| All of the electromagnetic phenomena happening in nature everyday are governedby Maxwell Equations,in which permittivity and permeability play an important role.God only constructed limited materials for us and our knowledge is also limited in anarrow region.While most of the people become used to the restrictions on mate-rial region imposed by the nature,someone are not satisfied with such a status.Asa representative,V.G.Veselago introduced the concept of negative index material in1968,whose permittivity and permeability are negative simultaneously which leads tomany interesting phenomena such as negative refraction,reversed Doppler effect andreversed Cerenkov effect.But his work is neglected for about 30 years because Goddidn't give us such kind of material.It seems that it is only a"fantasy"of mankind un-til J.B.Pendry picked up Veselago's work from the garbage and directed us to realizethis idea finally.Based upon the efforts of so many scientists,V,G.Veselago's idea isdemonstrated to be the highest kind of wisdom.This material is named as metamate-rial because of its extraordinary properties which open a new and hot scientific researcharea in the last ten years.While we recall its history,we find that even in ten years agoour knowledge of electromagnetic world is so narrow.So many unknown phenomenaand applications are buried in long time.In chapter 1,we will introduce the history ofthe metamaterial from which we will feel the importance of curiosity of mankind.In chapter 2,photonic crystal is introduced as another kind of novel electromag-netic metamaterial.Unexpected effects appear for photonic crystal containing negativeindex material,which can not be achieved by traditional photonic crystal.For exam-ple,it is a common sense before that two-dimensional or three-dimentional completeband gap must be realized by equal-dimensional photonic crystals which are not easy tobe fabricated in experiments.We study a one-dimensional photonic crystal containinganisotropic negative index material which can open two-dimensional complete bandgap.It is unbelievable at first glance because people naturally wonders how light isstopped along the lateral direction.Our work can not only provide appropriate dielec-tric and structural parameters to realize two-dimensional complete band gap,but alsoexplain the underlying mechanism.Here negative index material play an important role.A fundamental and important problem in metamaterial area is how to determine itseffective permittivity and permeability.People have introduced many effective mediumtheory,among which S-parameter retrieval method is the most popular one.Despite thegreat successes achieved by these methods,there are still several problems.For exam-ple,multiple solution problem exists in S-parameter retrieval method;it is doubtfulabout how to determine the effective parameters near the resonance frequency of meta-material;in some cases effective properties derived from single-layer system will benot applicable to bulk one.To address these problems,we establish a"quasi-mode"theory which can not only study the effective medium properties of metamaterial,butalso judge the qualities of obtained effective pararneters.Some details of our theorycan be found in chapter 3 if you are interested.Gradient materials have been widely studied before.More freedom have beenachieved by us to tune the dielectric parameters using metamaterial.In chapter 4,westudy a sandwich structure consisting of air,metamaterial and perfect metal amongwhich the permittivity and permeability of metamaterial layer have a gradient distribu-tion.Theoretical analysis reveals that scattering mode of the system can be a singlemode if the phase of the reflected waves can be tuned linearly.More interesting,insome special cases,all of waves incident upon our structure can be conversed to sur-face wave.Our prediction have been demonstrated by numerical calculation and modelsimulation.Next we will focus on designing realistic structures to realize the effect.Finally I will give a conclusion in chapter 5.
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