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  • 學位論文

表面電漿子及抗反射結構的電磁研究

Electromagnetic Study of Surface Plasmon and Antireflection Structures

指導教授 : 張宏鈞

摘要


本研究使用有限差分時域法分析多種具有表面電漿模傳播的結構並提出理論詮釋及可能的應用。我們完成的三維有限差分時域法程式碼包含週期性邊界及單軸完美匹配層,並成功將程式平行化,且使用輔助微分方程法來模擬色散材料。 一般而言,包含金屬和介電的複合材料可激發表面電漿態,而可見光及近紅外光為通常考的頻段。而同樣的複合材料在微波頻段可形成為傳統波導。我們研究表面電漿態從可見光到微波頻段的過渡過程,從理論發現對稱及非對稱表面電漿態有其對應的傳統波導模態。而表面電漿態也可從這些波導模態中分離出來。 過去實驗上發現三維柴堆結構金屬光子晶體的能隙有一異常傳播模,此傳播模的物理成因困擾學界許多年。我們提出物理模型搭配有限差分時域法,證明此一傳播模源自一等效的Fabry-Perot共振腔。我們成功解釋並預測它在頻譜上的特徵。 我們分析光與二維週期性次波長孔洞金屬膜的交互作用。應用有限差分時域法,我們探討週期共振模並討論其達到共振的物理成因。我們發現在週期性孔洞內的漸逝波具有最低模態的導波模。我們亦發現入射光的極化方向決定表面電漿模的傳播方向。 表面電漿態被視為在次波長提高透射效能的明日之星。最後,對於傳統提高透射效能的抗反射膜,我們提出了一個新的設計原則。不同於過去抗反射膜著重設計一個緩慢變化的折射率,我們提出,對於高入射角,光在抗反射膜中的傳播路徑對於抗反射的效能更形劇烈。我們理論分析並藉由數值計算驗證此一觀點的正確性。

並列摘要


Many aspects of plasmonics are studied theoretically and numerically using the finite-difference time-domain (FDTD) method. An in-house three-dimensional (3-D) FDTD program incorporating the periodic boundary condition and the uniaxial perfectly matched layer is developed with parallel computing. The dispersive materials are realized by means of the auxiliary differential equation method. The transition of plasmonic states bridging from visible frequencies to microwaves is examined. In particular, given the metal permittivity at microwaves, the plasmonic dispersion evolves into the conventional waveguide dispersion. We reveal the coupling effect of plasmonic modes, identify the symmetric and antisymmetric types, and discuss their relations to the conventional TEM (TM0) and TM1 modes. As the symmetric coupled plasmon mode is known to correspond to the TEM (TM0) mode, we find that the antisymmetric coupled surface plasmon mode is essentially related to the TM1 mode. The physical origin of an extraordinary propagation mode in a metallodielectric woodpile structure is investigated. It is proved that this allowed mode results from an equivalent Fabry-Perot cavity inherently presented in the woodpile. Our explanations are confirmed both by simulations and experimental data. We examine the resonance orders of surface plasmons in 2-D MHAs using the finite-difference time-domain method and describe how the electromagnetic intensity is built up at resonance in both space and time. The evanescent-tunneling mode profile in subwavelength cylindrical holes is demonstrated. Moreover, the polarization effect which ultimately decides the direction of the surface plasmon propagation is revealed. We demonstrate that the smoothness of the optical path can be used as a design criterion for omnidirectional antireflection coating profile. This concept is also used to explain the different performance between gradient-index pro‾les such as the Gausssian and Quintic profiles.

參考文獻


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