电磁超介质的多极矩方法及其在微波器件上的应用
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摘要
电磁超介质的出现,给人们世界观层面上带来了巨大的冲击,其表现出来的自然界所不具备的一系列奇异电磁特性,为电磁学领域开辟了新的研究空间。其在卫星通信、雷达、微电子、医学成像等应用领域的应用前景,更是推动了电磁超介质的迅猛发展。从某种意义上来说,电磁超介质为我们提供了一种按照自己意愿设计材料的全新途径,包括设计任意数值的介电常数、磁导率和折射率材料,也为我们研究某些物理现象及其隐晦特性提供了一种新方法。因而,探索电磁超介质的新特性,完善其理论计算体系和分析方法,推进其在各领域的应用具有重要的意义。
围绕电磁超介质的仿真、实验及应用,主要研究内容和创新成果如下：
1.提出了平面超薄负折射率材料的设计方法及其在吸波上的应用。针对传统负折射率介质中,电磁波从介质基底的侧面入射,造成结构繁琐,厚度大,以及存在二次散射等复杂干扰的缺点,设计了平面超薄负折射率超介质模型。重点研究了如何在有限的平面内实现有效的负磁响应的难点问题,仿真设计了“U”型和“环套圆”两种平面超薄负折射率电磁超介质模型,以及其在超薄平面吸波材料上的应用。实验表明,所设计的吸波材料的厚度仅仅为0.5mm(0.015凡),吸波率达到了99%以上
2.提出了不同单元组合和一体化的设计方法实现双频电磁超介质的设计。电磁超介质设计的基本单元—谐振环,其本征频率强烈地依赖于其自身尺寸,所以通过改变单元的结构,就可以达到调控其谐振频率的目的。本文设计双频电磁超介质的第一种方法就是组合法。通过在一个周期单元中引入不同本征频率的谐振单元,得到了不同谐振频率。在组合法中,单个结构单元中引入多个不同的尺寸设计,会增大其周期尺寸,从而产生类似频率选择表面中的栅瓣效应。针对这一缺点,本文接着利用一体化设计方法实现双频电磁超介质,通过实验验证,证明了不同极化角度和入射角度下,超介质依旧可以保持优异的电磁特性。
3.首次提出电环偶极子并开展了模型仿真设计与实验验证,建立了多极矩分析立体超介质电磁特性的方法。由于螺绕环立体超介质的复杂性,其可以等效的看作多个“超原子”组成。其与电磁波之间的相互作用,除了“原子”本身的谐振特性,还与其“原子”之间互耦有关。多极矩能量计算的方法,结合电流、电／磁场的分布,不仅有清晰的物理图像,便于分析其内部机理,而且在设计具有一定宏观电磁特性的立体超介质时,由于其从构建基本的电磁多极子(“原子”)的层次出发,使得在设计上更具有可控性。论文围绕螺绕环经典模型,从圆二色性的角度出发,研究了多极子之间的谐振耦合和能量散射。从多极矩能量辐射功率计算中,我们发现,对于频率4GHz和9.5GHz出现的圆二色性,主要来源于电偶极矩、磁偶极矩和电四极矩之间的耦合。接着通过多极矩分析方法验证了一种新的多极矩效应—环偶极矩(磁偶极子首尾相接产生的轴向上的环偶极矩)。同时,基于电与磁的对偶性,我们第一次提出与之对应的电环偶极矩,即首尾相接的电偶极矩产生的轴向上的电环偶极矩。通过设计U型环立体超介质,抑制了电偶极矩和磁偶极矩等其它多极矩能量的干扰,在频率6.55GHz成功提取了电环偶极矩能量。同时,多极矩分析方法也贯穿于负折射率材料和吸波材料设计中,重点研究产生负介电常数和负磁导率的电偶极矩和磁偶极矩能量。
4.基于互补SRR谐振环,利用单元组合法设计并实验验证了双频宽带带阻滤波器。传统SRR谐振环设计微波器件谐振带宽非常窄,而互补SRR谐振环结构可以有效的提高带宽,同时利用单元组合法,在频率6.03GHz和7.10GHz实现双频宽带带阻滤波器设计,其相对带宽分别为11.1%和11.3%。结果表明,基于电磁超介质设计微波器件具有选择性高、尺寸小、谐振强、便于设计多频和宽频器件等很多优点。
论文中还探讨了电磁超介质的其它重要特性,比如设计电磁参数微小变化的非谐振超介质模型、低损耗异向介质设计思路、基于高阻抗表面特性设计超薄吸波材料、常用的平面电谐振单元模型汇总,电磁超介质在设计双频窄带滤波器和天线上的应用等等。总之,受到电磁超介质的吸引,我们设计了多种电磁超介质模型,基于电流、电/磁场分析及多极矩分析方法,研究不同形式下其与电磁波的相互作用和内部机理,并探讨其在微波器件上的应用。
Metamaterials (MMs) make people have a qualitative change on their understanding to substance. They have opened a new research domain for electromagnetic field because of their unique electromagnetic properties and tremendous application value. MMs have a huge application prospect in the fields of satellite communications, radar, microelectronics, medical imaging and so on. This promotes the rapid development of MMs. In a sense, MMs have provided us with a new way to design materials of our own volition. We can design any values of epsilon, mu and refraction index. MMs also provide a new way for us to study some physical phenomena and obscure features. Therefore, to explore MMs'new properties and complete its theoretical system and analytical methods has a very significance in applications such as microwave devices.
