本研究主要是探討多重開口螺旋狹縫生成電漿子渦流的電場振幅和相位分佈，當偏振光通過螺旋狹縫金屬結構時，會在金屬表面產生表面電漿震盪，而在缺陷耦合機制的作用下，會有部分的表面電漿發生輻射並且散射至空間中，這些被散射的電漿子本身攜帶的軌道角動量，會讓電漿子在空間中沿著中心處旋轉，由於中心處電場為零，因此形成環狀電場分佈以及相位不連續的特性。利用此現象，我們根據阿基米德螺線設計了多重開口的狹縫，透過改變開口數量和拓樸電荷來得到不同型態的電漿子渦流，並觀察環狀電場振幅分佈以及相位奇點。
本文使用Meep模擬軟體研究，運算方法採用有限時域差分法對網格空間中電磁場進行計算。模擬結果顯示，電漿子渦流型態會根據總軌道角動量變化，而總軌道角動量是由拓樸電荷和入射光的偏振態所決定，因此藉由改變開口數量、開口寬度和偏振型態就能夠實現對電漿子渦流的控制。其獨特的光學性質可以在空間通訊、光學鑷子、量子計算、光學量測、天文學等領域得到廣泛應用。

The purpose of this thesis is to discuss the electric field amplitude and phase distribution of the plasmon vortex. When polarized light is perpendicularly incident on the metal spiral slit,it will excite surface plasma on the metal surface. Based on defect coupling, part of the surface plasmon is radiated and scattered into space.These scattered plasmas carry orbital angular momentum,which causes the plasma to rotate in along the center of the space.We designed the structure of the multiple opening slit based on Archimedean spirals to obtain different types of plasma vortices by varying the number of openings and the topographic charge. In this experiment, we can obtain the ring-shaped electric field distribution and phase singularity.
This thesis uses the simulation software Meep to research, and uses the finite time domain difference method to calculate the electromagnetic field in the definition grid. The simulation results show that the plasmon vortex varies according to the total orbital angular momentum. By changing the topological charge and polarization, the plasmon vortex can be controlled. The above results can be used in the communications space, optical tweezers, quantum computing, optical measurement and astronomy.

[1]. Alison M.Yao,Miles J.Padgett,Orbital angular momentum:origins,behavior and applications,Advances in Optics and Photonics,Vol.3,lssue 2,pp.161-204
[2]. L.Marrucci,E.Karimi et al.,Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications, Journal of Optics, review article,pp.1-3 (2011)
[3]. L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light” Prog. Opt. 39, 291‒ 372
[4]. Miles Padgett,Johammess Courtial,Les Allen,Light’s Orbital Angular Momentum,Physics Today,57,5,35 (2004)
[5]. 魏功祥,劉曉娟,劉云燕,付聖貴, 光的自旋和軌道角動量, Laser & Optoelectronics Progress, 51, 100004,pp1-8 (2014)
[6]. Enrique J.Galvez,’’Structured Light and Its Applications’’,ch3,pp63-77 (2008)
[7]. Xiaocong Yuan,Changjun Min, Novel Plasmonic Microscopy: Principle and Applications, Handbook of Photonics for Biomedical Engineering,pp1-8 (2016)
[8]. Wei Ji, Chun-Hong Lee, Peng Chen, Wei Hu, Yang Ming, Lijian Zhang, Tsung-Hsien Lin, Vladimir Chigrinov &Yan-Qing Lu,Meta-q-plate for complex beam shaping, Scientific Reports volume 6,25528 (2016)
[9]. Lorenzo Marrucci, ‘’The q-plate and its future’’,Journal of Nanophotonics, Vol. 7,078598,p1-4 (2013)
[10]. Robert Charles Devlin, Antonio Ambrosio et al, Spin-to-orbital angular momentum conversion in dielectric metasurfaces,Optics Express,
Vol.25,lssue1,pp. 377-393 (2017)
[11]. C. Bohren and D. Huffman, “Absorption and Scattering of Light by Small Particles” Wiley,New York (1983)
[12]. U. Fano, The Theory of Anomalous Diffraction Gratings and of Quasi-Stationary Waves on Metallic Surfaces, Journal of the Optical Society of America,Vol.31,Issue3,pp. 213-222 (1941)
[13]. 吳民耀、劉威志,表面電漿子理論和模擬,物理雙月刊28卷2期,pp486-496 (2006)
[14]. 邱國斌、蔡定平,金屬表面電漿子簡介,物理雙月刊28卷2期,pp473-485 (2006)
[15]. 張勝雄、戴朝義,奈米電漿子波導元件於積體光學之應用,物理雙月刊4卷6期 (2008)
[16]. Zhiqiang Liang,Jun Sun,Yueyue Jiang et al., Plasmonic Enhanced Optoelectronic Devices,Plasmonics9(4),pp1-8 (2014)
Ordal, M. A., Bell, R. J., Alexander, R. W., Long, Jr. L. L., and Querry, M. R.,
‘’Optical properties of Al, Fe, Ti, Ta, W, and Mo at submillimeter wavelengthsAppl’’. Opt. 24, Vol27,lssue6,pp1203-12099 (1985).
