含有各向异性和手征性的特异材料的负折射及光束偏移效应研究
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摘要
特异材料（metamaterials）主要是指人工制备的复合材料，有着天然材料所不具备的超常物理性质。其中电磁特异材料具有巨大的调控光电信息潜力，新奇的物理现象和机制又使人们可以突破现有技术限制，开拓出崭新的应用前景。因此特异材料的制备、光学特性及其应用都是当前研究的热点。本文主要针对特异材料的负折射率的实现和基本的光学特性，研究了各向异性和手征性特异材料负折射的实现以及光束偏移效应。具体研究内容分以下几方面：
1.各向异性层状复合材料的负折射率的调控
虽然对各向异性特异材料的负折射问题，已经有众多的文献进行了讨论，但对于复合体系中，如何通过组分的浓度，入射频率等参数对实现负折射区域的调控却没有明确给出。我们就此开展了由各向同性金属材料和各向异性磁材料构成的层状结构中的负折射率问题的研究。利用传输矩阵法，获得长波极限下等效特异材料的有效介电张量和有效磁导率张量。为了实现具有负折射率的准左手材料（NI-QLHM）（即绝对准左手材料），探讨了磁性材料组分浓度、入射角以及入射频率对实现绝对准左手材料的频率区域的影响。结果显示了对于给定的磁性材料体积分数，在某一频率区域内可以实现等效复合材料的负折射率，并且存在一个优化的体积分数，使绝对准左手材料的频率区域最大化，另外通过改变入射频率可以实现准左手材料正负折射率之间的转换。
2.单轴各向异性特异材料的反射光束侧向偏移效应
对于各向异性特异材料中光束的侧向偏移效应，已经有研究表明各向异性材料的电磁参数、材料的吸收、平板厚度及入射角等会对侧向位移产生很大的影响，但所研究的各向异性特异材料的电磁参数既不是来自实际材料，也不能加以调控。而实验结果表明已经可以制备出能实现负折射的含有平行金属纳米线的各向异性特异材料。因此我们从实际材料出发，构建由金属纳米棒嵌入介电材料基质构成的单轴各向异性半无限特异材料体系，研究TM极化波入射情况下的反射光束的侧向位移。基于Bruggeman有效媒质理论，获得了实现负折射的依赖于入射波长λ和金属体积分数f的电磁参数条件。结果表明通过适当调整f和λ，可以获得特异材料的正或负折射率区域。然后利用稳态相位法得到含有吸收的各向异性特异材料的反射光束的GH位移表达式，探讨了f和λ对GH位移的影响。数值结果表明对于吸收较小的情况，GH位移在赝布儒斯特角附近得到增强，并可以通过λ来调控正折射率特异材料中增强的GH位移由负到正的转变；而通过f来调控负折射率特异材料中增强的GH位移由正到负的转变。当吸收较大时，GH位移将在掠入射时得到增强。高斯光束的数值模拟结果表明了只要入射光束足够宽，稳态相位法对各向异性的特异材料也是适用的。最后，通过COMSOL软件模拟了负折射率特异材料的反射光束在赝布儒斯特角附近的GH位移，直观而明确的证实了以上的分析。
3.手征特异平板材料反射光束在赝布儒斯特角附近的侧向偏移效应
通过对一般特异材料的研究，发现吸收、平板厚度以及入射角等参数都会对侧向位移产生很大的影响，而对手征特异材料中的侧向偏移效应只考虑了界面及材料无吸收的情况。因此对具有吸收的手征特异平板材料的侧向偏移效应的研究更具有实际意义。我们首先对任意极化入射光束在手征特异平板材料中的反射和透射特性进行了详细的推导，并利用角谱表象法推出了特殊线极化（TE）波入射时的反射光束中垂直和平行分量的侧向（GH）位移的近似表达式。通过比较正和负手征特异材料的GH位移，表明反射光束中的垂直和平行分量的侧向位移都在赝布儒斯特角附近得到增强，而负手征特异材料中的侧向位移的变化趋势与正手征特异材料相反。对于负手征特异材料，结果还显示了通过手征参数可以调控反射光束中垂直和平行分量的侧向位移的正负增强和增强峰的个数。同时平板厚度对侧向位移的影响还依赖于入射角，而手征特异材料中吸收的增加，将导致增强的侧向位移减小，相应的赝布儒斯特角消失。最后利用高斯光束进行了数值模拟，表明数值结果与理论结果基本符合，高斯光束越宽，与理论结果的差异越小。
4.手征特异平板材料中光自旋霍尔效应及自旋依赖的光束分离
考虑到光自旋霍尔效应（SHEL）的本质就是横向（IF）偏移，而之前对手征特异材料中的SHEL效应的研究都是针对SHEL中光束重心的横向偏移。因此我们将通过分析反射光束的RCP和LCP分量的空间横移来研究手征特异平板材料中光自旋霍尔效应（SHEL）及光束分离现象。首先建立以角谱表象为基础的波传播模型，将手征特异平板材料的反射和透射光束用自旋基矢（RCP和LCP）来表示，给出包含两个自旋依赖分量（RCP和LCP）的反射光束的空间横移的表达式，然后探讨手征特异平板材料的参数和入射高斯光束的极化态对空间横移的影响。结果显示了对于正和负手征材料，由SHEL引起的自旋分量的分离是不对称的，通过调整入射角可以实现自旋分量空间横移在赝布儒斯特角附近的正负值的调控，从而实现自旋霍尔效应的增强或抑制。同时适当调整手征特异平板材料的物理参数，如手征参数κ和平板厚度d等，可以获得SHEL的增强及两个自旋依赖分量的分离。结果显示了手征材料中对于特殊的线极化（TE和TM）波，也存在SHEL，这是一般材料所不具备的。另外通过调整入射光束的极化态，可以实现空间横移较大的正或负值以及正负值之间的转变，从而获得RCP和LCP反射分量的分离。这意味着我们的结果为调制SHEL提供了一个可行的路径。
