電子束(Electron beams)除了是電子顯微鏡(electron-microscopy)的探針之外，因為史密斯-珀塞爾輻射(Smith-Purcell radiation)、制動輻射(bremsstrahlung radiation)、過渡輻射(transition radiation)、表面電漿子引起的輻射(Surface plasmon induced radiation)等電子輻射的機制，所以電子束也可以被用來驅動輻射源稱之為電子驅動光子源(electron-driven photon sources)。
一般來說表面電漿振盪(surface plasmon polariton)是侷限在金屬表面對輻射沒有貢獻的，但是透過金屬表面的缺陷結構，可以使表面電漿振盪在缺陷結構處轉換成電漿子輻射，基於這個機制，我們以偶極子源替代電子束在金屬表面激發表面電漿子，然後設計阿基米德螺旋(Archimedes spiral)的缺陷結構，讓表面電漿振盪引起的電漿子輻射形成渦旋光束(vortex beam)，論文中利用改變缺陷結構的幾何參數探討了：渦旋光束的形成與軌道角動量(orbital angular momentum)、表面電漿渦流(plasmon vortex)的耦合和兩個渦旋光束的干涉。

Electron beams are not only probes for electron microscopy because of electron radiation mechanisms such as Smith-Purcell radiation, Bremsstrahlung radiation, transition radiation, surface plasmon-induced radiation, etc. An electron beam can be used as a radiation source, known as an electron-driven photon source. Generally, surface plasmon polariton are confined to the metal surface and do not contribute to radiation, but through the defect structure of the metal surface, the surface plasmon polariton can be converted into electromagnetic radiation at the defect structure. We use a dipole source instead of an electron beam to excite surface plasmon waves on the metal surface, and then design the defect structure of the Archimede’s spiral, so that the radiation is caused by the surface plasmons forms a vortex beam. By changing the geometric parameters of the structure, the formation of vortex beams, coupling of plasmon vortices, and the interference of two vortex beams are discussed.

[1] Joshua Christopher, Masoud Taleb, Achyut Maity, Mario Hentschel, Harald Giessen and Nahid Talebi, “Electron-driven photon sources for correlative electron-photon spectroscopy with electron microscopes,” Nanophotonics, 9, 4381–4406(2020).
[2] M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Physical review B, 79, 113405(2009).
[3] Jordan A. Hachte, Sang-Yeon Cho, Roderick B. Davidson, Matthew A. Feldman, Matthew F. Chisholm, Richard F. Haglund, Juan Carlos Idrobo, Sokrates T. Pantelides and Benjamin J. Lawrie, “Spatially and spectrally resolved orbital angular momentum interactions in plasmonic vortex generators,” Light: Science & Applications, 8, 1(2017).
[4] Jordan A. Hachtel, “The Nanoscale Optical Properties of Complex Nanostructures,” Springer Cham (2017).
[5] Sen Gong, Min Hu, Renbin Zhong, Xiaoxing Chen, Ping Zhang, Tao Zhao, and Shenggang Liu, “Electron beam excitation of surface plasmon polaritons,” Optics Express, 21, 16, 19252-19261(2014).
[6] Toon Coenen, Ernst Jan R. Vesseur, Albert Polman, and A. Femius Koenderink, “Directional Emission from Plasmonic Yagi Uda Antennas Probed by Angle-Resolved Cathodoluminescence Spectroscopy,” Nano Lett., 11, 9, 3779–3784(2011).
[7] G. Adamo, J. Y. Ou, J. K. So, S. D. Jenkins, F. De Angelis, K. F. MacDonald, E. Di Fabrizio, J. Ruostekoski, and N. I. Zheludev, “Electron-Beam-Driven Collective-Mode Metamaterial Light Source,” Phys. Rev. Lett., 109, 217401 (2012).
[8] Guanhai Li, Brendan P. Clarke , Jin-Kyu So, Kevin F. MacDonald and Nikolay I. Zheludev, “Holographic free-electron light source,” Nature Communications, 7, 13705 (2016).
[9] Nika van Nielen, Mario Hentschel, Nick Schilder, Harald Giessen, Albert Polman, and Nahid Talebi, “Electrons Generate Self Complementary Broadband Vortex Light Beams Using Chiral Photon Sieves,” Nano Lett., 20, 5975-5981 (2020).
[10] Ernst Jan R. Vesseur, Javier Aizpurua, Toon Coenen, Alejandro Reyes Coronado, Philip E. Batson and Albert Polman, “Plasmonic excitation and manipulation with an electron beam,” MRS Bulletin, 37, 8(2012).
