二维色散介质光子晶体的能带结构求解问题研究  

Numerical Analysis of the Band Structure of Two-Dimensional Dispersive Dielectric Photonic Crystals

作　　者：钟相辉 袁健华[1] Zhong Xianghui;Yuan Jianhua(School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China)

机构地区：[1]北京邮电大学理学院,北京100876

出　　处：《激光与光电子学进展》2023年第9期378-384,共7页Laser & Optoelectronics Progress

基　　金：国家自然科学基金(11871115,12171052)。

摘　　要：给出了一种计算二维色散介质光子晶体能带结构的方法,研究二维色散介质光子晶体的特性。考虑色散光子晶体,即介电常数ε=ε(ω)与频率ω相关,求解一个非线性特征值问题得到能带结构。首先,基于光子晶体电磁波传播的控制方程组推导出变分形式,对离散以后的非线性问题选择合适的解作为初始值,基于牛顿法对不同的波矢k值求解该非线性问题,获得色散关系ω(k),从而得到光子晶体的能带结构分布。基于数值方法,求解了几种不同的色散介质光子晶体在横电(TE)、横磁(TM)模式下的能带结构,数值结果表明该方法是有效的。In this study,the characteristics of twodimensional dispersive dielectric photonic crystals are studied via a numerical approach that combines the finiteelement method(FEM)with Newton’s iterative method.For a dispersive photonic crystal whose permittivity is dependent on the frequency,the band structure problem is formulated as a nonlinear eigenvalue problem.In this study,first,a discrete variational formulation is derived from Maxwell’s equations based on the FEM.Thereafter,by selecting approximate solutions as the initial values for the iteration,this nonlinear problem is solved for different values of the wave vector k based on Newton’s iterative method.Consequently,the band structure of dispersive dielectric photonic crystals is obtained numerically.Several dispersive photonic crystals in the transverse electric(TE)and transverse magnetic(TM)modes are investigated.The numerical results reveal that the proposed method is effective for dispersive photonic crystals.

关 键 词：色散光子晶体 能带结构 有限元方法 光子带隙 牛顿法 

分 类 号：O242.21[理学—计算数学]