電子束在經過期性結構中時會產生Smith-Purcell輻射(SPR)，我們利用半導體材料在兆赫波波段下與金屬有相似特性，將半導體材料作為週期性結構基底，並將表面電漿效應導入並吻合輻射波段，產生出兆赫波(Terahertz Radiation)輻射源。半導體材料在不同的溫度下引發的表面電漿效應也會有所不同，因此我們會先對金屬中的表面電漿色散關係式加以了解。
在常溫下的色散關係式中，調控光柵週期使Smith-Purcell 輻射吻合激發表面電漿條件，藉由激發出表面電漿效應使輻射源增強。並在不同的調控變因如: 電子束能量、環境溫度、材料特性、光柵的厚度與週期變化做分析。在此利用有限時域差分法軟體Lumerical驗證了我們的理論，本文研究提供一種產生兆赫波的方法，在日後的研究中可以藉由改變不同的材料與色散關係式使輻射源產生不同的效果。

In this work, we propose and analyze a temperature controlled InSb-based grating with ability of producing THz light. Due to the design based on the combination of spoof surface plasmon polariton and Smith-Purcell free-electron lasers possess the ability of producing coherent monochromatic radiation at relevant frequency and angle. By using finite-difference time-domain (FDTD) method and considering the feature of dispersion curve of investigated grating, the mechanism of producing THz light is elucidated. The proposed device can be dynamically reconfigured by simply changing the magnitude of temperature, it would provide a practical route for realizing the compact and tunable radiation light source.

[1] 邱國斌, 蔡定平, ”金屬表面電漿簡介”, 物理雙月刊, 28卷, 2期, pp. 472-482, 2006.
[2] 吳民耀, 劉威志, ”表面電漿子理論與模擬”, 物理雙月刊, 28卷, 2期, pp. 486-496, 2006.
[3] 鐘佩鋼, 顏順通, ”兆赫波源之發展與原理簡介”, 物雙月刊,31卷,2期, pp.109-110, 2009.
[4] 李青翰, 林凡異, ”兆赫波漫談”, 物雙月刊,31卷,2期, pp.97-101,2009.
[5] D. Li, M. Hangyo, Y. Tsunawaki, Z. Yang, Y. Wei, S. Miyamoto, M. R. Asakawa, K. Imasaki, ” Theoretical Analysis on Smith-Purcell Free-Electron Laser”, Free Electron Lasers, Dr. Sandor Varro (Ed.), 2012.
[6] J. Urata, M. Goldstein, M. F. Kimmitt et al, ”Superradiant Smith-Purcell Emission”, Phys. Rev. Lett. 80.516, 1998.

[7] S. Taga, K. Inafune, E. Sano, ” Analysis of Smith-Purcell radiation in optical region”, Opt Express. Nov 26;15(24):16222-9, 2007.
[8] J. Zhou, M. Hu, Y. Zhang, P. Zhang, W. Liu, S. Liu, ” Numerical analysis of electron-induced surface plasmon excitation using the FDTD method”, J. Opt, Vol 13, Issue 3, 2011.
[9] 葛德彪, 闫玉波, ”電磁波時域有限差分法(第二版)”, 西安電子科技大學出版社,2005.
[10] X. Dai, Y. Xiang, S. Wen, H. He, ”Thermally tunable and omnidirectional terahertz photonic bandgap in the one-dimensional photonic crystals containing semiconductor InSb”J. Appl. Phys. 109, 2011.
[11] S. C. Howells,L. A. Schlie,”Transient terahertz reflection spectroscopy of undoped InSb from 0.1 to 1.1 THz”, Appl. Phys. Lett. 69, 1996.
[12] H. A. Atwater, ”The promise of plasmonics”, Sci Am. Apr;296(4):56-63, 2007.
[13] F. J. García de Abajo, ”Optical excitations in electron microscopy”, Rev. Mod. Phys. 82, 209, 2010.
[14] 藍永強, 邱行偉, ”電漿模擬”, 物雙月刊,28卷,2期, pp.498, 2006.
[15] Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, G. S. Park, ” Superradiant terahertz Smith-Purcell radiation from surface plasmon excited by
counterstreaming electron beams ”, Appl. Phys. Lett. 90, 031502 , 2007.
[16] J. K. So, J.Y Ou, G. Adamo, K. F. MacDonald, Javier García de Abajo, N. I. Zheludev, ” Ampli fi cation of the Evanescent Field of Free Electrons”, ACS Photonics, pp.1236-1240, 2015.
[17] A. Alù, N. Engheta, ” Multifrequency Optical Invisibility Cloak with Layered Plasmonic Shells ”, Phys. Rev. Lett. 100, 2008
[18] P. Genevet, D. Wintz, A. Ambrosio, A. She, R. Blanchard ,F. Capasso, ” Controlled steering of Cherenkov surface plasmon wakes with a one-dimensional metamaterial”, Nature Nanotechnology 10,pp. 804–809, 2015
[19] B. H. Cheng, Y. Z. Ho, Y. C. Lan,D. P. Tsai, ”Optical Hybrid-Superlens Hyperlens for Superresolution Imaging”, IEEE J. Sel. Top. Quantum Electron, Vol. 19, Issue. 3, 2013.
[20] Y. M. Shin1, J. K. So1, K. H. Jang1, J. H. Won1, A. Srivastava1, G.S. Park, ” Superradiant terahertz Smith-Purcell radiation from surface plasmon excited by counterstreaming electron beams”, Appl. Phys. Lett. 90, 2007.