The research results in this thesis can be summarized as follows on the base of MMs'simulation and experiment.
1. We have a research on the design method of ultrathin planar negative refraction index MMs and their applications in absorbers. Electromagnetic wave is incident on the side of traditional negative refraction index MMs. This makes the MMs have a cumbersome and thicker structure. Complex interference such as secondary scattering also exists in these MMs. Hence, we design a new type of planar and ultrathin MMs. The aporia of design this kind of MMs is how to achieve effective negative magnetic response in a limited plane. This thesis has designed two type of ultrathin planar negative refraction index MMs. Research on MMs'application in ultrathin planar absorbers is also studied. Experiments show that these MMs absorbers have a thickness of0.5mm (0.15λ0) with absorptivity of more than99%.
2. We propose two design methods of combination and unique configuration methods to design dual-band MMs. Ring resonator is a basic element of MMs. Its eigenfrequency is strongly dependent to its own size. For this reason, we can regulate and control its resonant frequency by the way to change the unitcell's size. The first way to design dual-band MMs in this thesis is the combination method. Different resonant frequencies can be achieved in one periodic unitcell by importing different unitcells with their own eigenfrequency. Nevertheless, the combination method will increase its unitcell size after introduce several different size. Thereby the MMs will produce a grating lobe effect similar to the frequency selecting surface. Then we improved the dual-band design method to unique configuration and verified by experiment. Experiments show that polarization angle and incident angle almost have no side effect on their characteristics.
3. We propose an electric toroidal dipole model verified by simulation and experiment. Then multipole analytical method is built to analyze stereo MMs' electromagnetic properties. Toroidal MMs have complex electromagnetic coupling among their effective'atoms'. Its interaction with electromagnetic wave has relationship with the resonant characteristics of the'atom'itself and cross coupling among these 'atoms'. Therefore, its resonance characteristic mechanism will become more intricate. But the method to calculate multipole scattered energy combined with current and electric/magnetic field distribution analysis has a clear physical picture of the internal mechanism. It also makes the design of stereo MMs more controllable. We have a research on toroidal MMs'coupling among multipole and scattered energy from circular dichroism. The circular dichroism at4GHz and9.5GHz links to the coupling among electric dipole, magnetic dipole and electric quadrupole moments. Then we verified a new multipole which can be achieved by a closed loop of magnetic dipole arranged head-to-tail. This new multipole is magnetic toroidal dipole. Based on the duality of electricity and magnetism, we first propose the electric toroidal dipole corresponding to the magnetic toroidal dipole. It can also be generated by a closed loop of electric dipoles arranged head-to-tail. We modeled U-shape stereo MMs to achieve electric toroidal MMs. This model has a peak of electric toroidal dipole energy at6.55GHz by inhibiting multipole energy. At the same time, we also use multipole analytical method when we design the negative refraction index MMs and absorbers. It's used to calculate the scattered energy of electric dipole and magnetic dipole.
4. We have designed and tested a dual-and broad-band band stop filter based on the complementary split ring resonator (CSRR). Combination method has been used to design this filter. Due to the narrow band of filters with traditional SRR, The complementary SRR can increase bandwidth effectively. Hence, we can achieve a dual-and broad-band band stop filter with relative bandwidth of11.1%and11.3at6.03GHz and7.10GHz, respectively. These results show that there are many advantages to design MMs-based devices, such as high selectivity, small size, strong resonance, multi-band and broadband.
