运动特异电磁介质的物性研究
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摘要
光是生命的能量之源,可以说没有光就没有现在的自然界。光是如此重要,但是人类对光的认识却一直各持己见。1864年,麦克斯韦建立起电磁场的系统理论,且指出：光也是电磁波的一种形式,随后这一论断被很多实验所证实,至此,人们才对光有了进一步的认识。人们认识光其实是为了更好地调控光,为人类的生活提供更多的便捷,从麦克斯韦的系统理论(麦克斯韦方程)中可以看出,我们可以借助两个电磁参量(介电常数ε和磁导率μ)有效地调节光使其沿着我们需要的方式而发展。当明白这些事情后,我们却失望地发现自然界提供给我们的ε和μ实在太少了,比如有些材料满足(ε<0,μ>0),如光频段的金属；比如有些材料满足(ε>0,μ>0),如常规的介电材料；当然也有些材料可以在微波段实现μ<0,如铁磁材料,但这些材料不仅损耗很大,而且无法推到光频,可见,自然界给我们提供的材料是很有限的,根本无法满足人类的需要。1968年,前苏联物理学家V. G. Veselago从理论上提出了对于一种材料同时具有负的介电常数ε和负的磁导率μ,而且还预言了这种材料里所具有的很多奇异效应。V. G. Veselago的这一独特想法几十年来一直没有引起人们的关注,直到上个世纪90年代,英国物理学家J. B. Pendry提出可以利用有限长的金属棒实现负的介电常数ε,利用金属开口圆环实现负的磁导率μ,结合这两种结构作为最小的材料单元,可以实现在微波段介电常数ε和磁导率μ同时为负的材料,随后不久这一思想就被来自美国的科学家D.R. Smith等人用实验证实。至此,人们才逐渐意识到利用比波长小很多的结构单元来调控光的潜力,而这一方向则渐渐地发展成为一个全新的研究领域,通常称为Metamaterial,中文意为特异材料,或超材料。顾名思义,这种材料不同于自然界的一些已有材料,他的出现使得人们对光的调控能力有了很大的提升,很多奇异的物理效应也都在这种人工材料中实现,如反多普勒效应和反切伦科夫效应等等。本篇论文将在第一章中粗略地介绍人工电磁特异材料的研究进展和当前的一些研究热点。
特异材料具有很多自然材料难以比拟的优点,比如它与常规材料组成的界面可以呈现负折射现象,它作为棱镜可以成一个打破衍射极限的像等。但这方面的很多工作都是在静止体系中进行的,如果我们考虑把一块特异介质平板置于运动体系,那么会有什么新奇的现象呢?当然,我们首先想到的就是多普勒效应,在研究中我们发现当把源和接受器都置于负折射率介质平板的表面,当它们运动时,接受器接受到的信号非常之奇怪,除了一个峰可以和经典的多普勒信号相对应外,还有其它几个峰完全出乎我们的意料,同时,我们也研究了这几个奇异的峰和源的工作频率以及相互运动速度之间的关系,最后,我们发现这几个奇异的峰是源与平板的表面波相互作用引起的。在论文的第二章,我们基于四维时空的洛伦兹变换和格林函数理论,发展了一套可以用来解决运动体系光学性质的严格方法；接着在论文的第三章中我们就运用此方法,详细讨论运动体系中负折射率介质平板相关的光学现象,我们不仅可以处理上述的奇异多普勒效应,还可以研究运动负折射介质平板的超成像效果,研究中我们发现运动平板较之静止平板成像的效果发生明显的变化,通过对比两种情况下板的表面波色散关系,我们发现运动平板的表面波色散关系会发生明显地扭曲,使得在像点收集到的瞬态波的成分发生很大的变化,直接导致像的质量改变。
手征材料的本构关系不同于一般材料的本构关系,手征材料中电和磁的分量是有效地耦合在一起的,在其中传播电磁波的电/磁分量不仅可以诱发体系的电/磁极化,同时也可以诱发体系的磁/电极化。由于在实验上要实现负折射,需要制造一个介电常数和磁导率同时为负的材料,具有一定的难度,特别在光频段更加难以实现；但是利用手征材料我们就可以降低实现负折射的难度,因此引起了部分科学家的兴趣。在论文的第四章,我们就研究金属开口圆环的手征特性,发现以此为共振单元形成材料的手征参量具有非对角项。之前关于手征材料的很多研究都只关心手征参量的对角项,那么这个非对角项对电磁波具有怎样的调控作用呢?通过研究我们发现,线偏振电磁波在此体系的界面发生折射时会发生双折射现象,特别之处在于,其中一束折射光仍为线偏振,另一束则为椭圆偏振,这和传统的双折射有很大的不同,最后我们还用全波模拟看到了这种双折射现象。
论文的第五章,我会对整篇论文进行一个简短的总结和回顾。
Light is the energy source of the lives. We may say that there aren't nowadays na-ture without light. Light is so important to us, but human always have different views on the light. In 1864, Maxwell founded the electromagnetical theory. He pointed out that the light is a kind of electromagnetic waves, and then this prediction was proved by the experiment. Thus people understood the light clearer. People aim to manipu-late the light as understanding them, so it can give us more convenience. According to the Maxwell's equations we can find there are two parameters permittivityεand permeabilityμ, which can be used to manipulate the light efficiently. However, we despairingly found that the nature gave us so few materials. For example, there are some materials withε< 0,μ> 0, like metal, and some materials withε> 0,μ> 0, like the dielectrics. Also there are some materials withμ< 0, like ferromagnetic, but they have very large loss and a very narrow band width. Obviously, the nature gives us so few materials and can't supply the demand of human. In 1968, V. G. Veselago, a physicist from Union of Soviet Socialist Republics, in theory presented the materials with both negativeεand negativeμ, and he predicted there were many anomalous effects in these materials. This idea haven't attracted many attentions for many years. Until 90th in last century, J. B. Pendry, a physicist from England, presented that we can realize negativeεbased on finite metallic wires and negativeμbased on the split metallic rings. Combining these two units we can get both negative materials in micro wave region, and soon this idea