波导作为一种重要的能量传输结构，在电磁领域中具有重要的地位与作用。以波导结构为基础的器件在微波与毫米波领域实现了众多应用。然而，波导的色散作为波导的重要特性，对它的研究往往局限于波导的导通模式，忽略了波导在截止频率以下的性质。为此，本论文从理论上研究并分析了截止波导的工作模式和色散特性，并根据截止波导不同工作状态的性质设计了截止波导的多种新型应用，开拓了波导研究的新性质、新功能。具体而言，本文的研究主要分为以下四个方面。首先，针对常用的矩形波导结构提出了波导等效媒质理论，系统性地研究并分析了波导在截止频率以下的色散特性，建立起了截止波导的分析理论与方法。本论文将波导色散的特性研究从截止频率以上拓展到了全频带。针对波导不同工作模式，可以将截止波导等效为近零指数媒质和等离子体材料。并利用其独特的电磁特性，实现全新的波导器件与应用。其次，面向工作在截止频率的波导，针对波导在截止频率处的色散特性，可以实现近零指数媒质。基于近零指数媒质的超耦合效应，论文提出了一种宽带波导形变结构。在本工作中，利用近零介电常数模式和法布里-珀罗模式叠加，在波导中实现了宽带的超耦合现象，并在此基础上实现了一个基片集成波导交叉传输线，可以实现宽带的波导交叉，同时不占据额外的剖面。这种宽带波导交叉传输线以其性能良好，结构灵活的特点，进一步拓展了在复杂集成波导系统的应用。再次，面向工作在截止频率以下的波导，针对波导在截止频率以下的色散特性，可以实现等离子体材料。论文提出了阶梯波导超材料，实现了表面等离激元模式。由于避免了天然等离子体材料的使用，阶梯波导超材料避免了传统表面等离激元模式损耗较大的问题，同时又能与传统表面等离激元模式直接互连。最后，面向波导的完整色散曲线，本论文设计了波导中的集总电路元件，并实现了波导中的负电路元件。通过在波导传输线内插入介电常数与背景媒质不同的介质薄膜，利用其色散特性对应的阻抗特性，实现了集总的电感或电容元件，其中包括负电容和负电感元件。同时通过实验进一步验证了负电容和负电感的在电路设计中的性能优势，实验采用负电感对正电感进行阻抗匹配，可实现41.36%的阻抗匹配带宽，相比传统正电路元件13.62%的匹配带宽具有很大优势。
As an important energy transmission structure, waveguide plays an important role in the electromagnetic area. Devices based on waveguide structures have realized many applications in microwave and millimeter wave fields. However, as a significant characteristic of waveguides, the study of waveguide dispersion is often limited to the waveguide operating region, ignoring the performance and dispersion characteristics of waveguides operating below the cutoff frequency. Therefore, this paper theoretically studies and analyzes the performance and dispersion characteristics of the cut-off waveguide, and designs a variety of new applications of the cut-off waveguide according to the properties of different working states, and opens up new properties and functions of the waveguide research. Specifically, the research of this paper is mainly divided into the following four aspects.Firstly, the theory of waveguide effective medium is proposed for the commonly used rectangular waveguide structures, and the dispersion characteristics below the cutoff frequency are systematically studied and analyzed, establishing the theory and methodology on cut-off waveguide analysis. In this paper, the waveguide dispersion is extended from above the cut-off frequency to the full frequency band. According to different operating performances of waveguides, the cut-off waveguides can be effectively regarded as epsilon-near-zero medium and plasmonic material. Taking advantage of their unique electromagnetic characteristics, novel waveguide devices and applications can be realized.Secondly, for waveguides operating at exactly the cutoff frequency, the effective epsilon-near-zero medium can be realized according to the dispersion characteristics of waveguides at the cutoff frequency. Based on the supercoupling effect of epsilon-near-zero medium, a wideband transition through height-restricted obstacles is proposed. In this work, the superposition of epsilon-near-zero mode and Fabry-Perot mode is applied to realize wide-band transition in waveguides, and on this basis, a dielectric-integrated waveguide crossover is achieved, which can realize wideband waveguide crossover without extra profile. This kind of wideband waveguide crossover with its good performance and flexible structure, has further expanded potential application in complex integrated waveguide systems.Thirdly, for waveguides operating below the cutoff frequency, effective plasmonic materials can be realized according to the dispersion characteristics of waveguides below the cutoff frequency. In this paper, a stepped waveguide metamaterial is proposed and the surface plasmonic polaritons mode is realized. By avoiding the usage of natural plasmonic materials, the stepped waveguide metamaterials avoid the problem of large loss in traditional surface plasmonic polaritons, and could be directly interconnected with regular surface plasmonic polaritons.Finally, for the complete dispersion curve of the waveguide, the lumped circuit element in the waveguide is designed and the negative circuit element in the waveguide is realized. Lumped inductor or capacitor elements, including negative capacitors and negative inductors, are realized by inserting a dielectric slab whose permittivity is different from the host medium into the waveguide transmission line and utilizing the impedance characteristic corresponding to its dispersion characteristic. At the same time, the performances of negative capacitors and negative inductors in circuit design are further verified through experiments. The impedance matching between negative inductor and positive inductor can achieve 41.36% impedance matching bandwidth, which exhibits better performance compared with the 13.62% matching bandwidth of traditional positive circuit components.