非线性人工电磁媒质的电磁波传播特性研究
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摘要
近十年来,人们对于电磁波在新型人工电磁媒质中的传播特性及其物理机制有了越来越清楚地认识,人工电磁媒质的相关理论和设计方法也已经得到了越来越多的实际应用,如电磁隐身衣、超透镜、左手传输线微波器件、电磁波吸波结构等等。但是,目前大部分关于人工电磁媒质研究都限于线性媒质,即其宏观等效电磁参数与外部入射场强或者传播场强的变化无关。最近的初步探索表明将材料的非线性引入人工电磁媒质的设计,实现非线性人工电磁媒质,将进一步拓展其对电磁波的调控作用,增加新型电磁功能器件的设计和开发空间。左手传输线是一类具有代表性的微波人工电磁媒质,其结构简单、尺寸紧凑、便于加工、损耗低而且工作频带宽,已经成为研究微波段人工电磁媒质特性及开发新型微波器件的一个重要研究平台。基于上述发展趋势,本文主要对基于传输线结构的非线性人工电磁媒质进行深入分析,探索非线性人工电磁媒质中电磁波传播的特异性质。除此之外还对新型人工电磁媒质的一些其他问题进行了有益的分析。论文的主要内容和贡献包括：
(1)建立了一维非线性左手传输线模型,分析了电磁波在一维非线性左手传输线媒质中的色散关系和传播特性；采用背靠背微波变容二极管为非线性元件,替代左手传输线中的串联定值电容,在传输线型人工电磁媒质中引入了非线性；经过仔细的电路分析发现只要选择合适的电路参数,微波电路中的波包演绎方程就能简化为一维非线性薛定谔方程,这种一维非线性媒质将支持暗孤立子波。以连续波或高斯调制脉冲为输入信号进行微波电路的时域瞬态仿真分析,验证了暗孤立波的形成,而其频谱表明薛定谔类型孤立子的形成同时会导致传输线中三谐频的产生。另外,理论分析和仿真实验表明非线性人工媒质中的损耗有助于在较短距离就形成稳态暗孤立子。这一研究结果将有助于新型通信系统的建立。
(2)建立了以串联非线性电容为基础的二维非线性左手传输线模型,从理论上分析了这种非线性人工电磁媒质的色散关系和传播特性；详细介绍了二维非线性左手传输线人工电磁媒质的设计和实现方法,分析了不同泵浦源功率下的非线性效应,以及基波、二次谐波、三次谐波的传播特性,通过对实际二维微波电路网络的仿真实验验证了相应的特异传播性质。研究表明非线性左手传输线人工电磁媒质的传播特性可由入射场的强度进行控制,实现其在左手媒质和右手媒质之间的切换。
(3)通过二维非线性左手传输线人工电磁媒质实现了近场聚焦和超透镜平板成像。详细介绍了非线性在手传输线媒质和右手传输线媒质在谐频匹配的设计方法,仿真实验观察到左、右手传输线网络交界处有强烈的表面波,其结果与左手线性超透镜的理论分析一致。另外,设计了非线性左手传输线平板透镜,其对源的基频波不透明,却能够通过谐频场实现亚波长成像。
(4)针对复杂各向异性光学人工电磁媒质,通过严格的数学分析得到了用复介电常数和复磁导率张量参数表示的赝布儒斯特角的显性计算公式；对该计算公式的有效性进行了验证；基于合理的物理近似,探讨了一些关于赝布儒斯特角的有趣特性和可能应用。
(5)通过理论推导得到了单层高磁损耗吸波串联发生谐振吸收时的厚度要求,发现该厚度小于1/4介质内波长；通过已有实验数据进行了有效验证。
In the past ten years, people have come to know the propagation properties and the physical mechanism of the metamaterials, and the relevant theories and realizations of metamaterials have been utilized in many applications, such as electromagnetic invisibility cloaking, superlens that can overcome the diffraction limit, the left-handed microwave components and so on. So far, most research findings on metamaterials focused on the passive control and linear properties of these composite structures, i.e., the effective parameters of the structure do not depend on the intensity of the applied field or the propagating electromagnetic waves. However, recent preliminary explorations on nonlinear metamaterials have found the ability to dynamically control the material's properties in real time through nonlinear response, which expand the space on the design and development of new electromagnetic components.
