 3 DESIGN AND SIMULATIONS.................................25
3.1 MOTIVATION......................................................................25
3.2 SIMULATION METHOD: TRANSFER MATRIX METHOD...................................................................................25
3.3 EXPERIMENT DESIGN......................................................29
3.4 SIMULATION RESULTS AND DISCUSSION..................32
CHAPTER 4 EXPERIMENTAL RESULTS.....................................34
4.1 FABRICATION PROCESS..................................................34
4.2 OTTO AND KRETSCHMANN GAP OPTIMIZATION.....37
4.3 MEASUREMENT RESULTS..............................................38
CHAPTER 5 CONCLUSIONS.........................................................43
REFERENCE LIST...........................................................................44

1 Noginov, M., Lapine, M., Podolskiy, V. & Kivshar, Y. Focus issue: hyperbolic metamaterials. Opt. Express 21, 14895-14897, doi:10.1364/OE.21.014895 (2013).
2 Poddubny, A., Iorsh, I., Belov, P. & Kivshar, Y. Hyperbolic metamaterials. Nat Photon 7, 948-957, doi:10.1038/nphoton.2013.243 (2013).
3 Shekhar, P., Atkinson, J. & Jacob, Z. Hyperbolic metamaterials: fundamentals and applications. Nano Convergence 1 (2014).
4 Ferrari, L., Wu, C., Lepage, D., Zhang, X. & Liu, Z. Hyperbolic metamaterials and their applications. Progress in Quantum Electronics 40, 1-40 (2015).
5 Smith, D. R. & Schurig, D. Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors. Phys. Rev. Lett 90, 077405 (2003).
6 Rytov, S. M. Electromagnetic Properties of a Finely Stratified Medium. JETP 2, 466 (1956).
7 Jacob, Z., Alekseyev, L. V. & Narimanov, E. Optical hyperlens: Far-field imaging beyond the diffraction limit. Opt. Express 44, 8247–8256 (2006).
8 Liu, Z., Lee, H., Xiong, Y., Sun, C. & Zhang, X. Far-field optical hyperlens magnifying sub-diffraction-limited objects. Science 315, 1686–1686 (2007).
9 Liu, Z., Lee, H., Xiong, Y., Sun, C. & Zhang, X. Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects. Science 315, 1686-1686, doi:10.1126/science.1137368 (2007).
10 Sreekanth, K. V., Luca, A. D. & Strangi, G. Negative refraction in graphene-based hyperbolic metamaterials. Applied Physics Letters 103, 023107 (2013).
11 Yao, J. et al. Optical negative refraction in bulk metamaterials of nanowires. Science 321, 930 (2008).
12 Liu, Y., Bartal, G. & Zhang, X. All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region. Opt. Express 16, 15439–15448 (2008).
13 Hoffman, A. J. et al. Negative refraction in semiconductor metamaterials. Nat Mater 6, 946–950 (2007).
14 Peng, L. et al. Experimental observation of left-handed behavior in an array of standard dielectric resonators. Phys. Rev. Lett. 98 (2007).
15 Jacob, Z., Smolyaninov, I. I. & Narimanov, E. E. Broadband purcell effect: Radiative decay engineering with metamaterials. Applied Physics Letters 100, 181105 (2012).
16 Sreekanth, K. V., Biaglow, T. & Strangi, G. Directional spontaneous emission enhancement in hyperbolic metamaterials. Journal of Applied Physics 114, 134306 (2013).
17 Lu, D., Kan, J. J., Fullerton, E. E. & Liu, Z. Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials. Nat Nano 9, 48–53 (2014).
18 Kim, J. et al. Improving the radiative decay rate for dye molecules with hyperbolic metamaterials. Opt. Express 20, 8100-8116 (2012).
19 Krishnamoorthy, H. N. S., Jacob, Z., Narimanov, E., Kretzschmar, I. & Menon, V. M. Topological transitions in metamaterials. Science 336, 205–209 (2012).
20 Yang, X., Yao, J., Rho, J., Yin, X. & Zhang, X. Experimental realization of threedimensional indefinite cavities at the nanoscale with anomalous scaling laws. Nat Photon 6 (2012).
21 Guo, Y. & Jacob, Z. Thermal hyperbolic metamaterials. Opt. Express 21, 15014–15019 (2013).
22 Guo, Y., Cortes, C. L., Molesky, S. & Jacob, Z. Broadband super-planckian thermal emission from hyperbolic metamaterials. Applied Physics Letters 101, 131106 (2012).
23 Neira, A. D. Eliminating material constraints for nonlinearity with plasmonic metamaterials. Nat Commun 6, doi:doi:10.1038/ncomms8757 (2015).
24 Barnes, W. L., Dereux, A. & Ebbesen, T. W. Surface plasmon subwavelength optics. Nature 424, 824–830 (2003).
25 Pitarke, J. M., Silkin, V. M., Chulkov, E. V. & Echenique, P. M. Theory of surface plasmons and surface-plasmon polaritons. Reports on Progress in Physics 70, 1 (2007).
26 Zayats, A. V. & Smolyaninov, I. I. Near-field photonics: surface plasmon polaritons and localized surface plasmons. Journal of Optics 5, S16 (2006).
27 Deng, Y. & Liu, G. Surface plasmons resonance detection based on the attenuated total reflection geometry. Procedia Engineering 7, 432 – 435 (2010).
28 Wood, B., Pendry, J. B. & Tsai, D. P. Directed subwavelength imaging using a layered metal-dielectric system. Physical Review B 74, 115116 (2006).
29 Un, I. W. & Yen, T. J. Interface States and Interface-Bulk Correspondence of One-dimensional Hyperbolic Metamaterials. Scientific Reports 7, doi:10.1038/srep43392 (2017).