负折射率材料的基础研究
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摘要
负折射率材料(negative index materials，简称NIM)，又称“左手材料”(left-handed material，简称LHM)。指的是电磁波在这种特殊介质中传播时，波矢k、电场强度E和磁场强度H三者不再遵守右手定则k=E×H，而是遵守左手定则k=E×H，使得坡印廷矢量S的方向和波矢k的方向相反。当平面电磁波从一般的右手材料入射到左手材料中时，在左手材料内部会发生入射光线和折射光线位于法线同侧的现象，根据推广的Snell定律，可以认为左手材料的折射率为负值。负折射率材料体现出诸多的奇特性质，例如反常多普勒效应、反常切伦科夫辐射和反常古斯汉欣位移等。同时，由于负折射率材料可以用于制作突破衍射极限的理想透镜、新型天线、新型带隙材料和高密度光学存储器等，是近十年来光学、材料学以及微电子学等诸多学科的重点研究领域。目前，研究还处于起步阶段，由于在自然界中没有天然的负折射率材料，因此学术界研究的重点仍集中在如何设计和获得性能优越的负折射率材料上。
本文主要着眼于负折射率材料的基础理论研究，分为三个部分。第一部分研究了基于光子晶体以及类光子晶体结构的负折射率材料；第二部分基于天然的掺杂型锰钙钛矿材料，研究了此类材料在铁磁共振时的负折射特性。在外加磁场时，此类特殊材料在环境温度低于居里温度时体现金属特性，提供负的介电函数，铁磁共振时能得到负的磁导率，因而满足负折射率材料的要求；第三部分研究了反常多普勒效应，在国际上首次在光频段实验验证了负折射材料中的非相对论反常多普勒效应。
第一部分的研究内容包括：
1)利用理想的二维光子晶体，设计和研究了全角度等效折射率为-1的光子晶体平板透镜，研究了平板透镜的成像质量。
2)计算了更接近实际情况的有限高光子晶体平板的能带结构随高度的变化关系，研究结果表明，平板的高度能够对光子晶体的能带结构产生很大的影响，从而改变光子晶体的等效折射率。因此，在设计光子晶体平板透镜时要注意平板高度对折射率的影响，同时也可以利用这一点来设计所需的光子晶体负折射器件。
3)计算了不同外磁场下，磁流体光子晶体平板的能带结构，研究表明可以通过改变外磁场的强弱来调节光子晶体平板的等效负折射率，为设计和制作折射率可调的负折射率材料提供了一条新的思路。
第二部分的研究包括：
1)研究了电子强关联效应对掺杂型锰钙钛矿电子结构的影响，通过比较分析获得了合适的在位库仑能，为接下来的理论模拟工作铺平了道路。
2)通过计算eg电子带宽，研究了晶格结构对材料居里温度的影响，发现居里温度主要取决于材料的平均Mn-O-Mn键角的大小，受平均Mn-O键长的影响很小，并分析了成因，为后续的实验选材工作指明了方向。
3)理论计算了铁磁共振时材料的磁导率函数和介电函数，研究了等效磁导率和共振频率随外磁场的变化情况，发现通过调节外磁场，能够在很宽广的频率范围内实现负折射。同时还计算分析了此类材料在铁磁共振时的电磁波传播特性。为实验工作提供了理论依据。
第三部分的研究包括：
1)设计了易于制备且具有负折射特性的光子晶体棱镜，并对实际光子晶体棱镜的负折射特性进行了实验验证。
2)设计了反常多普勒效应的测量光路，得到了明确的判据来判断实验观测到的现象是否为反常多普勒效应，实验结果证明了负折射材料确实具有这种奇异的物理性质，在国际上首次观测到了光频段的反常多普勒现象。
In1968, Veselago showed theoretically that material with simultaneously negativeε and μ possess a number of unusual and often counterintuitive properties. If ε <0and μ <0, the vectors E, H and k form a “left-handed” triplet as k=E×H, andthe refractive index is negative using an extended snell's law, i.e. n=εμ. The caseis referred to as negative-index materials (NIMs) or “left-handed materials”(LHMs).The NIMs have shown many novel properties, such as inverse Doppler effects, inverse erenkov radiation and inverse Goos-H nchen shift, and have many potentialapplications in superlens, new type Antennas, band gap materials and high-densityoptical memory et al. So this field has attracted great attention in optics, materialsengineering and microelectronics for decade. Nevertheless, no materials with ε andμ being simultaneously negative had been found in nature or demonstratedexperimentally prior to the year2000. Until now, the most works focus on the problemof the NIMs how to realize.