Metamaterials are referred to as the composite material with artificial preparation,which exhibit superior physical properties not observed in the nature materials. Andelectromagnetic metamaterials have great potential for modulating the optoelectronicinformation and existing technical limitations can be broken through due to the novelphysical phenomena and mechanism. At this point, the preparation, optical characteristicsand application of the metamaterials are currently the research hotspot. In this thesis, wemainly aim at the realization and the optical characteristics of the metamatials, the negativerefraction and the beam deflection effect of the anisotropic and chiral metamaterials areinvestigated. The major contents and most important results of our work are listed asfollows:
1. Modulating the effective negative refraction in anisotropic layeredcomposites
The negative refraction of an anisotropic metamaterial has been investigated innumerous literatures, but for the composite system, it has not explicity given about how tomodulate the negative refraction by the volume fraction of the inclusion, the incidentfrequency and other parameters. In this regard, we investigate the characteristics ofelectromagnetic wave propagation in a two-component layered structure composed ofalternating isotropic metal material and anisotropic magnetic material. With transfer matrixmethod, effective permittivity and permeability tensors of the composite system arederived in the limit of long wavelength. For realizing the quasi-left-handed material withnegative refractive index, i.e., the absolute quasi-left-handed material, the influence of thevolume fraction of the magnetic material, the angle of incidence and the incident frequency are discussed. Numerical results show that for a given volume fraction of the magneticmaterial, the composite system behaves as an absolute quasi-left-handed material in acertain frequency region, and there exists an optimal volume fraction, at which the absolutequasi-left-handed frequency region has a maximal width. Moreover, the transition betweenpositive and negative index takes place by the adjustment of the incident frequency.