This thesis also explores MMs'other important characteristics. For example, we can design non-resonant MMs with small changes in electromagnetic parameters, low-loss MMs and absorbers based on high-impedance surface MMs. We can also have a summary on planar electric resonance unitcells. In a word, we designed a variety of MMs models. The method of multipole scattered energy combined with current and electric/magnetic field distribution analysis has been proposed. This method can be used to study the interaction between MMs and electromagnetic wave and MMs'internal mechanism. At last we explore MMs'application in microwave devices.
围绕电磁超介质的仿真、实验及应用,主要研究内容和创新成果如下：
1.提出了平面超薄负折射率材料的设计方法及其在吸波上的应用。针对传统负折射率介质中,电磁波从介质基底的侧面入射,造成结构繁琐,厚度大,以及存在二次散射等复杂干扰的缺点,设计了平面超薄负折射率超介质模型。重点研究了如何在有限的平面内实现有效的负磁响应的难点问题,仿真设计了“U”型和“环套圆”两种平面超薄负折射率电磁超介质模型,以及其在超薄平面吸波材料上的应用。实验表明,所设计的吸波材料的厚度仅仅为0.5mm(0.015凡),吸波率达到了99%以上
2.提出了不同单元组合和一体化的设计方法实现双频电磁超介质的设计。电磁超介质设计的基本单元—谐振环,其本征频率强烈地依赖于其自身尺寸,所以通过改变单元的结构,就可以达到调控其谐振频率的目的。本文设计双频电磁超介质的第一种方法就是组合法。通过在一个周期单元中引入不同本征频率的谐振单元,得到了不同谐振频率。在组合法中,单个结构单元中引入多个不同的尺寸设计,会增大其周期尺寸,从而产生类似频率选择表面中的栅瓣效应。针对这一缺点,本文接着利用一体化设计方法实现双频电磁超介质,通过实验验证,证明了不同极化角度和入射角度下,超介质依旧可以保持优异的电磁特性。
3.首次提出电环偶极子并开展了模型仿真设计与实验验证,建立了多极矩分析立体超介质电磁特性的方法。由于螺绕环立体超介质的复杂性,其可以等效的看作多个“超原子”组成。其与电磁波之间的相互作用,除了“原子”本身的谐振特性,还与其“原子”之间互耦有关。多极矩能量计算的方法,结合电流、电／磁场的分布,不仅有清晰的物理图像,便于分析其内部机理,而且在设计具有一定宏观电磁特性的立体超介质时,由于其从构建基本的电磁多极子(“原子”)的层次出发,使得在设计上更具有可控性。论文围绕螺绕环经典模型,从圆二色性的角度出发,研究了多极子之间的谐振耦合和能量散射。从多极矩能量辐射功率计算中,我们发现,对于频率4GHz和9.5GHz出现的圆二色性,主要来源于电偶极矩、磁偶极矩和电四极矩之间的耦合。接着通过多极矩分析方法验证了一种新的多极矩效应—环偶极矩(磁偶极子首尾相接产生的轴向上的环偶极矩)。同时,基于电与磁的对偶性,我们第一次提出与之对应的电环偶极矩,即首尾相接的电偶极矩产生的轴向上的电环偶极矩。通过设计U型环立体超介质,抑制了电偶极矩和磁偶极矩等其它多极矩能量的干扰,在频率6.55GHz成功提取了电环偶极矩能量。同时,多极矩分析方法也贯穿于负折射率材料和吸波材料设计中,重点研究产生负介电常数和负磁导率的电偶极矩和磁偶极矩能量。
4.基于互补SRR谐振环,利用单元组合法设计并实验验证了双频宽带带阻滤波器。传统SRR谐振环设计微波器件谐振带宽非常窄,而互补SRR谐振环结构可以有效的提高带宽,同时利用单元组合法,在频率6.03GHz和7.10GHz实现双频宽带带阻滤波器设计,其相对带宽分别为11.1%和11.3%。结果表明,基于电磁超介质设计微波器件具有选择性高、尺寸小、谐振强、便于设计多频和宽频器件等很多优点。
论文中还探讨了电磁超介质的其它重要特性,比如设计电磁参数微小变化的非谐振超介质模型、低损耗异向介质设计思路、基于高阻抗表面特性设计超薄吸波材料、常用的平面电谐振单元模型汇总,电磁超介质在设计双频窄带滤波器和天线上的应用等等。总之,受到电磁超介质的吸引,我们设计了多种电磁超介质模型,基于电流、电/磁场分析及多极矩分析方法,研究不同形式下其与电磁波的相互作用和内部机理,并探讨其在微波器件上的应用。
Metamaterials (MMs) make people have a qualitative change on their understanding to substance. They have opened a new research domain for electromagnetic field because of their unique electromagnetic properties and tremendous application value. MMs have a huge application prospect in the fields of satellite communications, radar, microelectronics, medical imaging and so on. This promotes the rapid development of MMs. In a sense, MMs have provided us with a new way to design materials of our own volition. We can design any values of epsilon, mu and refraction index. MMs also provide a new way for us to study some physical phenomena and obscure features. Therefore, to explore MMs'new properties and complete its theoretical system and analytical methods has a very significance in applications such as microwave devices.
