层状材料迭代Debye无色散模型研究  

Research on Iterative Debye Non-dispersion Model of Layered Materials

作　　者：贺之莉[1] 金梦琪 杨文彬 钱雨卿 张永亮[2] HE Zhili;JIN Mengqi;YANG Wenbin;QIAN Yuqing;ZHANG Yongliang(School of lnformatioji Engineering,Chang'an University an 710064,China;Institute of Transportation,Inner Mongolia University,Hohhot Q10Q70,China)

机构地区：[1]长安大学信息工程学院,西安710064 [2]内蒙古大学交通学院,呼和浩特010070

出　　处：《内蒙古大学学报（自然科学版）》2022年第3期299-308,共10页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金资助项目(42074170);陕西省自然科学基金基础研究计划(2020-JQ351)。

摘　　要：色散性质是电介质材料的重要电学性质,其对光子晶体薄板、新型集成导光板等无色散元器件的设计带来严重困扰。基于描述均匀损耗介质电色散特性的经典Debye模型,提出了层状结构材料无色散条件的理论公式,该方法将对层状无色散元器件的设计及横向均匀各向异性测量样本的设计提供理论意义。以层状结构材料在垂直方向的等效电路参数为基础,建立其垂直方向等效电参数计算的迭代Debye模型。另一方面,水平方向等效电路参数理论结果表明层状模型在水平方向的等效电参数与频率无关。由此可见,层状模型可以等效为横向均匀各向异性材料,而其呈现等效电参数无色散的关键在于需要满足垂直方向等效电参数的无色散条件。根据迭代Debye模型理论推导得出无色散条件下各层材料的几何参数和电参数之间的关系,设计满足该关系的层状结构材料并采用有限元方法仿真提取模型的等效电参数。仿真结果与理论结果高度吻合,表明了层状结构无色散理论的有效性。相比于数值仿真,本文方法基于理论推导,具有物理概念清晰,计算结果准确,计算效率高的优势。Dispersion property is an important electrical property of dielectric materials,which brings serious problems to the design of non-dispersion components such as photonic crystal thin plates and new integrated light guide plates.Based on Debye model which describes the electrical dispersion of a uniform lossy material a theoretical formula is proposed for the non-dispersion condition of layer structural materials.This method will provide theoretical significance for the design of layered non-dispersion components and the design of transverse uniform an anisotropy measurement samples.Based on the equivalent circuit parameters of layered materials in vertical direction,an iterative Debye model is established to calculate the equivalent electrical parameters of layered materials in vertical direction.On the other hand,the theoretical results of horizontal equivalent circuit parameters show that the horizontal equivalent electrical parameters of the layered model are independent of frequency.It can be seen that the layered model can be equivalent to the material with transverse uniform anisotropy,and the key to presenting the equivalent electric parameter no dispersion is to satisfy the equivalent electric parameter no dispersion condition in the vertical direction.Based on the iterative Debye model theory,the relationship between the geometric parameters and electrical parameters of each layer of material under the condition of no dispersion is deduced.The layered structure material satisfying the relationship is designed and the equivalent electrical parameters of the model are extracted by the Finite Element Method.The simulation results are in highly consistent with the theoretical results,which shows the effectiveness of the non-dispersion theory of the layered structure.Compared with numerical simulation,the method is based on theoretical derivation and has the advantages of clear physical concepts,accurate calculation results and high calculation efficiency.

关 键 词：层状模型 迭代Debye模型 无色散 等效电参数 各向异性 

分 类 号：TM201[一般工业技术—材料科学与工程]