[11] Zengji Yue, Haoran Ren, Shibiao Wei, Jiao Lin and Min Gu, “Angular-momentum nanometrology in an ultrathin plasmonic topological insulator film,” Nature Communications, 9, 4413, 1 7(2018).
[12] Zhongyi Guo, Zixiang Li, Jingran Zhang, Kai Guo, Fei Shen, Qingfeng Zhou and Hongping Zhou, “Review of the Functions of Archimedes Spiral Metallic Nanostructures,” Nanomaterials, 7, 12, 405(2017).
[13] J. H. Poynting, “The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light,” Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences 82, 557, 560-567(1909).
[14] Richard A. Beth, “Mechanical Detection and Measurement of the Angular Momentum of Light,” Physical Review, 50, 115-125(1936).
[15] L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw and J. P. Woerdman, “Orbital angular momentum of light and transformation of Laguerre Gaussian Laser modes,” Physical review A, Atomic, molecular, and optical physics, 45, 11, 8185 8189(1992).
[16] Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the Spin-Based Plasmonic Effect in Nanoscale Structures,” Phys. Rev. Lett., 101, 043903(2008).
[17] Yanan Dai, “Imaging Light with Photoelectrons on the Nano Femto Scale,” Springer (2020).
[18] G. Spektor, D. Kilbane, A. K. Mahro, B. Frank, S. Ristok, L. Gal, P. Kahl, D. Podbiel, S. Mathias, H. Giessen, F.-J. Meyer zu Heringdorf, M. Orenstein and M. Aeschlimann, “Revealing the subfemtosecond dynamics of orbital angular momentum in nanoplasmonic vortices,” Science, 355, 6330, 1187-1191(2017).
[19] 邱國斌,蔡定平, “金屬表面電漿子簡介,” 物理雙月刊, 28卷, 2期, 473 485 (2006).
[20] Naoki Yamamoto and Takahiro Suzuki, “Conversion of surface plasmon polaritons to light by a surface step,” Appl. Phys. Lett., 93, 093114(2008).
[21] J. T. van Wijngaarden, E. Verhagen, A. Polman, C. E. Ross, H. J. Lezec and H. A. Atwater, “Direct imaging of propagation and damping of near-resonance surface plasmon polaritons using cathodoluminescence spectroscopy,” Appl. Phys. Lett., 88, 221111 (2006).
[22] Heinz Raether, “Surface Plasmons on Smooth and Rough Surfaces and on Gratings,” Springer Berlin Heidelberg (1988).
[23] Kane Yee, “Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media,” IEEE Transactions on Antennas and Propagation, 14, 3, 302-307(1966).
[24] H. De Raedt, K. Michielsen, J. S. Kole and M. T. Figge, “One-step finite-difference time-domain algorithm to solve the Maxwell equations,” Physical Review E 67, 5 Pt 2, 056706(2003).
[25] Han Wang, Lixia Liu, Changda Zhou, Jilian Xu, Meina Zhang, Shuyun Teng and Yangjian Cai, “Vortex beam generation with variable topological charge based on a spiral slit,” Nanophotonics, 8, 2, 317-324(2019).
[26] Jean-Pierre Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” Journal of Computational Physics, 114, 2, 185-200(1994).
[27] N. B. Simpson, K. Dholakia, L. Allen and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Optics Letters, 22, 1, 52-54(1997).
[28] Kosta Ladavac and David G. Grier, “Microoptomechanical pumps assembled and driven by holographic optical vortex arrays,” Optics Express, 12, 6, 1144-1149(2004).
[29] K. T. Gahagan and G. A. Swartzlander, Jr., “Trapping of low-index microparticles in an optical vortex,” Journal of the Optical Society of America B, 15, 2, 524-534(1998).
[30] Paramasivam Senthilkumaran, Jr., “Optical phase singularities in detection of laser beam collimation,” Applied Optics, 42, 31, 6314 6320(2003).
[31] Marc D. Levenson, Takeaki Ebihara, Grace Dai, Yasutaka Morikawa Naoya Hayashi and Sze Meng Tan, Jr., “Optical vortex masks for via levels,” Journal of Micro/Nanolithography, MEMS, and MOEMS, 3, 2, 293(2004).
[32] NahidTalebi, “Spectral Interferometry with Electron Microscopes,” Scientific Reports, 6, 1, 33874(2016).
[33] Juan Zhao, Baixin Chen, Mitsuo Takeda and Wei Wang, “Observation of the Fujiwhara effect in optical coherence function by using coherence holography,” Imaging Systems and Applications, ITh2B, 6(2019).