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基于FDTD的亚波长孔阵列金属薄膜光透射率研究

The Study of Optical Transmittance of Subwavelength Hole Arrays on Metallic Film by FDTD Numerical Method

作者: 专业:物理电子学 导师:王新林 年度:2011 学位:硕士  院校: 南华大学

Keywords

subwavelength hole array, extraordinary optical transmission, surface plasmon polaritons, finite difference time domain, direction of polarization

        Ebbesen等人在1998年首次在实验中观察到亚波长圆孔正方阵列金属薄膜的光超强透射(Extraordinary Optical Transmission, EOT)现象,并分析孔径、孔周期、薄膜厚度、金属类型和孔点阵类型等因素对孔阵列金属薄膜的透过率的影响。为了理解光超强透射现象的物理本质,人们对其进行了大量的实验和理论研究。普遍认为,孔阵列金属薄膜的EOT现象与表面等离子体激元(Surface Plasmon Polaritons, SPPs)效应紧密相关。本论文进一步探索亚波长孔阵列金属薄膜的EOT现象的物理机制,理解SPPs效应与光超强透射效应之间的联系,采用时域有效差分(Finite Difference Time Domain, FDTD)方法模拟超快激光脉冲垂直照射亚波长圆孔阵列金属薄膜的物理过程的电磁场分布。本文的主要包括以下内容:(1)表面等离子体激元是沿着金属表面传播的表面波,垂直于表面的电磁场分量按离表面的距离指数衰减。SPPs具有光场局域化和局域场增强等独特性能,在很多领域有其广泛的应用。并详细介绍电磁场的时域有限差分数值方法及吸收边界条件和周期性边界条件。(2)总结了描述色散金属的介电系数的Drude模型、Lorentz模型和Drude-Lorentzs模型三种模型,并介绍采用增加辅助变量及相应的辅助差分方程(additional (auxiliary) differential equation, ADE)的方法,把金属的色散特性引入到时域有限差分迭代方程中,得到不同的模型相应的FDTD离散迭代求解方法。(3)采用Drude模型描述金属银的介电系数,通过时域有限差分数值方法模拟飞秒激光脉冲通过孔阵列银薄膜相互作用后产生的电磁场分布,然后通过傅里叶变换求其透过率谱。主要计算了正方和正六角孔阵列的不同结构参数(孔径、孔周期、薄膜厚度)和入射光不同偏振方向对垂直入射到亚波长圆孔阵列银薄膜的透过率的影响,分析和讨论其物理过程,得到主要结论:1)孔周期决定透过率峰值位置,在孔径与孔周期之比为2/3附近时,其归一化透过率峰值表现为最大;2)孔阵列的透过率一般随着银薄膜厚度增大而逐渐减小;透过峰的宽度随柱状孔的纵横比(薄膜厚度与孔径之比(T/D))值变小而变宽;3)在正方阵列中,波长为孔周期处,孔阵列的透过率一般为极小值;4)亚波长圆孔正方阵列银薄膜的透过率不随着入射光偏振方向变化而变化,而亚波长圆孔正六角阵列银薄膜的透过率随着入射光偏振方向变化而变化,特别是在波长为孔周期处变化较大。
    The phenomenon of extraordinary light transmission (EOT) through metallic films perforated by subwavelength hole square arrays at optical frequencies was first observed by Ebbesen et al. in 1998. They tested the dependence on all the possible variables, such as hole diameter, periodicity, thickness, type of metal and type of lattice. To understand the physical origin of EOT phenomenon, lots of the experimental and theoretical works have been carried out. It is mostly considered that it’s be closely related to surface plasmon polaritons (SPPs) effect. In order to go forward to understand the underlying physical processes of EOT phenomenon in detail, we simulate ultrafast pulse incident on silver film with subwavelength hole arrays, and calculate the electric and magnetic field by finite difference time domain (FDTD) numerical method. The main work mainly includes as follow:(1) Surface plasmon polaritons modes are surface wave propagate along the metal/dielectric interface. The electromagnetic fields are confined to the surface and decay exponentially from the metal/dielectric interface. It also can enhance the local electromagnetic fields around interface. So there are various applications about it. Then, we introduce finite difference time domain (FDTD) numerical simulate method, absorbing boundary conditions, periodic boundary conditions, and so on.(2) We summarize three models which could describe the relative permittivity of metallic dispersion, such as Drude model, Lorentz model, Drude-Lorentzs model. We discuss the solution of Maxwell equation about metallic dispersion by adding an additional (auxiliary) differential equation between electric displacement density and polarization. (3) We use Drude model to describe the relative permittivity of silver’s dispersion, simulate femtosecond pulse incident on silver film perforated by subwavelength hole arrays by FDTD method, then we calculate transmittance spectra by Fourier transforming the electric and magnetic fields on a surface above the holes and constructing the surface integral of the outward Poynting vector. Our research on the transmittance of square array and hexagonal array, focus on the dependence on hole diameter, periodicity, thickness, type of lattice, and direction of polarization of incident light. In conclusion, 1) The periodicity of the array determines the position of the peaks; when the diameter of hole is about the 2/3 of periodicity, the peak of normalized transmittance is maximal. 2) The peaks decreases approximately with increasing of thickness; the width of peaks appears to widen as decresing the ratio (thickness divided by diameter, T/D) of cylindrical holes. 3) The normalized transmittance is minimal at the periodicity of array in square array. 4) The normalized transmittance of square array don’t vary with the direction of polarization of incident light, while the normalized transmittance of hexagonal array vary with the direction of polarization of incident light,especially when wavelength is the periodicity of array.
        

基于FDTD的亚波长孔阵列金属薄膜光透射率研究

摘要3-5
ABSTRACT5-6
第一章 绪论9-17
    1.1 简介表面等离子体及其应用9-12
    1.2 超强透射现象及物理机制12-15
    1.3 本论文的主要内容15-17
第二章 表面等离子体激元的基本性质和研究方法17-34
    2.1 表面等离子体的基本性质17-22
    2.2 表面等离子体激元的数值研究方法22-33
    2.3 本章小结33-34
第三章 色散金属的时域有限差分方法34-41
    3.1 金属介质的色散性质及模型34-37
    3.2 基于不同模型的时域有限差分求解方法37-40
    3.3 本章小论40-41
第四章 亚波长圆孔正方阵列银薄膜的光超强透射效应研究41-55
    4.1 孔正方阵列的透过率随着孔直径变化的研究44-46
    4.2 孔正方阵列的透过率随着薄膜厚度变化的研究46-48
    4.3 孔正方阵列的透过率随着入射光的偏振方向变化的研究48-54
    4.4 本章小结54-55
第五章 亚波长圆孔正六角阵列银薄膜的光超强透射效应研究55-74
    5.1 孔正六角阵列的透过率随着孔直径变化的研究57-59
    5.2 孔正六角阵列的透过率随着薄膜厚度变化的研究59-61
    5.3 孔正六角阵列的透过率随着孔周期和孔直径变化的研究61-63
    5.4 孔正六角阵列的透过率随着入射光不同偏振方向变化的研究63-71
    5.5 讨论与分析71-72
    5.6 本章小结72-74
第六章 论文总结与展望74-76
    6.1 研究工作总结与主要结论74
    6.2 有待进一步研究的内容及展望74-76
参考文献76-81
发表论文及参与科研情况81-82
致谢82
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