摘要
本文采用多级方法(MPM)对涂覆石墨烯的双椭圆和圆柱并行纳米线波导的基模的有效折射率进行了计算,并采用有限元法(FEM)对计算结果进行了验证。本文研究了两种计算方法的结果之间的相对误差随MPM展开项数的最大值、工作波长、费米能、椭圆柱形纳米线的半长轴及半短轴、纳米线表面之间的横向间距,以及圆柱形纳米线的相对高度等变化的规律。通过对照计算结果得到以下规律:随着级数展开项数增大,MPM的结果越接近FEM的结果;随着工作波长和费米能增大,有效折射率实部和虚部的相对误差均增大;随着圆柱形电介质纳米线的半径和椭圆柱形纳米线的半长轴增大,有效折射率实部的相对误差增大,而其虚部的相对误差减小;随着椭圆柱形纳米线的半短轴增大,有效折射率实部的相对误差减小,而其虚部的相对误差增大;随着纳米线表面之间的横向间距和圆柱形纳米线的相对高度增大,有效折射率实部和虚部的相对误差均减小。这些现象均可以通过场分布得到解释。在本文的计算范围内,相对误差均保持在10-3量级。该研究工作为混合型电介质并行纳米线波导的设计、制作和应用提供了理论基础。
Objective The waveguide structure based on graphene materials has been a research hotspot in recent years.By employing the finite element method(FEM),the characteristics of the five lowest-order modes supported by the waveguide based on graphene-coated double elliptical and cylindrical parallel nanowires were reported.Since a purely numerical method is adopted in this study,it is impossible to give a clear physical image of the mode formation mechanism.To this end,we intend to employ the multipole method(MPM)to reanalyze the fundamental mode of the waveguide structure discussed before,and give a clear physical image of the mode formation mechanism.Meanwhile,the MPM correctness is verified by comparing the relative error between the results of the two calculation methods with the maximum value of the term number expanded by the MPM,the working wavelength,the Fermi energy,the semi-major and semi-minor axes of the elliptical cylindrical nanowires,the lateral spacing between the surfaces of the nanowires,and the relative height of the cylindrical nanowires.Methods We leverage the MPM to calculate the characteristics of modes supported by the waveguide based on graphenecoated double elliptical and cylindrical parallel nanowires.First,we assume that the double elliptical cylindrical nanowires and the cylindrical nanowire exist alone and that the longitudinal components of the field are expanded into series form in their coordinate systems respectively.Then,according to the field superposition principle,the longitudinal components of the field in each region of the combined waveguide are obtained.Then,the radial and angular components of the field are obtained by the relationship between the lateral component and the longitudinal component of the field.The involved derivatives can be obtained via the gradient of the scalar field and the point product of the unit vector.Then,graphene is regarded as a conductor boundary without thickness,and a linear algebraic equation system is established by the boundary relationship an
作者
杜易达
李宁
薛文瑞
李慧慧
张越
李昌勇
Du Yida;Li Ning;Xue Wenrui;Li Huihui;Zhang Yue;Li Changyong(College of Physics and Electronic Engineering,Shanxi University,Taiyuan 030006,Shanxi,China;State Key Laboratory of Quantum Optics and Quantum Optics Devices,Institute of Laser Spectroscopy,Shanxi University,Taiyuan 030006,Shanxi,China;Collaborative Innovation Center of Extreme Optics,Shanxi University,Taiyuan 030006,Shanxi,China)
出处
《光学学报》
EI
CAS
CSCD
北大核心
2023年第22期197-207,共11页
Acta Optica Sinica
基金
国家自然科学基金(61378039,61575115)
国家基础科学人才培养基金(J1103210)。
关键词
石墨烯
纳米线
波导
多极方法
有限元法
graphene
nanowires
waveguides
multipole method
finite element method