2. Lateral shift of the reflected wave through an uniaxial anisotropicmetamaterial
For the lateral shifts in the anisotropic metamaterial, the results of some researcheshave been shown that the lateral shifts will be affected by the electromagnetic parametersof anisotropic materials, the absorption of the material, the thickness of the slab and theangle of incidence. But in their studies, the electromagnetic parameters are not chosenfrom the actual material, and can not be modulated. However, the preparation of theanisotropic metamtereial containing parallel metallic nanowires has already been done inexperiment, which can exhibit negative refraction. Then we proceed from actual materials,consider a semi-infinite anisotropic metamaterial system consisting of aligned metallicnanowires in a dielectric matrix, and the lateral (Goos–H nchen, GH) shift of atransverse-magnetic (TM) wave reflected from the metamaterial is investigated. Based onBruggeman effective medium theory, we obtain the electromagnetic parameters conditionsfor realizing the negative refraction, which are dependent on both the incident wavelengthλ and the volume fraction of metallic inclusions f. The results show that the metamaterialwith positive or negative refraction can be obtained by suitable adjustment of λ and f. Nextthe expression of GH shift of the reflected beam is obtained with the stationary-phasemethod, and the influences of λ and f on the GH shift are discussed. It is shown that in thecase of weakly absorption, the GH shift can be enhanced near the pseudo-Brewster angle.Meanwhile, the transition from negative GH shift to the positive one can be realized byadjusting λ for the positive metamatrial, while the transition from positive GH shift to thenegative one can be realized by adjusting f for the positive metamatrial. As the absorptionis large, the GH shift will be enhanced at the close-to-grazing incidence. Numericalsimulations are performed for a Gaussian-shaped beam and the validity of the stationary-phase approach is demonstrated. In the end, by using COMSOL simulation, acomprehensive understanding is given and the above analysis is confirmed.
3. Lateral shifts near pseudo-Brewster dip on reflection from a chiralmetamateria slab
The research for the general metamaterial shows the GH shifts will be greatly affectedby the parameters, such as the absorption of the material, the thickness of the slab, and theangle of incidence. And for the chiral metamaterial, the GH shift is investigated only byconsidering the chiral interface and without absorption. In fact, it is more meaningful tostudy the GH shifts from a chrial metamaterial slab of lossy. The reflection andtransmission characteristic of arbitrarily polarized incident beam in chiral metamaterialslab are derived firstly. On the basis of angular spectrum representation, the formalismwith both perpendicular and parallel components of the reflected field is established tostudy the lateral (GH) shifts from a chiral slab of lossy for the transverse electric(TE)-polarized incident wave. By comparing the GH shifts in the negative and positivechiral metamaterial, the GH shifts can be enhanced near the pseudo-Brewster angle forboth the perpendicular and parallel components of the reflected beam, and the behavior ofthe GH shifts for a negative chiral slab is opposite to that for a positive chiral slab. For thenegative chiral slab, it also shows that the enhanced GH shifts with positive or negativevalue and the number of the enhanced peak can be adjusted by the chirality parameter forboth the perpendicular and parallel components of the reflected beam. Meanwhile, theinfluence of the thickness of the chiral slab on the GH shifts is also dependent on the angleof incidence. Moreover, in the presence of inevitable loss of the chiral slab, the enhancedlateral shifts will be decreased, and the pseudo-Brewster angle will disappearcorrespondingly. In the end, numerical simulation of a Gaussian-shaped beam shows thatthe wider the incident beams are, the smaller the discrepancy is.
4. Spin Hall Effect and spin-dependent split of light beam in a chiralmetamaterial slab
Since the essence of the Spin Hall Effect of light (SHEL) is the transverse (IF) shift,and special attention to the SHEL of the centers of the refrlected and refracted beams forthe chiral metamterial is paid. Then, the spin Hall Effect of light (SHEL) for the chiralmetamaterial slab is investigated by analyzing the spatial transverse shifts (TSs) of the twospin-dependent components of the reflected beam. A propagation model is establishedbased on the angular spectrum representation, and the expression is given to describe theIF shifts of the reflected beams composed of two circularly polarized components. Theinfluences of the parameters of the chiral slab and the polarization of the incident beam arediscussed. The results show that the two spin-dependent components are asymmetric dueto caused by SHEL, the positive and negative values of the transverse shifts of the twocomponents can be modulated near the pseudo Brewster angle by adjusting the angle ofincidence, and the SHEL can be enhanced or suppressed. Meanwhile, by adjusting theparameters of the chiral slab, such as the chirality parameterκ and the thickness of theslab d, the SHEL can be enhanced and the splitting of the two components. We also findthe SHEL exists in the chiral metamaterial for the special linear polarization (TE and TM)of the incident beam, which is not found in a general material. Moreover, the largenegative or positive IF shifts and the transition between them can be obtained by theadjustment of the polarization of the incident beam and the splitting of the twospin-dependent components can be obtained. It means that an opportunity will be providedto realize and control the transverse splitting of the light for the chiral metamaterial.
