【作者】 王茂琰；

【导师】 徐军； 吴健；

【作者基本信息】 电子科技大学 ， 无线电物理， 2008， 博士

【摘要】 自2001年Smith D R等人根据Pendry J B等的研究结果，首次构造出介电系数ε和磁导系数μ同时为负的人工异向介质以来，对异向介质的研究已经成为国际学术界一个引人注目的前沿领域。本论文用时域有限差分(FDTD：Finite-Difference Time-Domain)方法和Mie级数方法对电磁波在异向介质中的传播和散射特性进行了理论上的深入研究，探讨其在隐身和波束分离器等各种工程中的应用。本文主要内容为：1．理论和实验研究了基本结构偏移、切割、旋转对异向介质传输特性的影响。比较了提取的标准和偏移后的异向介质有效介质参数，结果表明：偏移使左手透射峰峰值降低，通带带宽减小；若将组成异向介质的结构单元旋转，完整的左手透射峰将不复存在；不同方向的切割会不同程度的改变异向介质透射峰的性质。2．基于Mie级数解研究了金属球被异向介质覆盖的散射。推导了可以用于计算单层和双层均匀色散介质球电磁散射的Mie级数解。比较了金属球被异向介质和铁氧体覆盖的散射，Mie级数解计算结果表明：覆盖层异向介质不同介质组合对金属球后向散射截面有一定影响。3．引入磁色散，推导了基于辅助差分(ADE：Auxiliary Differential Equation)和移位算子(SO：Shift Operator)的FDTD方法。用极化和磁化等离子体Drude和Lorentz模型来模拟异向介质，将μ表示以jω为自变量的Pad(?)近似，用(?)／(?)t代替jω，过渡到时域，再引入离散时域移位算子代替时间微分算子来处理μ，进而推导出SO-FDTD方法计算中磁感应强度B和磁场强度H之间的关系。推导了描述异向介质场与流的微分方程组，将其离散得到二维ADE-FDTD递推表达式。FDTD方法数值计算表明：(i)．异向介质覆盖层较大地减少金属柱后向和小双站角范围内的散射能量，而对前向和大双站角范围的散射则基本起增强作用。(ii)．一般而言，随着覆盖层异向介质中等离子体频率、等离子体碰撞频率、异向介质厚度的增加，金属柱的后向散射逐渐减小。(iii)．异向介质的匹配和各向同性的程度对金属球的后向散射有着重要的影响。适当选取异向介质参数，可以使异向介质包层能有效地减小目标的雷达回波。探讨了异向介质在隐身方面的应用。4．用FDTD方法仿真高斯波束在异向介质中的传播。首先模拟了高斯波束在各向同性异向介质板中的会聚效应、负折射、相位补偿、平凹透镜成像；ADE-FDTD方法数值结果得到：各向异性异向介质(AMM：anisotropic metamaterial)板的相对磁导系数μ_x决定波矢量是正常还是反常折射，而μ_z决定能流发生了正折射还是负折射，AMM板中波矢量和能流不总是平行或反平行；最后用SO-FDTD方法分析了多层结构中AMM参数对激励产生的前向、后向表面波和导波方向的影响。探讨异向介质在谐振器、透镜成像、波束分离器、线偏振器、固体光谱学等中的应用。更多还原

【Abstract】 Since Smith D R et al.fabricated metamaterials whose permittivityεandpermeabilityμare negative by using Pendry J B et al.’s theoretical results for the firsttime in 2001,the study of metamaterials has become a conspicuous front field in theinternational science field.In this thesis,the electromagnetic (EM) wave propagation and scattering inmetamaterials are investigated with finite-difference time-domain (FDTD) method andMie series method.The applications of metamaterials in cloak and beam splitter et al.are discussed.The main results in the paper are as follows:1.The effects caused by disorder,cutting and rotating in transmissioncharacteristic of metamaterials are investigated in theory and experiments.Theextracted real parts of the permittivity,permeability and index of refraction for thestandard metamaterials are compared with those for disorder metamaterials.It is foundthat the disorder on the split ring resonators results in a lower left-handed transmissionand narrower pass bands.The left-handed transmission peak disappears when the cellsof metamaterials are rotated.The cuts of metamaterials in different directions destroythe properties of metamaterials in different degrees.2.The scattering of metallic sphere coated by metamaterials based on Mie seriessolution is studied.Mie series formulas for EM scattering of one-layer and two-layerhomogeneous dispersive media spheres are derived.The scattering of metallic spherecoated by metamaterials or ferrite is compared.Results of Mie series solution show thatthe different material parameters of metamaterials play an important part in thebackward radar cross section (RCS) of metallic sphere.3.By introducing magnetic dispersion,the auxiliary differential equation (ADE)method and shift operator (SO) method in FDTD method for metamaterials are derived.Lossy Drude and Lorentz polarization and magnetization models are used to simulatemetamaterials.The permeabilityμof metamaterials may be described by Pad(?)approximation in jω.Jωis then replaced by (?)/(?)t.By introducing z_t defined as a shift operator,the relation between B and H in SO-FDTD method is derived.We deduce thedifferential equations that describe characters of electromagnetic wave in metamaterials.We obtain two-dimension ADE-FDTD formulation for metamaterials by dispersing theequations.Numerical results of FDTD method show that (i),Though metamaterialsmake the scattering of backward and little bistatic angles decrease,the scattering offorward and big bistatic angles increase inversely.(ii),Generally speaking,the increaseof metamaterials’plasma frequency,damping frequency,and depth leads to the decreaseof RCS of metallic column.And (iii),The degree of metamaterials’ match and isotropyplays important parts in the decrease of the back scattering of the metallic sphere.Witha careful selection of metamaterials’ parameters,the echo of radar targets can beeffectively decreased.The application of metamaterials in cloak is discussed.4.Wave propagation in metamaterials is simulated with FDTD method.Firstly,theinteraction between Gaussian beam and isotropic metamaterials slab is simulated,suchas negative index,phase compensation,piano-concave lens imaging.Then thenumerical results of ADE-FDTD method show that the sign ofx component of relativepermeability tensor of anisotropic metamaterials (AMM) determines the refraction isregular or anomalous,whereas the sign of z component of relative permeability tensorof AMM determines the energy flow is positively refracted or negatively refracted.Thewave vector and energy flow density in AMM are not always parallel or antiparallel.Finally,the directions of the forward and backward surface and guided wave excitedinfluenced by the material parameters of AMM in multi-layered structures are analyzedwith SO-FDTD method.Their applications of metamaterials in resonator,lens imaging,beam splitter,linear polarizer,solid-state spectroscopy et al.are discussed.更多还原