[17]. Yanan Dai,Plasmon ,Orbital Angular Momentum Generation, Imaging Light with Photoelectrons on the Nano-Femto Scale pp 79-95 (2020)
[18]. Stefan A. Maier, Surface Plasmon Polaritons at Metal / Insulator Interfaces, Plasmonics: Fundamentals and Applications,pp 21-37 (2007)
[19]. Jun Zhuabc,Wenju Xuabc, Zhengjie Xuab et al.,’’Surface plasmon polariton mode in the Metal-insulator-Metal waveguide’’,Optik Optics,Volume134, pp187-193 (2017)
[20]. Henrique T. M. C. M. Baltar, Krystyna Drozdowicz-Tomsia and Ewa M. Goldys, Propagating Surface Plasmons and Dispersion Relations for Nanoscale Multilayer Metallic-Dielectric Films, Plasmonics – Principles and Applications,CH6,pp135-155 (2012)
[21]. E.N. Economou, Surface plasmons in thin films, Phy. Rev. Vol.182,pp539-554 (1969)
[22]. Maier, S. A,’’Surface Plasmon Polaritons at Metal / Insulator Interfaces. Plasmonics: Fundamentals and Applications’’, ch2,pp21–37(2007)
[23]. ZHUO LI,YUNHE SUN et al.,Tuning the dispersion of effective surface plasmon polaritons with multilayer systems,Optics Express,Vol26,No.4,pp1-12 (2018)
[24]. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Transactions on Antennas and Propagation, vol. 14, pp. 302-307 (1996)
[25]. 葛德彪、閻玉波,電磁波時域有限差分方法(第二版),pp1-154 (2005)
[26]. Gedney S D,’’An anusitropic perfect matched layer absorbing media for the truncation of FDTD lattices’’,IEEE Trans.Antennas Propagat,AP-44(12) (1996)
[27]. 許良彥,’’ 表面電漿子耦合共振能量轉移’’, 自然科學簡訊第三十卷第四期,pp130-134 (2018)
[28]. Yijie Shen, Xuejiao Wang et al.,’’ Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities’’,Light Science and Applocations8,Article number:90 ,pp1-29 (2019)
[29]. Julio Cesar Gutierrez Vega,Carlos López-MariscalCarlos,’’ Nondiffracting vortex beams with continuous orbital angular momentum order dependence’’, Journal of Optics A Pure and Applied Optics 10(1):015009,pp1-8 (2008)
[30]. Yanan Dai,’’ Imaging Light with Photoelectrons on the Nano-Femto Scale’’,ch6,pp79-95 (2020)

[31]. G.Spektor1, D.Kilbane etal.,Revealing the subfemtosecond dynamics of orbital angular momentum in nanoplasmonic vortices, Science,Vol. 355,
Issue 6330, DOI:10.1126,pp.1187-1191 (2017)

[32]. Han Wang, Lixia Liu et al., Vortex beam generation with variable topological charge based on a spiral slit, Nanophotonics, Volume 8,Issue 2,pp317-324 (2018)
[33]. Yu Wang, Peng Zhao et al., Dynamically sculpturing plasmonic vortices: from integer to fractional orbital angular momentum, scientific reports, 6:36269 | DOI: 10.1038,pp1-10 (2016)
[34]. Jordan A. Hachtel, Sang-Yeon Cho, Spatially and spectrally resolved orbital angular momentum interactions in plasmonic vortex generators, Light: Science & Applications, Article number: 33,pp1-9 (2019)
[35]. Zhongyi Guo et al., Review of the Functions of Archimedes’ Spiral
Metallic Nanostructures,nanomaterials,v.7(11),pp1-21 (2017)
[36]. Hwi Kim, Junghyun Park et al., Synthesis and Dynamic Switching of Surface Plasmon Vortices with Plasmonic Vortex Lens,Nano,pp529-536 (2010)
[37]. Pierfrancesco Zilio,Elettra Mari et al., Angular momentum properties of
electromagnetic field transmitted through holey plasmonic vortex lenses, OPTICS LETTERS,Vol. 37, No.15,pp3234-3236 (2012)
[38]. Zengji Yue, Haoran Ren et al., Angular-momentum nanometrology in an ultrathin plasmonic topological insulator film, NATURE COMMUNICATIONS 9, Article number: 4413,pp1-7 (2018)
