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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/30334

Title: 克爾介質與金屬界面之表面電漿之色散
Dispersion Relations of Surface Plasmon at a Metal-Kerr Dielectric Interface
Authors: Jung-Hao Huang
黃榮浩
Contributors: NTOU:Institute of Optoelectronic Sciences
國立臺灣海洋大學:光電科學研究所
Keywords: 克爾介質;表面電漿;色散
Date: 2011
Issue Date: 2011-11-25T07:39:59Z
Abstract: 表面電漿子(Surface Plasmon)是發生在金屬與電介質之界面上之一種傳導電子之集體共振現象,在許多研究文獻中,尤其是最近十年來,包含金屬與電介質之界面之表面電漿之研究,呈現出具有十分豐富之基礎物理內涵及廣泛之應用,其中,當表面電漿被激發時,界面附近存在著強大之局域場,使週邊材料之非線性光學性質被呈現出來,可以用來提高拉曼散射、多光子吸收或光學克爾效應等之效率。 在此論文中,我們針對金屬與克爾介質之界面,以及金屬薄膜與克爾介質之界面上之光學特性進行理論之研究。由於金屬與克爾界面附近存在著強大之局域場,將使克爾介質材料之非線性光學性質被呈現出來,一般在非線性材料中之微分方程式,都是利用數值方法求解,然而,對於金屬與克爾介質之界面問題,可以利用馬克斯威爾方程式,進一步推導克爾介質中的首次積分(First Integral)方程,並加入電磁場之邊界條件,以及金屬之Drude介電係數模型,我們計算出在金屬與克爾介質界面上,表面電漿之色散與金屬與克爾界面上之電場強度關係,因此我們再分別對不同之正負克爾係數,得出有趣的頻率與場強關係,同時,我們也對克爾介質在與金屬界面附近,其表面電漿產生的量子漲落,作一些計算。另一方面,我們也對克爾介質與金屬界面上表面電漿之非局域效應(Nonlocal effect)進行研究,當金屬中自由電子之平均自由路徑長度與電場在空間之快速變化之長度相當時,金屬中之介電常數就會是波向量的函數,我們依據金屬之流體力學模型,重新定義金屬上之非局域介電係數,再依據半古典無限壁壘(Simi-classical Infinite Barrier)方法,將金屬區域之波方程式轉換到傅氏空間,代入金屬之非局域介電係數,並將傅氏空間上之電場求解,最後將電場反傅氏轉換,我們可以得到電場在克爾介質界面上之關係,將此電場關係代入首次積分公式,即得到非局域效應在金屬與克爾電介質界面上的表面電漿色散關係,此非局域之效應,要在波向量kx較高時,才會顯現出來,當非局域之效應展現出來時,其表面電漿頻率ωsp會與波向量kx成正比,至於非線性之效應,會在非局域之作用下被消弱。接下來,我們再次應用首次積分與SCIB方法推演金屬薄膜與克爾介質之非局域色散關係,包括一個首次積分(First Integral)公式、兩個邊界條件、以及兩個來自於反傅氏轉換之公式,我們得到非局域之金屬薄膜與克爾介質之色散關係,該非局域色散公式,可應用到包括線性-局域、非線性-局域、線性-非局域以及非線性-非局域之問題上,本論文即針對非對稱(asymmetry)金屬薄膜之Kerr-metal-Vacuum之結構進行研究,並計算出其非局域效應的表面電漿色散關係,並探討金屬薄膜厚度、非線性及非局域效應對金屬薄膜兩邊之模態交互作用之物理,我們利用克爾介質與金屬界面之結果,合理解釋了金屬薄膜上之色散現象,包括了膜厚與兩個表面電漿耦合之色散關係及非線性-非局域所造成之影響。
Abstract Surface plasmon (SP) is a sort of collective oscillations of conduction electrons occurring at metallic surfaces. Last two decades has witnessed rapid developments in this field due to its fundamental physics as well as a wide variety of applications. The key ingredient in most of observed phenomena and newly developed devices associated with SP is the strong local field at the surface of metal, which enhances a number of nonlinear optical processes such as Raman scattering, multi-photon absorption, and optical Kerr effect. In this dissertation, we theoretically investigate the optical properties of structures containing metal/Kerr medium interfaces. The strong local field is expected to enhance the optical Kerr effect at the metallic surface and the character of SP can be changed correspondingly. The solutions of nonlinear field equations are usually very difficult to find and numerical methods are not avoidable. However in the planar metal/Kerr systems, it has been found that the first integral methods can help to solve the equations exactly in the Kerr medium. The dispersion relation of SP thus evaluated are shown to be significantly dependent on the surface field intensity. This rigorously calculated SP frequency has also been used to evaluate the quantum fluctuation of the SP mode in response to the Kerr effect. Besides, we also investigate the properties of SP when the nonlocal character of the metal is taken into account. “Nonlocal” means that dielectric function depends on the wave number due to the finite mean free path of electrons as well as the rapid variation of electric field in metal. In the present work, the nonlocal dielectric function is obtained from hydrodynamic model, the simplest one to exhibit the nonlocality. The boundary condition for a nonlocal metallic surface is treated by the method of SCIB (semiclassical infinite barrier). When we take into account altogether the nonlinearity and nonlocality, it is found that they counteract each other, resulting in quenching of nonlinear effect in large wave number. Furthermore, a metallic thin film in contact with Kerr medium in one side is studied by the same methods. The interplay of the effects of nonlinearity, nonlocality, and the thickness is analyzed in detail.
URI: http://ethesys.lib.ntou.edu.tw/cdrfb3/record/#G0D97880001
http://ntour.ntou.edu.tw/handle/987654321/30334
Appears in Collections:[光電科學研究所] 博碩士論文

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