In this paper, the mode properties of graphene-coated asymmetric parallel dielectric nanowire waveguides are analyzed by the multipole expansion method. First, the surface plasmon modes supported by the waveguides are classified. Then, the influences of frequency, geometry parameters and graphene Fermi energy on the effective refractive index and propagation length of the seven low order modes are studied in detail. The seven low order modes can be divided into two categories: cos mode and sin mode. The cos mode includes modes 0, 2, 4 and 6, while sin mode includes modes 1, 3 and 5. The results show that the characteristics of the modes can be adjusted in a wide range by changing the frequency, geometrical parameters and the Fermi energy of graphene. When the frequency increases from 10 THz to 50 THz, the number of graphene surface plasmon modes increases and the effective refractive index of each mode increases monotonically. Moreover, with the increase of frequency, the propagation length of cos mode decreases monotonically, and the propagation length of sin mode shows the trend of first increasing and then decreasing. As the distance between the two dielectric nanowires increases, the mode properties of modes 0 and 1 change drastically, while the effective refractive indexes and propagation lengths of other modes vary very little. As the radius of one of the dielectric nanowires increases, the number of modes increases in the calculated range, while the effective refractive index and propagation length of each mode are less affected. In the process of increasing the Fermi energy of graphene from 0.3 eV to 0.7 eV, the effective refractive index and propagation length of each mode vary greatly. Moreover, the effective refractive index of each mode decreases monotonically, while the propagation length increases. It is also found that the compositions of the low order modes vary with the size of the two nanowires for this asymmetric structure. The comparison with the finite element method shows that the semi-analytical results based on multipole method are in good agreement with the numerical results from the finite element method. The present work may provide a theoretical basis for designing and fabricating the asymmetric parallel dielectric nanowires coated with graphene.%采用多级展开方法,对涂覆石墨烯的非对称并行电介质纳米线波导的模式特性进行了分析.首先对这种波导中的表面等离子模式进行分类,然后对七种低阶模式的有效折射率和传播长度随工作频率、几何结构参数和石墨烯费米能的依赖关系进行详细的分析.结果表明,通过改变工作频率、几何结构参数和石墨烯的费米能,可以在较大范围内调节模式的特性.与有限元法进行的对比表明,基于多级方法的半解析结果与有限元法的数值结果非常符合.研究结果可为涂覆石墨烯的非对称并行电介质纳米线的设计和制作提供一定的理论基础.
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