在奈米尺度下的表面電漿行為，可以利用金屬導波管陣列觀察到表面電漿的布洛赫週期震盪(Bloch Oscillations)現象。
在導波管中的介質，隨著每一層介電係數漸變，可以讓表面電漿在傳播時，因為梯度的關係，感受到一個位勢的變化，表面電漿也會隨著位勢的變化做加速；當表面電漿的動量符合特定的條件(Bragg Condition)時，又會受到一個與位勢變化相反的力。由於位勢產生的力和布拉格條件形成的力相反，可以讓表面電漿出現在空間上的震盪(Bloch Oscillations)。
而在本研究著重於分析與討論，在這樣條件下的表面電漿震盪運動的機制，以及建立理論預測的模型。

A kind of metal waveguide array structure designed for observing plasmon Bloch Oscillations in nanoscale is presented.
The gradient of plasmon propagation constants across the metal waveguide array is set up by changing the permittivity of the dielectrics in the guides. Because of the chirped permittivity between two metal layer , plasmon will be accelerated . Plasmon is accelerated until its momentum satisfies the Bragg Condition associated with the structure and is reflected . According to these elements , plasmon appear oscillations in spatial domain (Bloch Oscillations).
This aim of this study is to analyze and discuss the phenomenon (Bloch Oscillations) , and establish a theoretical model(Hamiltonian Optics) to predict the light trajectory.

[1]G. Malpuech, A. Kavokin, G. Panzarini, and A. Di Carlo, Phys. Rev. B 63, 035108 (2001).
[2]T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
[3]金屬表面電漿簡介”蔡定平”
[4]Chien-Chang Chao, Sheng-Han Tu, Chih-Ming Wang, Hung-I Huang, Chii-Chang Chen, Jenq-Yang Chang(2009) , Impedance-Matching Surface Plasmon Absorber for FDTD Simulations
[5]U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23,1701 (1998).
[6]T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[7]V. Agarwal, J. A. del Rio, G. Malpuech, M. Zamfirescu,A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[8]X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 2006.
[9]W. Lin, X. Zhou, G.P. Wang and C.T. Chan, Appl. Phys. Lett. 91 (2007), p. 243113
[10] W. Lin, X. Zhou, G.P. Wang and C.T. Chan, Appl. Phys. Lett. 91 (2007), p. 243113
[11]T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[12]A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, New York, NY, 2006), 6th ed..
[13]H. S. Eisenberg et al., Phys. Rev. Lett. 85, 1863 (2000).
[14]L. Verslegers, P.B. Catrysse, Z. Yu and S. Fan, Phys. Rev. Lett. 103 (2009), p. 033902
[15]Fan, X. B. et al. All-angle broadband negative refraction of metal waveguide arrays in the visible range: Theoretical analysis and numerical demonstration. Phys. Rev. Lett. 97, 073901 (2006)
[16] 葛德彪, 闫玉波, 电磁波时域有限差分方法(第二版)，西安电
子科技大学出版社2005。
[17] A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House 2005.
[18] G. Lenz, I. Talanina and C.M. de Sterke, Phys. Rev. Lett. 83 (1999),
p. 963
[19]X. Fan and G. P. Wang, Opt. Lett. 31, 1322 (2006).
[20] J.A. Arnaud Beam and Fiber Optics, Academic Press, New York (1976), pp.220–227.
[21] S. T. Thornton and J. B. Marion, Classical Dynamics of Particles and Systems, 5th ed. (Brooks/Cole, New York, 2004), pp.265–267.
[22] http://ab-initio.mit.edu/wiki/index.php/Meep