was proved by an experiment which was carried out by American physicist D. R. Smith. So people understood the capabilities of manipu-lation light based on these subwavelength structures. This direction opens up as a new research region named Metamaterials. Different from the natural materials, this kind of materials can improve the human's abilities of manipulating light and many anom-alous effects can be realized in them, such as reversed Doppler effects and reversed Cerenkov effects. In the first chapter of this thesis, I will give a simple introduction on the progress of metamaterials research and some research hot recently.
Metamaterials have some advantages comparing with natural materials, such as negative refraction, and a metamaterial slab can be a super lens. However, almost all the researches are presented in the static environment. So if we put a metamaterial slab in a moving environment what will happen? Of course, we first think the Doppler effects. When both the source and receiver were putted near the surface of the slab and were moving, and then we found the received signals are very novel. Except one peak corresponding to the classical Doppler effect, other peaks were totally out of our imagination. We also got the relation between these anomalous peaks and the work-ing frequencies of source, and the velocities of them. At last we found these peaks result from the interaction between the source and surface waves of the slab. In the sec-ond chapter of this thesis, based on 4D Lorentz transformation, we present a rigorous Green's function approach which can be applied to solve movement-based problem.In the third chapter of this thesis, we discuss in detail the optical phenomena related to a moving metamaterial slab. We can deal with the above anomalous Doppler effects based on such approach, furthermore also can treat the super lensing effects of a mov-ing metamaterial slab. Comparing with the static slab, we found the image resolution change much. It was originated from the surface wave dispersion distortion when the slab was moving. This can directly cause the changing of image point collecting surface wave components.
The constitutive relations of chiral media are different from the traditional materials. The electric and magnetic components are coupling together in chiral media. When the electromagnetic waves are propagating in them, the electric (magnetic) field can induce both the electric (magnetic) polarization and magnetic (electric) polarization. As the realization of negative refraction, we need to create the material with both negativeεand negativeμsimultaneously. Actually, it's difficult to do especially in optical region. However, based on chiral media, we can reduce the difficulties, and this point attracted many attentions. In the fourth chapter of this thesis, we will discuss the chiral properties of the metallic split rings. We found the chirality parameter of such metallic split rings based materials can have off diagonal terms. Many researches only focused on the diagonal terms of chirality parameter, so what's new phenomena will occur in such media? We studied the refraction properties between air and such media. There was double refraction, but different from other double refraction, one refracted wave is linearly polarized and another is longitudinal elliptically polarized. At last, based on the full wave simulation, we predicted this effect.
In the fifth chapter of this thesis,1 will give a simple conclusion.
