光学复合体系中有效介质理论的适用条件  

Application Condition of Effective Medium Theory in Optical Composite System

作　　者：孙洋 张用友 Sun Yang;Zhang Yongyou(School of Physics,Beijing Institute of Technology,Beijing 102401,China)

机构地区：[1]北京理工大学物理学院,北京102401

出　　处：《光学学报》2023年第5期218-225,共8页Acta Optica Sinica

基　　金：国家自然科学基金(12074037)。

摘　　要：以纳米晶掺杂复合体系为例,研究该类多组分光学材料的有效介电系数随复合体系结构和组分介电系数的变化,进而分析有效介质理论的适用条件。假定纳米晶被周期性掺杂到背景晶体中,且均为各向同性材料。借助转移矩阵理论研究发现,当纳米晶和背景晶体的介电系数相差较大时,有效介电系数会表现出波长依赖性。此外,发现复合体系在其光学能隙处没有有效介电系数,说明此时基于等效介质思想的有效介质理论均不适合描述复合体系的光学性质,这是因为在物理上均一的光学材料无法形成光学能隙。Objective The rapid development of micro-nano fabrication technologies enables the synthesis of various optical metamaterials with complex microstructures.The size or component ratio of optical metamaterials can be tuned to control the dielectric properties of optical metamaterials in a wide range.Therefore,analyzing the effective optical parameters of metamaterials has always been a core issue in electromagnetic computing.It is known that the traditional analysis methods for effective optical parameters of composite materials include Maxwell-Garnet effective medium theory and Bruggeman effective medium theory.However,they can only analyze the cases with a small difference between the dielectric constants of the doped and background crystals.When such a difference is large,the error of effective permittivity given by the effective medium theory becomes large as well.This work uses the transfer-matrix method to analyze the effective permittivity of optical metamaterials and discusses the application scope of the effective medium theory.Methods For convenience,we assume that the nanocrystals are periodically doped into the background crystal to form a composite system and the nanocrystals and background crystal are isotropic.These allow us to use the transfer-matrix method to calculate the transmission spectrum of the composite system,and then obtain the effective dielectric constant of the composite system by comparing the transmission spectrum of the original structure with that of the equivalent crystal.The matching degree between equivalent transmission spectrum and original transmission spectrum is measured by the coefficient of determination R2.A larger value of R2 means the effective dielectric constant is more accurate.Results and Discussions This work analyzes the dependence of the effective dielectric constant of composite crystals on the dielectric constant of each component,the geometry parameters of composite crystals,and the light wavelength.The comparison of the effective dielectric constants obtaine

关 键 词：表面光学 光学超材料 转移矩阵理论 有效介质理论 有效介电系数 复合体系 

分 类 号：O436[机械工程—光学工程]