基于表面等離子體的MIM波導(dǎo)的色散特性研究

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摘要 表面等離子體激元( Surface Plasmon Polaritons , SPPs)是光和金屬表面的自由電子相互作用所引起的一種電磁波模式。它能夠在亞波長(zhǎng)尺度內(nèi)沿著金屬-介質(zhì)表面?zhèn)鞑?，利用SPPs與光的相互作用我們可以主動(dòng)控制光的傳播，因此表面等離子體激元被廣泛應(yīng)用于納米光學(xué)，它對(duì)實(shí)現(xiàn)納米光學(xué)集成元件有著巨大的推動(dòng)作用，是近年來人們研究的熱點(diǎn)。在許許多多的表面等離子體波導(dǎo)結(jié)構(gòu)中，金屬-介質(zhì)-金屬（Metal Insulator Metal, MIM)是一種有眾多優(yōu)點(diǎn)備受關(guān)注的波導(dǎo)結(jié)構(gòu)，它結(jié)構(gòu)緊湊，體積小，集成度高，因而十分方便用于集成光學(xué)回路中。
本文中，我們理論分析了表面等離子體激元的色散關(guān)系以及其關(guān)鍵參數(shù)，了解其傳輸特性和研究意義，推導(dǎo)得到SPPs的關(guān)鍵參數(shù)。接下來，我們采用基于有限元法的COMSOL4.4軟件，通過Drude理論建立了MIM的表面等立體波導(dǎo)，并模擬了MIM結(jié)構(gòu)中光傳播的色散關(guān)系，得到了電磁波傳輸?shù)哪芰糠植紙D。為了進(jìn)一步了解MIM結(jié)構(gòu)中等離子體波的色散關(guān)系，我們先研究SPP在半無限長(zhǎng)金屬-介質(zhì)界面的傳輸模式，通過公式推導(dǎo)可知，該結(jié)構(gòu)中不存在TE模，SPP是以TM模的形式存在的表面電磁波。此外，我們?cè)谏㈥P(guān)系的基礎(chǔ)上求解了群速度、群速度色散。設(shè)定波導(dǎo)一定參數(shù)后，我們選取恰當(dāng)?shù)念l率點(diǎn)，優(yōu)化參數(shù)，達(dá)到最好的傳輸效果。我們的目的是保持慢群速度效應(yīng)的同時(shí)，也能抑制相應(yīng)群速度色散的特性，也就是在保證不產(chǎn)生破壞性失真的前提下可以應(yīng)用傳輸光信號(hào)。
由于金屬對(duì)光波有較強(qiáng)的吸收能力，因此即使MIM結(jié)構(gòu)能將電磁場(chǎng)約束在亞波長(zhǎng)尺寸內(nèi)，但是在光的傳播過程中將會(huì)產(chǎn)生巨大損耗。基于表面等離子體的研究還有很大的發(fā)展空間，這些研究工作將會(huì)極大推動(dòng)納米光學(xué)的發(fā)展。
關(guān)鍵詞：表面等離子體，金屬-介質(zhì)-金屬，色散關(guān)系，波導(dǎo)



Research on the dispersion properties of surface plasmon MIM waveguide
Abstract surface plasmon polaritons (SPPs) is an electromagnetic wave pattern caused by the interaction of light and free electron metal surface.It can spread along in a subwavelength scale on metal - dielectric surface , we can actively control the propagation of light by using the interaction of SPPs and light.Therefore, surface plasmons are widely used in nano-optics, it plays a huge role in promoting the development nano-optical integrated components ,it has been the research hotspot in recent years.during so many surface plasmon waveguide structures, the metal - dielectric - metal (MIM) waveguide has been concerned since his advantages including compact, small size, high integration, which is very convenient for integrated optical circuits.
In this paper, we analyze the theory of surface plasmon dispersion relation of plasma and its characteristic length, understand its transmission characteristics and significance, and key parameters of SPPs was derived. Next, we discuss the light propagation mode of MIM structure waveguide ,and establish the Drude model to get the dielectric constant of the metal in the form of the free electrons inside the reaction under the electromagnetic effect. To further understand the plasma wave structure , we first study transfer mode of the SPP in the semi-infinite metal - dielectric interface, by formula derivation shows that the TE mode does not exist in the structure , SPP is a kind of surface electromagnetic wave existing in the form of TM mode , we can obtain the formula of dispersion relation about SPP on the metal surface by solving the boundary conditions. We use COMSOL4.4 based on the finite element method and dispersion relation between dispersion relation in the MIM ,group velocity and group velocity dispersioncan be solved through the software . After setting the waveguide certain parameters, we select the appropriate frequency to achieve the best results. Our aim is to keep the effects of the slow group velocity, but also can restrain the characteristics of group velocity dispersion , that is, we can transform optical signals at slow group velocities under the premise of ensuring no destructive distortion.

Since the strong light absorption capacity of metal , even if the MIM structure waveguide can restrain electromagnetic field in subwavelength size, but a great loss will be produced during the transmission of light . There is still much room for development of research based on surface plasmons , these studies will greatly promote the development of nano-optics.
Keyword: Surface plasmon polaritons, Metal Insulator Metal，Dispersion relation，Waveguide




目錄
緒論 1
第一章 表面等離子體激元 3
1.1 等離子體簡(jiǎn)介 3
1.2 表面等離子體激元概念 3
1.3 表面等離子體激元的關(guān)鍵參數(shù) 5
第二章 慢光理論 7
2.1 基本概念 7
2.2 研究現(xiàn)狀與前景 9
第三章 表面等離子體波導(dǎo)結(jié)構(gòu)介紹 11
3.1 金屬的光學(xué)特性 11
3.2 MIM結(jié)構(gòu)介紹 13
3.3 MIM中波的傳輸模式 15
第四章 數(shù)值仿真 16
4.1 Drude模型 16
4.2 表面等離子體激元的色散關(guān)系 20
4.3 基于有限元的Comsol軟件的介紹 23
4.4 MIM模型的建立和分析 26
4.4.1 MIM模型的建立 26
4.4.2 色散關(guān)系求解和分析 27
4.4.3 MIM（Au）的群速度 28
4.4.4 MIM（Au）的共振能量分布和諧振腔性質(zhì) 28
4.4.5 MIM波導(dǎo)（Ag）內(nèi)的能量分布 29
第五章 總結(jié) 31
致謝 32
參考文獻(xiàn) 33