The research results in this thesis can be summarized as follows on the base of MMs'simulation and experiment.
1. We have a research on the design method of ultrathin planar negative refraction index MMs and their applications in absorbers. Electromagnetic wave is incident on the side of traditional negative refraction index MMs. This makes the MMs have a cumbersome and thicker structure. Complex interference such as secondary scattering also exists in these MMs. Hence, we design a new type of planar and ultrathin MMs. The aporia of design this kind of MMs is how to achieve effective negative magnetic response in a limited plane. This thesis has designed two type of ultrathin planar negative refraction index MMs. Research on MMs'application in ultrathin planar absorbers is also studied. Experiments show that these MMs absorbers have a thickness of0.5mm (0.15λ0) with absorptivity of more than99%.
2. We propose two design methods of combination and unique configuration methods to design dual-band MMs. Ring resonator is a basic element of MMs. Its eigenfrequency is strongly dependent to its own size. For this reason, we can regulate and control its resonant frequency by the way to change the unitcell's size. The first way to design dual-band MMs in this thesis is the combination method. Different resonant frequencies can be achieved in one periodic unitcell by importing different unitcells with their own eigenfrequency. Nevertheless, the combination method will increase its unitcell size after introduce several different size. Thereby the MMs will produce a grating lobe effect similar to the frequency selecting surface. Then we improved the dual-band design method to unique configuration and verified by experiment. Experiments show that polarization angle and incident angle almost have no side effect on their characteristics.
3. We propose an electric toroidal dipole model verified by simulation and experiment. Then multipole analytical method is built to analyze stereo MMs' electromagnetic properties. Toroidal MMs have complex electromagnetic coupling among their effective'atoms'. Its interaction with electromagnetic wave has relationship with the resonant characteristics of the'atom'itself and cross coupling among these 'atoms'. Therefore, its resonance characteristic mechanism will become more intricate. But the method to calculate multipole scattered energy combined with current and electric/magnetic field distribution analysis has a clear physical picture of the internal mechanism. It also makes the design of stereo MMs more controllable. We have a research on toroidal MMs'coupling among multipole and scattered energy from circular dichroism. The circular dichroism at4GHz and9.5GHz links to the coupling among electric dipole, magnetic dipole and electric quadrupole moments. Then we verified a new multipole which can be achieved by a closed loop of magnetic dipole arranged head-to-tail. This new multipole is magnetic toroidal dipole. Based on the duality of electricity and magnetism, we first propose the electric toroidal dipole corresponding to the magnetic toroidal dipole. It can also be generated by a closed loop of electric dipoles arranged head-to-tail. We modeled U-shape stereo MMs to achieve electric toroidal MMs. This model has a peak of electric toroidal dipole energy at6.55GHz by inhibiting multipole energy. At the same time, we also use multipole analytical method when we design the negative refraction index MMs and absorbers. It's used to calculate the scattered energy of electric dipole and magnetic dipole.
4. We have designed and tested a dual-and broad-band band stop filter based on the complementary split ring resonator (CSRR). Combination method has been used to design this filter. Due to the narrow band of filters with traditional SRR, The complementary SRR can increase bandwidth effectively. Hence, we can achieve a dual-and broad-band band stop filter with relative bandwidth of11.1%and11.3at6.03GHz and7.10GHz, respectively. These results show that there are many advantages to design MMs-based devices, such as high selectivity, small size, strong resonance, multi-band and broadband.
This thesis also explores MMs'other important characteristics. For example, we can design non-resonant MMs with small changes in electromagnetic parameters, low-loss MMs and absorbers based on high-impedance surface MMs. We can also have a summary on planar electric resonance unitcells. In a word, we designed a variety of MMs models. The method of multipole scattered energy combined with current and electric/magnetic field distribution analysis has been proposed. This method can be used to study the interaction between MMs and electromagnetic wave and MMs'internal mechanism. At last we explore MMs'application in microwave devices.
引文
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