The left-handed transmission line structure is one of the most important approaches to microwave metamaterials for its compact size, low loss and broad band. Most of all, such TL version of left-handed metamaterial provide a simple and easy-to-realize system to investigate the EM wave propagation in left-handed media. Therefore, this dissertation focuses on the unusual electromagnetic characteristics in left-handed nonlinear transmission line (LH NLTL) media. The main contributions of this dissertation are listed below:
1). We theoretically investigate the electromagnetic wave propagation in one-dimensional LH NLTL media. The nonlinear transmission line is periodically loaded with a nonlinear series capacitance composed of two back-to-back varactor diodes. By reducing the dispersion length and the nonlinear length, while increasing the dissipation of the transmission line, steady dark Schrodinger solitons are successfully realized in a short LH NLTL. The evolution of a Gaussian modulated pulse both in time and in frequency domain shows that increasing the dissipation in the metamaterials is helpful to attenuate the energy that prevents the steady soliton formation. The establishing of the Schrodinger solitons also results in harmonic generations in the transmission line, which may find potential applications in communication systems.
2). we present the electromagnetic theory describing the generation and propagation of the fundamental wave and its high harmonics (the second harmonic and the third harmonic) in a two-dimensional nonlinear metamaterial. Then, we show the detailed design of the realizable two-dimensional LH NLTL metamaterial. We have found through microwave circuit simulations that due to its nonlinear performance, such NLTL metamaterial could switch between left-handed medium and right-handed medium by tuning the incident field intensity.
3). we realize near-field focusing and near-perfect imaging at harmonic frequencies using the LH NLTL metamaterial. A detailed procedure is given to design LH NLTL and right-handed (RH) transmission line medium that matched at harmonic frequency. Then, with the aid of the microwave-circuit simulations we observe strong surface waves on the boundaries between RH and LH NLTL networks, which are consistent with the theoretical analysis of a LH linear superlens. We also show that the LH NLTL metamaterial can act as a flat nonlinear lens that can create, with a subwavelength resolution, an image of harmonic fields of the source being opaque for the fundamental frequency.
4). By taking into account the loss and anisotropy of the metamaterials, we present the explicit expression of PBA in terms of complex permittivity and permeability through rigorous analysis. Based on the explicit expression and reasonalbe physical approximation, some interesting features and potential applications of the PBA are discussed.
5). Films with high permeability, being thin and light, are very promising new microwave absorbers. We demonstrates analytically that the thickness of high-permeability thin films, which have the best absorption at certain frequencies, are less than a quarter dielectric wavelength. It also shows that the permeability of films has great impact on the bandwidth of absorption.
(1)建立了一维非线性左手传输线模型,分析了电磁波在一维非线性左手传输线媒质中的色散关系和传播特性；采用背靠背微波变容二极管为非线性元件,替代左手传输线中的串联定值电容,在传输线型人工电磁媒质中引入了非线性；经过仔细的电路分析发现只要选择合适的电路参数,微波电路中的波包演绎方程就能简化为一维非线性薛定谔方程,这种一维非线性媒质将支持暗孤立子波。以连续波或高斯调制脉冲为输入信号进行微波电路的时域瞬态仿真分析,验证了暗孤立波的形成,而其频谱表明薛定谔类型孤立子的形成同时会导致传输线中三谐频的产生。另外,理论分析和仿真实验表明非线性人工媒质中的损耗有助于在较短距离就形成稳态暗孤立子。这一研究结果将有助于新型通信系统的建立。
(2)建立了以串联非线性电容为基础的二维非线性左手传输线模型,从理论上分析了这种非线性人工电磁媒质的色散关系和传播特性；详细介绍了二维非线性左手传输线人工电磁媒质的设计和实现方法,分析了不同泵浦源功率下的非线性效应,以及基波、二次谐波、三次谐波的传播特性,通过对实际二维微波电路网络的仿真实验验证了相应的特异传播性质。研究表明非线性左手传输线人工电磁媒质的传播特性可由入射场的强度进行控制,实现其在左手媒质和右手媒质之间的切换。
(3)通过二维非线性左手传输线人工电磁媒质实现了近场聚焦和超透镜平板成像。详细介绍了非线性在手传输线媒质和右手传输线媒质在谐频匹配的设计方法,仿真实验观察到左、右手传输线网络交界处有强烈的表面波,其结果与左手线性超透镜的理论分析一致。另外,设计了非线性左手传输线平板透镜,其对源的基频波不透明,却能够通过谐频场实现亚波长成像。
(4)针对复杂各向异性光学人工电磁媒质,通过严格的数学分析得到了用复介电常数和复磁导率张量参数表示的赝布儒斯特角的显性计算公式；对该计算公式的有效性进行了验证；基于合理的物理近似,探讨了一些关于赝布儒斯特角的有趣特性和可能应用。
(5)通过理论推导得到了单层高磁损耗吸波串联发生谐振吸收时的厚度要求,发现该厚度小于1/4介质内波长；通过已有实验数据进行了有效验证。