The thesis is composed of three parts. In part one, the NIMs are achieved usingphotonic crystals (PCs), and the NIMs properties have been discussed in detail. In parttwo, the NIMs are achieved using doped perovskite oxides. Under magnetic field, thematerials show metal behavior below Curie temperature，i.e. Re ε <0. At the sametime, it can achieve Re μ <0during ferromagnetic resonance. The NIMs propertieshave been discussed in detail. In part three, we observed the inverse Doppler shift in aphotonic crystal (PC) prism for the first time, which has NIMs property at10.6μ mwavelength.
Part One:
1) A left-hand structure based on a two-dimensional (2D) PC with a negativerefractive index of–1has been proposed, and its imaging properties have beeninvestigated systematically.
2) Naturally, planar waveguides based on photonic crystals cannot be of infiniteheight, and guidelines for the design of finite-height waveguides are, therefore,important for the realization of planar photonic crystal waveguides. Thephotonic band structures of finite-height two-dimensional photonic crystal slabs have been calculations. The results show that the height of PC slabs playan important role on the band structures. It provides a new way to design theNIMs.
3) The model of tunable superparamagnetic photonic crystals self-assembled incolloidal magnetic fluids under externally applied magnetic fields isestablished. The photonic band structures of the guided modes propagating inthe PC slab have been calculated. The results that the tunable refractive indexmaterials can be achieved using magnetic fluids.
Part two:
1) The electronic structures of perovskite oxides were studied with the densityfunctional methods. Our calculations indicated that although the effects ofJahn-Teller distortion play a main role for getting the correct ground state, areasonable strong electron correlation correction is necessary for obtaining theexact band structure.3.5eV is a good choice for the on-site Coulombparameter U.
2) The correlations between structural effects and egbandwidth in hole-dopedmanganites were studied with the density functional methods. The calculationresults show that the bandwidth exhibits an oscillating behavior as the Mn-Odistances shorten, and the Mn-O-Mn angles play a major role in the bandwidthvariation in these materials.
3) The permeability and the permittivity of perovskite oxides were calculatedunder ferromagnetic resonance conditions. The negative refraction propertiesof the magnetic films have been discussed in detail.
Part three:
1) The PC prism, which has NIM property at10.6μm wavelength, has beendesigned. The experimental results show that the PC prism clearly exhibits anegative refraction behavior.
2) The experimental setup for detection of the inverse Doppler effect has beendesigned. A clear criterion has been found to clarify the normal and anomalousDoppler effects. The experimental result clearly indicates that the observedDoppler effect is anomalous, and the inverse Doppler effect has been explicitlyobserved at optical frequencies for the first time.
本文主要着眼于负折射率材料的基础理论研究，分为三个部分。第一部分研究了基于光子晶体以及类光子晶体结构的负折射率材料；第二部分基于天然的掺杂型锰钙钛矿材料，研究了此类材料在铁磁共振时的负折射特性。在外加磁场时，此类特殊材料在环境温度低于居里温度时体现金属特性，提供负的介电函数，铁磁共振时能得到负的磁导率，因而满足负折射率材料的要求；第三部分研究了反常多普勒效应，在国际上首次在光频段实验验证了负折射材料中的非相对论反常多普勒效应。
第一部分的研究内容包括：
1)利用理想的二维光子晶体，设计和研究了全角度等效折射率为-1的光子晶体平板透镜，研究了平板透镜的成像质量。
2)计算了更接近实际情况的有限高光子晶体平板的能带结构随高度的变化关系，研究结果表明，平板的高度能够对光子晶体的能带结构产生很大的影响，从而改变光子晶体的等效折射率。因此，在设计光子晶体平板透镜时要注意平板高度对折射率的影响，同时也可以利用这一点来设计所需的光子晶体负折射器件。
3)计算了不同外磁场下，磁流体光子晶体平板的能带结构，研究表明可以通过改变外磁场的强弱来调节光子晶体平板的等效负折射率，为设计和制作折射率可调的负折射率材料提供了一条新的思路。
第二部分的研究包括：
1)研究了电子强关联效应对掺杂型锰钙钛矿电子结构的影响，通过比较分析获得了合适的在位库仑能，为接下来的理论模拟工作铺平了道路。
2)通过计算eg电子带宽，研究了晶格结构对材料居里温度的影响，发现居里温度主要取决于材料的平均Mn-O-Mn键角的大小，受平均Mn-O键长的影响很小，并分析了成因，为后续的实验选材工作指明了方向。
3)理论计算了铁磁共振时材料的磁导率函数和介电函数，研究了等效磁导率和共振频率随外磁场的变化情况，发现通过调节外磁场，能够在很宽广的频率范围内实现负折射。同时还计算分析了此类材料在铁磁共振时的电磁波传播特性。为实验工作提供了理论依据。
第三部分的研究包括：
1)设计了易于制备且具有负折射特性的光子晶体棱镜，并对实际光子晶体棱镜的负折射特性进行了实验验证。
2)设计了反常多普勒效应的测量光路，得到了明确的判据来判断实验观测到的现象是否为反常多普勒效应，实验结果证明了负折射材料确实具有这种奇异的物理性质，在国际上首次观测到了光频段的反常多普勒现象。
