复杂等离子体光子晶体能带结构计算  

Band Structure Computation of Complex Plasma Photonic Crystals

作　　者：卢欣 旷盈 杨洁 王志杰 王立群[1,2] LU Xin;KUANG Ying;YANG Jie;WANG Zhijie;WANG Liqun(College of Science,China University of Petroleum-Beijing,Beijing 102249;Beijing Key Laboratory of Optical Detection Technology for Oil and Gas,China University of Petroleum-Beijing,Beijing 102249)

机构地区：[1]中国石油大学(北京)理学院,北京102249 [2]中国石油大学(北京)油气光学探测技术北京市重点实验室,北京102249

出　　处：《工程数学学报》2024年第2期341-364,共24页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(12171482);中国石油大学油气资源与探测国家重点实验室项目(PRP/DX-2307).

摘　　要：等离子体光子晶体是由等离子体和其他介电材料或者真空构成的,具有周期性结构,其可调控的带隙特性使得等离子体光子晶体在滤波器、等离子体隐身衣和等离子体透镜等军事医学器件制造上具有广泛的应用。因此,通过改变等离子体的密度、温度等参数来获取满足特定需求的能带结构特性便有着非常重要的意义。基于上述考虑,提出Petrov-Galerkin有限元计算方法来求解并分析等离子体光子晶体的带隙特性。该方法的核心思想是构造在边界上系数互为倒数的基函数和测试函数所构成的空间,在消除边界上积分的同时降低自由度。采用的网格为半笛卡尔投影网格,该网格能适应复杂等离子体柱形状。在建立弱形式时将界面非线性连续条件线性化,简化了界面积分项的处理。通过绘制数值算例的能带结构图,分析验证了等离子体电子密度、等离子体光子晶体柱的填充率和形状等因素对带隙宽度、带隙位置、耦合带隙以及截止频率造成的影响,从而实现等离子体光子晶体能带结构的可调控性。Plasma photonic crystals are composed of plasma and other dielectric materials or vacuum,and have a periodic structure.Their tunable band gap properties enable plasma photonic crystals to be widely used in the manufacture of military medical devices such as filters,plasma cloaks,and plasma lenses.Therefore,it is of great significance to obtain the energy band structure characteristics we need by changing the parameters such as the density and temperature of the plasma.Based on the above considerations,a Petrov-Galerkin finite element method is proposed to solve and analyze the band gap characteristics of plasmonic photonic crystals.The core idea of this method is to construct a basis function space and a test function space whose coefficients are reciprocal of each other on the boundary,and reduce the degree of freedom while eliminating the integral on the boundary.The adopted grid is a semi-Cartesian projected grid,which can adapt to complex plasma column shapes.When the weak form is established,the interface nonlinear continuous condition is linearized,which simplifies the processing of the interface integral term.By drawing the energy band structure diagram of the numerical example,the effects of the plasma electron density,the filling ratio and shape of the plasma photonic crystal column on the band gap width,band gap position,coupling band gap and cut-off frequency are analyzed and verified.Therefore,the controllability of the energy band structure of the plasma photonic crystal can be derived.

关 键 词：等离子体光子晶体 Petrov-Galerkin有限元法 半笛卡尔投影网格 界面非线性连续条件 能带结构 

分 类 号：O242.21[理学—计算数学]