1.各向异性层状复合材料的负折射率的调控
虽然对各向异性特异材料的负折射问题，已经有众多的文献进行了讨论，但对于复合体系中，如何通过组分的浓度，入射频率等参数对实现负折射区域的调控却没有明确给出。我们就此开展了由各向同性金属材料和各向异性磁材料构成的层状结构中的负折射率问题的研究。利用传输矩阵法，获得长波极限下等效特异材料的有效介电张量和有效磁导率张量。为了实现具有负折射率的准左手材料（NI-QLHM）（即绝对准左手材料），探讨了磁性材料组分浓度、入射角以及入射频率对实现绝对准左手材料的频率区域的影响。结果显示了对于给定的磁性材料体积分数，在某一频率区域内可以实现等效复合材料的负折射率，并且存在一个优化的体积分数，使绝对准左手材料的频率区域最大化，另外通过改变入射频率可以实现准左手材料正负折射率之间的转换。
2.单轴各向异性特异材料的反射光束侧向偏移效应
对于各向异性特异材料中光束的侧向偏移效应，已经有研究表明各向异性材料的电磁参数、材料的吸收、平板厚度及入射角等会对侧向位移产生很大的影响，但所研究的各向异性特异材料的电磁参数既不是来自实际材料，也不能加以调控。而实验结果表明已经可以制备出能实现负折射的含有平行金属纳米线的各向异性特异材料。因此我们从实际材料出发，构建由金属纳米棒嵌入介电材料基质构成的单轴各向异性半无限特异材料体系，研究TM极化波入射情况下的反射光束的侧向位移。基于Bruggeman有效媒质理论，获得了实现负折射的依赖于入射波长λ和金属体积分数f的电磁参数条件。结果表明通过适当调整f和λ，可以获得特异材料的正或负折射率区域。然后利用稳态相位法得到含有吸收的各向异性特异材料的反射光束的GH位移表达式，探讨了f和λ对GH位移的影响。数值结果表明对于吸收较小的情况，GH位移在赝布儒斯特角附近得到增强，并可以通过λ来调控正折射率特异材料中增强的GH位移由负到正的转变；而通过f来调控负折射率特异材料中增强的GH位移由正到负的转变。当吸收较大时，GH位移将在掠入射时得到增强。高斯光束的数值模拟结果表明了只要入射光束足够宽，稳态相位法对各向异性的特异材料也是适用的。最后，通过COMSOL软件模拟了负折射率特异材料的反射光束在赝布儒斯特角附近的GH位移，直观而明确的证实了以上的分析。
3.手征特异平板材料反射光束在赝布儒斯特角附近的侧向偏移效应
通过对一般特异材料的研究，发现吸收、平板厚度以及入射角等参数都会对侧向位移产生很大的影响，而对手征特异材料中的侧向偏移效应只考虑了界面及材料无吸收的情况。因此对具有吸收的手征特异平板材料的侧向偏移效应的研究更具有实际意义。我们首先对任意极化入射光束在手征特异平板材料中的反射和透射特性进行了详细的推导，并利用角谱表象法推出了特殊线极化（TE）波入射时的反射光束中垂直和平行分量的侧向（GH）位移的近似表达式。通过比较正和负手征特异材料的GH位移，表明反射光束中的垂直和平行分量的侧向位移都在赝布儒斯特角附近得到增强，而负手征特异材料中的侧向位移的变化趋势与正手征特异材料相反。对于负手征特异材料，结果还显示了通过手征参数可以调控反射光束中垂直和平行分量的侧向位移的正负增强和增强峰的个数。同时平板厚度对侧向位移的影响还依赖于入射角，而手征特异材料中吸收的增加，将导致增强的侧向位移减小，相应的赝布儒斯特角消失。最后利用高斯光束进行了数值模拟，表明数值结果与理论结果基本符合，高斯光束越宽，与理论结果的差异越小。
4.手征特异平板材料中光自旋霍尔效应及自旋依赖的光束分离
考虑到光自旋霍尔效应（SHEL）的本质就是横向（IF）偏移，而之前对手征特异材料中的SHEL效应的研究都是针对SHEL中光束重心的横向偏移。因此我们将通过分析反射光束的RCP和LCP分量的空间横移来研究手征特异平板材料中光自旋霍尔效应（SHEL）及光束分离现象。首先建立以角谱表象为基础的波传播模型，将手征特异平板材料的反射和透射光束用自旋基矢（RCP和LCP）来表示，给出包含两个自旋依赖分量（RCP和LCP）的反射光束的空间横移的表达式，然后探讨手征特异平板材料的参数和入射高斯光束的极化态对空间横移的影响。结果显示了对于正和负手征材料，由SHEL引起的自旋分量的分离是不对称的，通过调整入射角可以实现自旋分量空间横移在赝布儒斯特角附近的正负值的调控，从而实现自旋霍尔效应的增强或抑制。同时适当调整手征特异平板材料的物理参数，如手征参数κ和平板厚度d等，可以获得SHEL的增强及两个自旋依赖分量的分离。结果显示了手征材料中对于特殊的线极化（TE和TM）波，也存在SHEL，这是一般材料所不具备的。另外通过调整入射光束的极化态，可以实现空间横移较大的正或负值以及正负值之间的转变，从而获得RCP和LCP反射分量的分离。这意味着我们的结果为调制SHEL提供了一个可行的路径。