In the past ten years, people have come to know the propagation properties and the physical mechanism of the metamaterials, and the relevant theories and realizations of metamaterials have been utilized in many applications, such as electromagnetic invisibility cloaking, superlens that can overcome the diffraction limit, the left-handed microwave components and so on. So far, most research findings on metamaterials focused on the passive control and linear properties of these composite structures, i.e., the effective parameters of the structure do not depend on the intensity of the applied field or the propagating electromagnetic waves. However, recent preliminary explorations on nonlinear metamaterials have found the ability to dynamically control the material's properties in real time through nonlinear response, which expand the space on the design and development of new electromagnetic components.
The left-handed transmission line structure is one of the most important approaches to microwave metamaterials for its compact size, low loss and broad band. Most of all, such TL version of left-handed metamaterial provide a simple and easy-to-realize system to investigate the EM wave propagation in left-handed media. Therefore, this dissertation focuses on the unusual electromagnetic characteristics in left-handed nonlinear transmission line (LH NLTL) media. The main contributions of this dissertation are listed below:
1). We theoretically investigate the electromagnetic wave propagation in one-dimensional LH NLTL media. The nonlinear transmission line is periodically loaded with a nonlinear series capacitance composed of two back-to-back varactor diodes. By reducing the dispersion length and the nonlinear length, while increasing the dissipation of the transmission line, steady dark Schrodinger solitons are successfully realized in a short LH NLTL. The evolution of a Gaussian modulated pulse both in time and in frequency domain shows that increasing the dissipation in the metamaterials is helpful to attenuate the energy that prevents the steady soliton formation. The establishing of the Schrodinger solitons also results in harmonic generations in the transmission line, which may find potential applications in communication systems.
2). we present the electromagnetic theory describing the generation and propagation of the fundamental wave and its high harmonics (the second harmonic and the third harmonic) in a two-dimensional nonlinear metamaterial. Then, we show the detailed design of the realizable two-dimensional LH NLTL metamaterial. We have found through microwave circuit simulations that due to its nonlinear performance, such NLTL metamaterial could switch between left-handed medium and right-handed medium by tuning the incident field intensity.
3). we realize near-field focusing and near-perfect imaging at harmonic frequencies using the LH NLTL metamaterial. A detailed procedure is given to design LH NLTL and right-handed (RH) transmission line medium that matched at harmonic frequency. Then, with the aid of the microwave-circuit simulations we observe strong surface waves on the boundaries between RH and LH NLTL networks, which are consistent with the theoretical analysis of a LH linear superlens. We also show that the LH NLTL metamaterial can act as a flat nonlinear lens that can create, with a subwavelength resolution, an image of harmonic fields of the source being opaque for the fundamental frequency.
4). By taking into account the loss and anisotropy of the metamaterials, we present the explicit expression of PBA in terms of complex permittivity and permeability through rigorous analysis. Based on the explicit expression and reasonalbe physical approximation, some interesting features and potential applications of the PBA are discussed.
5). Films with high permeability, being thin and light, are very promising new microwave absorbers. We demonstrates analytically that the thickness of high-permeability thin films, which have the best absorption at certain frequencies, are less than a quarter dielectric wavelength. It also shows that the permeability of films has great impact on the bandwidth of absorption.
引文
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