等效微波媒质的特殊色散及其人工调控
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摘要
电磁波在媒质中的传播完全取决于媒质的色散。本文研究微波频段等效媒质(Metamateiral)的特殊色散及其人工调控。
本文首先研究了单轴人工媒质的色散,尤其是Plasma频率附近的特殊色散。通过理论分析、全波仿真和实验测量,本文在Plasma频率附近观察到了超快相速度,并首次报道了发生在非吸收谐振区域的、源于媒质色散曲面形变的负群速现象。本文同时测量得到了亚光速的电磁波波前速度(Front velocity)和包络畸变,验证了Sommerfeld和Brillouin关于电磁波波前速度在任何媒质中均不会超过自由空间中光速的论断。
其次,本文研究了基于有源方法的等效媒质色散的人工调控。本文通过在坡印廷定理的自由电流项中引入由入射电磁波场强控制的电流源,导出了微波频段增益媒质(Gain media)的构造条件。通过在人工媒质基本构造单元中引入负阻元件,得到了满足因果律(?)Krammers-Kronig关系的“有源”色散。仿真和实验结果表明,上述有源媒质可以结合光学增益媒质和传统无源人工媒质的优点,在补偿、甚至过补偿无源人工媒质固有损耗的同时,具有可任意调控的等效介电常数和磁导率。基于无源人工媒质的工程应用主要受制于其固有损耗的事实,微波增益媒质的实现为完美透镜和电磁隐身等人工媒质的新奇应用提供了可能的实现方案。
最后,本文研究了基于Kramers-Kronig关系的等效媒质色散的人工调控。以人工实现电磁波完美匹配层(PML:Perfectly matched layer)为例,本文通过引入集总元件和多重谐振,精确调控人工媒质的频率色散,使之部分满足计算电磁学中的单轴PML模型,物理实现了超薄、超宽带、全极化的PML吸收表面,其仿真和实测指标均接近Rozanov极限。此外,利用最新的3D打印技术,本文亦实现了接近无损的人工PML,得到了在设计频段内可等效为自由空间的人工微波媒质。对于TE入射的任意电磁波,该媒质呈现等于1的等效折射率和波阻抗,可用于实现材料的自我隐身、完美天线罩等诸多应用。此前,PML只能通过数学定义,本项研究展现了人工实现PML的良好前景。
本文研究所得的呈现特殊色散的新型人工微波媒质,从原理上突破了自然媒质和传统人工媒质的局限,其理论和方法可以扩展到电磁波的其它频段,具有广泛的潜在应用前景。
The propagation of electromagnetic waves in a medium is dictated by material dispersion. This dissertation focuses on the special dispersion of metamaterials and its artificial control.
The special dispersion of a uniaxial metamaterial is firstly investigated. The ultra-fost phase velocity and the negative group velocity are observed in the vicinity of plasma frequency. It is pointed out that the occurrence of the negative group velocity is due to the distortion of the dispersion surface, and its front velocity remains subluminal. This result validates the viewpoints of Sommerfeld and Brillouin, that the front velocity in any medium would never be faster than the speed of light in free space.
Secondly, the artificial control of metamateiral dispersion based on active devices is investigated. By adding incidence-controlled source in the free current term of Poynting's theorem, the condition of constructing a microwave gain medium is described. By introducing negative resistance elements into metamaterial units, an experimental microwave gain medium combining features of optical gain media and negative indexed metamaterials is obtained. While its loss can be compensated or even over-compensated, the dispersion of such an active medium obeys the Krammers-Kronig relations. Considering that the inherent loss of metamaterials is the fundamental issue plaguing their realistic applications such as superlenses and invisibility cloaks, the proposed gain metamaterial provides a potential solution for the realistic realization of such applications in the future.
Finally, the artificial control of metamaterial dispersion based on Krammers-Kronig relations is presented. Illustrating by the implementation of the perfectly matched layers (PML), the ultra-thin, ultra-wideband, polarization-independent PML absorbing surfaces that obey a modified model of PML are obtained by introducing lumped elements and multiple resonances in metamaterial units. Measured results show that the ultra-wideband PML-like absorption approaches the Rozanov limit. Moreover, a nearly lossless3D isotropic PML based on the3D printing technology, whose constitutive parameters are effectively the same as those in free space at designed frequencies is experimentally realized. Under an arbitrary TE incidence, this artificial PML behaves as a completely transparent object, which can be used to construct a perfect radome. Previously, these PML responses can only be found in theory and mathematically defined. This work demonstrates the potential of achieving a full-function PML.