In1968, Veselago showed theoretically that material with simultaneously negativeε and μ possess a number of unusual and often counterintuitive properties. If ε <0and μ <0, the vectors E, H and k form a “left-handed” triplet as k=E×H, andthe refractive index is negative using an extended snell's law, i.e. n=εμ. The caseis referred to as negative-index materials (NIMs) or “left-handed materials”(LHMs).The NIMs have shown many novel properties, such as inverse Doppler effects, inverse erenkov radiation and inverse Goos-H nchen shift, and have many potentialapplications in superlens, new type Antennas, band gap materials and high-densityoptical memory et al. So this field has attracted great attention in optics, materialsengineering and microelectronics for decade. Nevertheless, no materials with ε andμ being simultaneously negative had been found in nature or demonstratedexperimentally prior to the year2000. Until now, the most works focus on the problemof the NIMs how to realize.
The thesis is composed of three parts. In part one, the NIMs are achieved usingphotonic crystals (PCs), and the NIMs properties have been discussed in detail. In parttwo, the NIMs are achieved using doped perovskite oxides. Under magnetic field, thematerials show metal behavior below Curie temperature，i.e. Re ε <0. At the sametime, it can achieve Re μ <0during ferromagnetic resonance. The NIMs propertieshave been discussed in detail. In part three, we observed the inverse Doppler shift in aphotonic crystal (PC) prism for the first time, which has NIMs property at10.6μ mwavelength.
Part One:
1) A left-hand structure based on a two-dimensional (2D) PC with a negativerefractive index of–1has been proposed, and its imaging properties have beeninvestigated systematically.
2) Naturally, planar waveguides based on photonic crystals cannot be of infiniteheight, and guidelines for the design of finite-height waveguides are, therefore,important for the realization of planar photonic crystal waveguides. Thephotonic band structures of finite-height two-dimensional photonic crystal slabs have been calculations. The results show that the height of PC slabs playan important role on the band structures. It provides a new way to design theNIMs.
3) The model of tunable superparamagnetic photonic crystals self-assembled incolloidal magnetic fluids under externally applied magnetic fields isestablished. The photonic band structures of the guided modes propagating inthe PC slab have been calculated. The results that the tunable refractive indexmaterials can be achieved using magnetic fluids.
Part two:
1) The electronic structures of perovskite oxides were studied with the densityfunctional methods. Our calculations indicated that although the effects ofJahn-Teller distortion play a main role for getting the correct ground state, areasonable strong electron correlation correction is necessary for obtaining theexact band structure.3.5eV is a good choice for the on-site Coulombparameter U.
2) The correlations between structural effects and egbandwidth in hole-dopedmanganites were studied with the density functional methods. The calculationresults show that the bandwidth exhibits an oscillating behavior as the Mn-Odistances shorten, and the Mn-O-Mn angles play a major role in the bandwidthvariation in these materials.
3) The permeability and the permittivity of perovskite oxides were calculatedunder ferromagnetic resonance conditions. The negative refraction propertiesof the magnetic films have been discussed in detail.
Part three:
1) The PC prism, which has NIM property at10.6μm wavelength, has beendesigned. The experimental results show that the PC prism clearly exhibits anegative refraction behavior.
2) The experimental setup for detection of the inverse Doppler effect has beendesigned. A clear criterion has been found to clarify the normal and anomalousDoppler effects. The experimental result clearly indicates that the observedDoppler effect is anomalous, and the inverse Doppler effect has been explicitlyobserved at optical frequencies for the first time.
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