The Breakdown Of Maxwell Garnett Effective Medium Theory Due To Evanescent Field At Deep Subwavelength And Its Correction

The Effective Medium Theory(EMT)is a simple and widely used homogenization theory,which plays a great role in predicting the performance of composite materials.Maxwell-Garnett Effective Medium Theory(MG EMT)is an important part of EMT.Deep-subwavelength all-dielectric composite materials are believed to tightly obey the Maxwell-Garnett effective medium theory.Here,this paper proves that the Maxwell-Garnett theory could be no longer applicable due to evanescent fields in deep-subwavelength dielectric structures.By utilizing two-and three-dimensional dielectric composite materials with inhomogeneities at the scale ofl100,we show that local evanescent fields generally occur nearby the dielectric inhomogeneities.When tiny absorptive constituents are placed there,the absorption and transmission of the whole composite will show strong dependence on the positions of the absorptive constituents.The Maxwell-Garnett theory fails to predict such position-dependent characteristics,because it averages out the evanescent fields.By taking the distribution of the evanescent fields into consideration,we made a correction to the Maxwell-Garnett theory,such that the position-dependent characteristics become predictable.We reveal not only the breakdown of the Maxwell-Garnett theory,but also a unique phenomenon of “invisible” loss induced by the prohibition of electric fields at deep-subwavelength scales.Our work promises a route to control the macroscopic properties of composite materials without changing their composition,which is beyond the traditional Maxwell-Garnett theory.This article is divided into five chapters.The main contents are arranged as follows:The first chapter is introduction.We introduce the meaning and development of metamaterials and the origin of the effective medium method and the main constituent theories emphatically.The Maxwell-Garnett effective medium theory and related formulas studied in this paper are introduced in detail.The second chapter is the failure of Maxwell-Garnett’s effective medium theory.We mainly introduce the influence of the evanescent field caused by the inhomogeneity of the medium on the accuracy of Maxwell-Garnett effective medium theory,then analyze the process.The third chapter is correction of the traditional Maxwell-Garnett effective medium theory.This chapter is based on the breakdown of Maxwell-Garnett effective medium theory in Chapter 2.The Maxwell-Garnett effective medium theory is corrected according to the electric field distribution in the inhomogeneous medium and the details of derivation is given.The fourth chapter is simulation and verification of corrected Maxwell-Garnett formula.This chapter verifies the accuracy of the corrected Maxwell-Garnett effective medium theory proposed in Chapter 3.The simulation verification is carried out by different dielectric composite structures in two-dimensional and three-dimensional situations in the finite element analysis software COMSOL Multiphysics.It is finally proved that the accuracy of the corrected formula is very high.The last chapter is summary and discussion.We summarize the results of our work and its value in scientific research and discuss the results.