[39]. Qilong Tan,Qinghua Guo et al., Controlling the plasmonic orbital angular
momentum by combining the geometric and dynamic phases,Nanoscale,lssue 15,pp4944-4949 (2017)
[40]. Ching-Fu Chen,Chen-Ta Ku et al..Creating Optical Near-Field Orbital Angular Momentum in a Gold Metasurface,NANO letters,lssue15(4),pp2746-2750 (2015)
[41]. 曾軍,陳亞紅,劉顯龍,蔡陽健,’’部分相干渦旋光束研究進展’’,光學學報, 39(1): 0126004 (2019)
[42]. Yuanjie Yang, Xinlei Zhu etal.,Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation,Nanophotonics, Volume 7,Issue 3,pp677-682 (2018)
[43]. Netanel Biton,,Judy Kupferman,Shlomi Arnon,’’ OAM light propagation through tissue’’,scientific reports11, Article number: 2407,pp1-9 (2021)
[44]. Jian Wang, Jeng-Yuan Yang et al.,’’Terabit free-space data transmission employing orbital angular momentum multiplexing’’, Nature Photonics ,volume 6,pp488-496 (2012)
[45]. Jack Ng, Zhifang Lin, C. T. Chan,’’ Theory of Optical Trapping by an Optical Vortex Beam’’, PHYSICAL REVIEW LETTERS, volume 104,103601,pp1-4 (2010)
[46]. Zhimeng Li, Tong Liu, Yuan Ren, Song Qiu, Chen Wang,Hua Wang,’’ Direction-sensitive detection of a spinning object using dual-frequency vortex light’’, Optics Express Vol. 29, Issue 5, pp7453-7463 (2021)
[47]. Manuel Erhard, Robert Fickler, Mario Krenn , Anton Zeilinger,’’ Twisted photons: new quantum perspectives in high dimensions’’, Light: Science & Applications,volume 7 (17146),pp1-11 (2018)
[48]. Harwit, M.,’’Photon orbital angular momentum in astrophysics’’,The Astrophysical Journal,Vol 597, pp1266–1270 (2003)
[49]. H. A. Atwater, Sci. Am. 296, pp.56-62, 2007
[50]. Xavier Zambrana-Puyalto,’’ Control and characterization of nano-structures with the symmetries of light’’,MACQUARIE UNIVERSITY FACULTY OF SCIENCE,CH2,pp11-36 (2014)
[51]. John Vickers, Matt Burch, Reeta Vyas, and Surendra Singh,’’ Phase and interference properties of optical vortex beams’’, Optical Society of America A, Vol. 25, Issue 3, pp. 823-827 (2008)
[52]. Svetlana V. Boriskina,Thomas Cooper, Lingping Zeng et al.,’’Losses in Plasmonics: from mitigating energy dissipation to embracing lossenabled functionalities’’, Advances in Optics and Photonics,9(4),pp775-827 (2017)
[53]. 陳瑞琳,陳于堂,林家鴻,’’超常材料光波吸收體之簡介’’,pp1-7 (2007)
[54]. Qian Geng,Tian Wang, Lei Wu,Yueming Li,’’Defect coupling behavior and flexural wave energy harvesting of phononic crystal beams with double defects in thermal environments’’, Journal of Physics D: Applied Physics, Vol. 54
pp1-18 (2021)
[55]. Claudia Triolo, Salvatore Savasta, Alessio Settineri et al.,’’Near-field imaging of surface-plasmon vortex-modes around a single elliptical nanohole in a gold film’’, Scientific Reports volume 9, Article number: 5320 (2019)
[56]. Vaziri A,Pan J W,Jennewein T ,et al. Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum. Physical Review Letters,91( 22): 227902 (2003)
[57]. Lavery M P J , Speirits F C , Barnett S M , et al . Detection of a spinning object using light's orbital angular momentum. Science,341( 6145): 537- 540 (2013)
[58]. Tamburini F , Anzolin G , Umbriaco G , et al. Overcoming the rayleigh criterion limit with optical vortices. Physical Review Letters, 97( 16): 163903 (2006)
[59]. 林浩存、蔡定平,’’ 超穎介面介紹與其應用’’,物理雙周刊的36卷4期,pp264-271, (2014)
[60]. Tomoki Ohno and Shintaro Miyanishi,’’ Study of surface plasmon chirality induced by Archimedes’ spiral grooves’’,OPTICS EXPRESS,Vol.14,No. 13,pp6285-6290 (2006)