Research On Negative Refraction Behavior Of One-dimensional Photonic Crystalswith Fibonacci Sequence

Photonic crystal is a new kind of artificial materials with photons as its information carriers.It is a periodic structure in space composed of different refractive index mediums.Ever since the advent of photonic crystal,people have been getting a strong interest in itsvarious optical properties,especially in negative refraction behavior.After nearly 40 years of research,photonic crystals have been widely applied tovarious fields,such as communications,stealthtechnologyandmaterials,optical devices and other fields,greatly enriching human life.However,due to the existence of photonic band gaps in the photonic crystal,the negative refraction of it seems to be relatively complex.And in such photonic crystal structures,not only negative refraction of the left-handed behavioris possibe,but also may appear negative refraction which does not conform to the left-handed behavior under certain conditions.It becomes particularly significantto distinguish between the refraction of the right-handedbehaviorand the negative refraction ofthe left-handedbehaviorin the photonic crystal.Therefore,in this paper,the negative refraction in the one-dimensional photonic crystal of Fibonacci sequence is explored by analyzing the vector relationshipof the wave vector with the group velocity and the energy flow density.And the theoreticalcriterionwhich can effectively classify the refraction of the left-handed behavior and the right-handed behavior in the photonic crystal will be given clearly.The specific research contents are as follows:First,theoptical properties,application scope and research progress of left-handed materials and their negative refraction are briefly introduced,which leads to the comingexplanations of the concepts,classification standard and optical properties in photonic crystals.In particular,the research,development and application prospects of negative refraction are also systematically expounded here.Second,thorough study of negative refraction phenomena in photonic crystals.After the explainations of the basic concepts related to the photonic crystal theory,such as the lattice,the original cell and the inverted lattice,the Brillouin regions,as well as the Bloch theorem and the equal frequency surface,the energy band theory and several numerical analysis methods of equal frequency surfaces of the photonic crystal are demonstrated and compared with each other,which are popularly used by the academia.Particularly,both the application and the concrete analysis of the plane wave expansion method and the finite difference time domain method are emphatically studied.Next,the specific analysis process and the results of the negative refraction in the photonic crystal with the photonic crystal band structure diagram are described in the traditional research methods.In the meanwhile,based on the vector relationshipof the wave vector with the group velocity and the energy flow density,the criterion for the refraction of the left-handed behaviorand right-handed behavior in the photonic crystal is derived analytically.Moreover,by using the transfer matrix method,the dispersion relation and the group velocity expression of light propagatingin the photonic crystal are deduced.And the negative refraction of one dimensional photonic crystal in Fibonacci sequence is studied by analytical method.Third,according to the analytical study of the negative refraction in the one dimensional photonic crystal of Fibonacci sequence,the negative refraction of the 0 order and the 1 order one-dimensional photonic crystalsof Fibonacci sequencearerespectively analyzed in detail,the theoretical calculation results are compared with the numerical results as well.The findingsshow that when the electromagnetic wave propagates and refracts on the interface of the photonic crystal,if the point product of the unit group velocity and the unit wave vector is equal to +1,there will beacase of isotropic refraction with the right-handed behavior,and if the point product of the unit group velocity and the unit wave vector is equal to-1,then acase of isotropic negative refraction that conforms to the left-handed behavior can occur.In this paper,the analytical study of negative refraction in one dimensional photonic crystal of Fibonacci sequence can not only overcome the shortcomings of the obvious errors in the numerical calculation of the negative refraction in photonic crystals,but also has a very important significance for the study of the negative refraction behavior of one dimensional photonic crystal with a small refractive index.In addition,the one-dimensional photonic crystal structure model of Fibonacci sequence here can satisfy the transition from periodicity to quasiperiodicity with a large coverage.Moreover,through the deep analysis of the frequency band characteristics and the influence factors of the negative refraction characteristics shown by the photonic crystals,it is expected to provide a reference for the design and theoretical research of one-dimensional,even two-dimensional and three-dimensional photonic crystal devices.