Metamaterials are referred to as the composite material with artificial preparation,which exhibit superior physical properties not observed in the nature materials. Andelectromagnetic metamaterials have great potential for modulating the optoelectronicinformation and existing technical limitations can be broken through due to the novelphysical phenomena and mechanism. At this point, the preparation, optical characteristicsand application of the metamaterials are currently the research hotspot. In this thesis, wemainly aim at the realization and the optical characteristics of the metamatials, the negativerefraction and the beam deflection effect of the anisotropic and chiral metamaterials areinvestigated. The major contents and most important results of our work are listed asfollows:
1. Modulating the effective negative refraction in anisotropic layeredcomposites
The negative refraction of an anisotropic metamaterial has been investigated innumerous literatures, but for the composite system, it has not explicity given about how tomodulate the negative refraction by the volume fraction of the inclusion, the incidentfrequency and other parameters. In this regard, we investigate the characteristics ofelectromagnetic wave propagation in a two-component layered structure composed ofalternating isotropic metal material and anisotropic magnetic material. With transfer matrixmethod, effective permittivity and permeability tensors of the composite system arederived in the limit of long wavelength. For realizing the quasi-left-handed material withnegative refractive index, i.e., the absolute quasi-left-handed material, the influence of thevolume fraction of the magnetic material, the angle of incidence and the incident frequency are discussed. Numerical results show that for a given volume fraction of the magneticmaterial, the composite system behaves as an absolute quasi-left-handed material in acertain frequency region, and there exists an optimal volume fraction, at which the absolutequasi-left-handed frequency region has a maximal width. Moreover, the transition betweenpositive and negative index takes place by the adjustment of the incident frequency.