The obtained effective media with artificial dispersions fundamentally avoid the inherent limits of natural media and traditional metamaterials, showing a wide range of potential applications in the future.
本文首先研究了单轴人工媒质的色散,尤其是Plasma频率附近的特殊色散。通过理论分析、全波仿真和实验测量,本文在Plasma频率附近观察到了超快相速度,并首次报道了发生在非吸收谐振区域的、源于媒质色散曲面形变的负群速现象。本文同时测量得到了亚光速的电磁波波前速度(Front velocity)和包络畸变,验证了Sommerfeld和Brillouin关于电磁波波前速度在任何媒质中均不会超过自由空间中光速的论断。
其次,本文研究了基于有源方法的等效媒质色散的人工调控。本文通过在坡印廷定理的自由电流项中引入由入射电磁波场强控制的电流源,导出了微波频段增益媒质(Gain media)的构造条件。通过在人工媒质基本构造单元中引入负阻元件,得到了满足因果律(?)Krammers-Kronig关系的“有源”色散。仿真和实验结果表明,上述有源媒质可以结合光学增益媒质和传统无源人工媒质的优点,在补偿、甚至过补偿无源人工媒质固有损耗的同时,具有可任意调控的等效介电常数和磁导率。基于无源人工媒质的工程应用主要受制于其固有损耗的事实,微波增益媒质的实现为完美透镜和电磁隐身等人工媒质的新奇应用提供了可能的实现方案。
最后,本文研究了基于Kramers-Kronig关系的等效媒质色散的人工调控。以人工实现电磁波完美匹配层(PML:Perfectly matched layer)为例,本文通过引入集总元件和多重谐振,精确调控人工媒质的频率色散,使之部分满足计算电磁学中的单轴PML模型,物理实现了超薄、超宽带、全极化的PML吸收表面,其仿真和实测指标均接近Rozanov极限。此外,利用最新的3D打印技术,本文亦实现了接近无损的人工PML,得到了在设计频段内可等效为自由空间的人工微波媒质。对于TE入射的任意电磁波,该媒质呈现等于1的等效折射率和波阻抗,可用于实现材料的自我隐身、完美天线罩等诸多应用。此前,PML只能通过数学定义,本项研究展现了人工实现PML的良好前景。
本文研究所得的呈现特殊色散的新型人工微波媒质,从原理上突破了自然媒质和传统人工媒质的局限,其理论和方法可以扩展到电磁波的其它频段,具有广泛的潜在应用前景。
The propagation of electromagnetic waves in a medium is dictated by material dispersion. This dissertation focuses on the special dispersion of metamaterials and its artificial control.
The special dispersion of a uniaxial metamaterial is firstly investigated. The ultra-fost phase velocity and the negative group velocity are observed in the vicinity of plasma frequency. It is pointed out that the occurrence of the negative group velocity is due to the distortion of the dispersion surface, and its front velocity remains subluminal. This result validates the viewpoints of Sommerfeld and Brillouin, that the front velocity in any medium would never be faster than the speed of light in free space.
Secondly, the artificial control of metamateiral dispersion based on active devices is investigated. By adding incidence-controlled source in the free current term of Poynting's theorem, the condition of constructing a microwave gain medium is described. By introducing negative resistance elements into metamaterial units, an experimental microwave gain medium combining features of optical gain media and negative indexed metamaterials is obtained. While its loss can be compensated or even over-compensated, the dispersion of such an active medium obeys the Krammers-Kronig relations. Considering that the inherent loss of metamaterials is the fundamental issue plaguing their realistic applications such as superlenses and invisibility cloaks, the proposed gain metamaterial provides a potential solution for the realistic realization of such applications in the future.
Finally, the artificial control of metamaterial dispersion based on Krammers-Kronig relations is presented. Illustrating by the implementation of the perfectly matched layers (PML), the ultra-thin, ultra-wideband, polarization-independent PML absorbing surfaces that obey a modified model of PML are obtained by introducing lumped elements and multiple resonances in metamaterial units. Measured results show that the ultra-wideband PML-like absorption approaches the Rozanov limit. Moreover, a nearly lossless3D isotropic PML based on the3D printing technology, whose constitutive parameters are effectively the same as those in free space at designed frequencies is experimentally realized. Under an arbitrary TE incidence, this artificial PML behaves as a completely transparent object, which can be used to construct a perfect radome. Previously, these PML responses can only be found in theory and mathematically defined. This work demonstrates the potential of achieving a full-function PML.
The obtained effective media with artificial dispersions fundamentally avoid the inherent limits of natural media and traditional metamaterials, showing a wide range of potential applications in the future.
引文
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