In this paper, a periodic chain composed of a two-dimensional single-layer dielectric cylinder is studied by the Fourier series expansion method combined with the perfectly matched layer approach. The phase constant and attenuation constant of the conduction mode, the forward propagation leakage mode, and the backward propagation leakage mode are analyzed conceptually under different radii. Then, the numerical properties and field pattern distribution characteristics of single-layer cylindrical periodic structures of different radii are discussed. The odd and even modes are found to coexist in structures with a larger radius, which can be applied to transmission devices such as multimode communication. However, there is only a single mode in structures with a smaller radius, which can reduce cross talk and is applicable to single-mode communication. In addition, the mode-guiding capability of a finite array with only 20 medium rods under plane mode excitation of a specific mode length is discussed. The finite array with different conducting capabilities (propagation, attenuation, cutoff) can be used in mode guiding, sensors, filters, etc.

中文翻译：

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可变尺寸链结构的多模和单模传播特性研究

本文采用傅立叶级数展开法和完全匹配层法相结合的方法研究了由二维单层介质圆柱构成的周期链。从概念上分析了在不同半径下传导模式，前向传播泄漏模式和后向传播泄漏模式的相位常数和衰减常数。然后，讨论了不同半径的单层圆柱周期结构的数值性质和场型分布特征。发现奇数和偶数模式共存于具有较大半径的结构中，可以将其应用于诸如多模式通信的传输设备。但是，在半径较小的结构中只有一种模式，可以减少串扰，适用于单模通信。此外，还讨论了在特定模式长度的平面模式激励下仅具有20个中棒的有限阵列的模式引导能力。具有不同传导能力（传播，衰减，截止）的有限阵列可用于模式引导，传感器，滤波器等。