2. Lateral shift of the reflected wave through an uniaxial anisotropicmetamaterial
For the lateral shifts in the anisotropic metamaterial, the results of some researcheshave been shown that the lateral shifts will be affected by the electromagnetic parametersof anisotropic materials, the absorption of the material, the thickness of the slab and theangle of incidence. But in their studies, the electromagnetic parameters are not chosenfrom the actual material, and can not be modulated. However, the preparation of theanisotropic metamtereial containing parallel metallic nanowires has already been done inexperiment, which can exhibit negative refraction. Then we proceed from actual materials,consider a semi-infinite anisotropic metamaterial system consisting of aligned metallicnanowires in a dielectric matrix, and the lateral (Goos–H nchen, GH) shift of atransverse-magnetic (TM) wave reflected from the metamaterial is investigated. Based onBruggeman effective medium theory, we obtain the electromagnetic parameters conditionsfor realizing the negative refraction, which are dependent on both the incident wavelengthλ and the volume fraction of metallic inclusions f. The results show that the metamaterialwith positive or negative refraction can be obtained by suitable adjustment of λ and f. Nextthe expression of GH shift of the reflected beam is obtained with the stationary-phasemethod, and the influences of λ and f on the GH shift are discussed. It is shown that in thecase of weakly absorption, the GH shift can be enhanced near the pseudo-Brewster angle.Meanwhile, the transition from negative GH shift to the positive one can be realized byadjusting λ for the positive metamatrial, while the transition from positive GH shift to thenegative one can be realized by adjusting f for the positive metamatrial. As the absorptionis large, the GH shift will be enhanced at the close-to-grazing incidence. Numericalsimulations are performed for a Gaussian-shaped beam and the validity of the stationary-phase approach is demonstrated. In the end, by using COMSOL simulation, acomprehensive understanding is given and the above analysis is confirmed.
3. Lateral shifts near pseudo-Brewster dip on reflection from a chiralmetamateria slab
The research for the general metamaterial shows the GH shifts will be greatly affectedby the parameters, such as the absorption of the material, the thickness of the slab, and theangle of incidence. And for the chiral metamaterial, the GH shift is investigated only byconsidering the chiral interface and without absorption. In fact, it is more meaningful tostudy the GH shifts from a chrial metamaterial slab of lossy. The reflection andtransmission characteristic of arbitrarily polarized incident beam in chiral metamaterialslab are derived firstly. On the basis of angular spectrum representation, the formalismwith both perpendicular and parallel components of the reflected field is established tostudy the lateral (GH) shifts from a chiral slab of lossy for the transverse electric(TE)-polarized incident wave. By comparing the GH shifts in the negative and positivechiral metamaterial, the GH shifts can be enhanced near the pseudo-Brewster angle forboth the perpendicular and parallel components of the reflected beam, and the behavior ofthe GH shifts for a negative chiral slab is opposite to that for a positive chiral slab. For thenegative chiral slab, it also shows that the enhanced GH shifts with positive or negativevalue and the number of the enhanced peak can be adjusted by the chirality parameter forboth the perpendicular and parallel components of the reflected beam. Meanwhile, theinfluence of the thickness of the chiral slab on the GH shifts is also dependent on the angleof incidence. Moreover, in the presence of inevitable loss of the chiral slab, the enhancedlateral shifts will be decreased, and the pseudo-Brewster angle will disappearcorrespondingly. In the end, numerical simulation of a Gaussian-shaped beam shows thatthe wider the incident beams are, the smaller the discrepancy is.
4. Spin Hall Effect and spin-dependent split of light beam in a chiralmetamaterial slab
Since the essence of the Spin Hall Effect of light (SHEL) is the transverse (IF) shift,and special attention to the SHEL of the centers of the refrlected and refracted beams forthe chiral metamterial is paid. Then, the spin Hall Effect of light (SHEL) for the chiralmetamaterial slab is investigated by analyzing the spatial transverse shifts (TSs) of the twospin-dependent components of the reflected beam. A propagation model is establishedbased on the angular spectrum representation, and the expression is given to describe theIF shifts of the reflected beams composed of two circularly polarized components. Theinfluences of the parameters of the chiral slab and the polarization of the incident beam arediscussed. The results show that the two spin-dependent components are asymmetric dueto caused by SHEL, the positive and negative values of the transverse shifts of the twocomponents can be modulated near the pseudo Brewster angle by adjusting the angle ofincidence, and the SHEL can be enhanced or suppressed. Meanwhile, by adjusting theparameters of the chiral slab, such as the chirality parameterκ and the thickness of theslab d, the SHEL can be enhanced and the splitting of the two components. We also findthe SHEL exists in the chiral metamaterial for the special linear polarization (TE and TM)of the incident beam, which is not found in a general material. Moreover, the largenegative or positive IF shifts and the transition between them can be obtained by theadjustment of the polarization of the incident beam and the splitting of the twospin-dependent components can be obtained. It means that an opportunity will be providedto realize and control the transverse splitting of the light for the chiral metamaterial.
引文
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