特异材料具有很多自然材料难以比拟的优点,比如它与常规材料组成的界面可以呈现负折射现象,它作为棱镜可以成一个打破衍射极限的像等。但这方面的很多工作都是在静止体系中进行的,如果我们考虑把一块特异介质平板置于运动体系,那么会有什么新奇的现象呢?当然,我们首先想到的就是多普勒效应,在研究中我们发现当把源和接受器都置于负折射率介质平板的表面,当它们运动时,接受器接受到的信号非常之奇怪,除了一个峰可以和经典的多普勒信号相对应外,还有其它几个峰完全出乎我们的意料,同时,我们也研究了这几个奇异的峰和源的工作频率以及相互运动速度之间的关系,最后,我们发现这几个奇异的峰是源与平板的表面波相互作用引起的。在论文的第二章,我们基于四维时空的洛伦兹变换和格林函数理论,发展了一套可以用来解决运动体系光学性质的严格方法；接着在论文的第三章中我们就运用此方法,详细讨论运动体系中负折射率介质平板相关的光学现象,我们不仅可以处理上述的奇异多普勒效应,还可以研究运动负折射介质平板的超成像效果,研究中我们发现运动平板较之静止平板成像的效果发生明显的变化,通过对比两种情况下板的表面波色散关系,我们发现运动平板的表面波色散关系会发生明显地扭曲,使得在像点收集到的瞬态波的成分发生很大的变化,直接导致像的质量改变。
手征材料的本构关系不同于一般材料的本构关系,手征材料中电和磁的分量是有效地耦合在一起的,在其中传播电磁波的电/磁分量不仅可以诱发体系的电/磁极化,同时也可以诱发体系的磁/电极化。由于在实验上要实现负折射,需要制造一个介电常数和磁导率同时为负的材料,具有一定的难度,特别在光频段更加难以实现；但是利用手征材料我们就可以降低实现负折射的难度,因此引起了部分科学家的兴趣。在论文的第四章,我们就研究金属开口圆环的手征特性,发现以此为共振单元形成材料的手征参量具有非对角项。之前关于手征材料的很多研究都只关心手征参量的对角项,那么这个非对角项对电磁波具有怎样的调控作用呢?通过研究我们发现,线偏振电磁波在此体系的界面发生折射时会发生双折射现象,特别之处在于,其中一束折射光仍为线偏振,另一束则为椭圆偏振,这和传统的双折射有很大的不同,最后我们还用全波模拟看到了这种双折射现象。
论文的第五章,我会对整篇论文进行一个简短的总结和回顾。
Light is the energy source of the lives. We may say that there aren't nowadays na-ture without light. Light is so important to us, but human always have different views on the light. In 1864, Maxwell founded the electromagnetical theory. He pointed out that the light is a kind of electromagnetic waves, and then this prediction was proved by the experiment. Thus people understood the light clearer. People aim to manipu-late the light as understanding them, so it can give us more convenience. According to the Maxwell's equations we can find there are two parameters permittivityεand permeabilityμ, which can be used to manipulate the light efficiently. However, we despairingly found that the nature gave us so few materials. For example, there are some materials withε< 0,μ> 0, like metal, and some materials withε> 0,μ> 0, like the dielectrics. Also there are some materials withμ< 0, like ferromagnetic, but they have very large loss and a very narrow band width. Obviously, the nature gives us so few materials and can't supply the demand of human. In 1968, V. G. Veselago, a physicist from Union of Soviet Socialist Republics, in theory presented the materials with both negativeεand negativeμ, and he predicted there were many anomalous effects in these materials. This idea haven't attracted many attentions for many years. Until 90th in last century, J. B. Pendry, a physicist from England, presented that we can realize negativeεbased on finite metallic wires and negativeμbased on the split metallic rings. Combining these two units we can get both negative materials in micro wave region, and soon this idea was proved by an experiment which was carried out by American physicist D. R. Smith. So people understood the capabilities of manipu-lation light based on these subwavelength structures. This direction opens up as a new research region named Metamaterials. Different from the natural materials, this kind of materials can improve the human's abilities of manipulating light and many anom-alous effects can be realized in them, such as reversed Doppler effects and reversed Cerenkov effects. In the first chapter of this thesis, I will give a simple introduction on the progress of metamaterials research and some research hot recently.
Metamaterials have some advantages comparing with natural materials, such as negative refraction, and a metamaterial slab can be a super lens. However, almost all the researches are presented in the static environment. So if we put a metamaterial slab in a moving environment what will happen? Of course, we first think the Doppler effects. When both the source and receiver were putted near the surface of the slab and were moving, and then we found the received signals are very novel. Except one peak corresponding to the classical Doppler effect, other peaks were totally out of our imagination. We also got the relation between these anomalous peaks and the work-ing frequencies of source, and the velocities of them. At last we found these peaks result from the interaction between the source and surface waves of the slab. In the sec-ond chapter of this thesis, based on 4D Lorentz transformation, we present a rigorous Green's function approach which can be applied to solve movement-based problem.In the third chapter of this thesis, we discuss in detail the optical phenomena related to a moving metamaterial slab. We can deal with the above anomalous Doppler effects based on such approach, furthermore also can treat the super lensing effects of a mov-ing metamaterial slab. Comparing with the static slab, we found the image resolution change much. It was originated from the surface wave dispersion distortion when the slab was moving. This can directly cause the changing of image point collecting surface wave components.
The constitutive relations of chiral media are different from the traditional materials. The electric and magnetic components are coupling together in chiral media. When the electromagnetic waves are propagating in them, the electric (magnetic) field can induce both the electric (magnetic) polarization and magnetic (electric) polarization. As the realization of negative refraction, we need to create the material with both negativeεand negativeμsimultaneously. Actually, it's difficult to do especially in optical region. However, based on chiral media, we can reduce the difficulties, and this point attracted many attentions. In the fourth chapter of this thesis, we will discuss the chiral properties of the metallic split rings. We found the chirality parameter of such metallic split rings based materials can have off diagonal terms. Many researches only focused on the diagonal terms of chirality parameter, so what's new phenomena will occur in such media? We studied the refraction properties between air and such media. There was double refraction, but different from other double refraction, one refracted wave is linearly polarized and another is longitudinal elliptically polarized. At last, based on the full wave simulation, we predicted this effect.
In the fifth chapter of this thesis,1 will give a simple conclusion.
引文
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