In this paper, the equations for the transfer matrix method of one-dimensional cylindrical magnetized plasma photonic crystals are proposed, and its nonreciprocal properties based on the Thue–Morse sequence are also studied. By adding the influence of the magnetic field into Maxwell’s equations in the cylindrical coordinate system, the transmission matrix equation of cylindrical wave propagation in the cylindrical medium is obtained and a quasi-periodic structure with the Thue–Morse sequence is designed to study its nonreciprocal features. By considering Maxwell’s equations and the equations of motion of charged particles, the relative dielectric function of plasma under the $z$-axis magnetic field is achieved. Considering the influences of this dielectric function in the cylindrical coordinate system, the transmission matrix equations of cylindrical wave propagation in the cylindrical medium are derived, and those equations are used to design a cylindrical structure with two layers of ordinary medium and one layer of plasma satisfying the Thue–Morse sequence. It is concluded that the nonreciprocal phenomenon becomes more and more obvious with the increase of the plasma frequency, the relative dielectric constant of the medium, and the incident angle. But with the increase of ${\omega _c}$, the nonreciprocal propagation is attenuated, and there is no significant change when the collision frequency is enlarging.

中文翻译：

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一维圆柱磁化等离子体光子晶体的非互易性质研究

本文提出了一维圆柱磁化等离子体光子晶体传递矩阵法的方程，并研究了基于Thue-Morse序列的非互易性质。通过在圆柱坐标系的麦克斯韦方程组中加入磁场的影响，得到圆柱波在圆柱介质中传播的传输矩阵方程，并设计了具有Thue-Morse序列的准周期结构来研究其非互易特征. 通过考虑麦克斯韦方程和带电粒子的运动方程，在$z$下等离子体的相对介电函数轴磁场实现。考虑该介电函数在圆柱坐标系中的影响，推导出圆柱波在圆柱介质中传播的传输矩阵方程，并利用这些方程设计了两层普通介质和一层等离子体的圆柱结构，满足Thue-Morse 数列。得出结论，随着等离子体频率、介质相对介电常数和入射角的增加，非互易现象变得越来越明显。但随着${\omega _c}$ 的增加，非互易传播减弱，碰撞频率增大时无明显变化。