Investigating Of Negative Refraction And Valley-topological States Transport In Photonic Crystals

Photonic crystals is an artificial composite materials with periodic spatial structure and band gaps,which has been paid great attentions to their unprecedented ability for the manipulation of electromagnetic wave.At present,the concept and design method of photonic crystals have been widely adopted in optical communication and sensing and other fields.It has also been used in the development of highperformance,miniaturized,highly integrated micro-nano photonic devices and new optical materials.The degeneracy of the Bloch eigenstate can realize an energy band structure called Dirac cone in the photonic crystal.Due to this unique physical characteristics,the linear dispersion relationship of Dirac cone dispersion relation ship has an important application prospect in the field of manipulating waves,etc.This paper focuses on the physical mechanism and application of Dirac cone dispersion relation ship.The negative refractive index near Dirac-like points and topological effects of Dirac cones are discussed by finite element simulation and average field theory.The main research work and results are as follows:1.Numerically study the three-fold accidental degeneracy conical dispersion(Driac-like cone)at the Brillouin zone center of the two-dimensional photonic crystals,which are arranged in triangular lattice.The effective permittivity and permeability near the Dirac-like point evolve from negative to positive by the method of the averaging the eigen-fields.Also,the isotropic behaviour of the Dirac-like cone is revealed by analyzing the isofrequency contours.Moreover,the negative refractive index characteristics of the designed structure are verified with numerical simulations including the reverse Snell's law effect,negative Goos-H?nchen shifts and superfocusing lens.2.Construct the two-dimensional plasmonic crystals composed of graphene nanodisks where the chemical potential varies in triangular symmetry are proposed.A particular band structure of Dirac-like cone dispersion is obtained at the center of Brillouin zone.A refractive index of the plasmons from negative to positive is calculated by using the theory of the averaging the eigen-fields.In addition,the significant transmission characteristics including the reverse Snell's law effect,directional emission,deep sub-wavelength focusing and negative Goos-H?nchen shifts are simulated with numerical models.Furthermore,the comparison of negative refractive index transmission characteristics between graphene plasmonic crystals and photonic crystals are carried out.3.A honeycomb two-dimensional photonic crystal is designed to construct a valley topological insulator.To achieve this purpose,the Dirac cone is realized at K point in the Brillouin Zone of photonic crystals by using the finite element method.The energy valley at K/K ' is realized by breaking the spatial inversion symmetry of the photonic crystal.As an energy extrema in momentum space,energy valley an offer a new degree of freedom for carrying information.Furthermore,the valley Chern number and the orbital angular momentum at the energy valley are calculated.In addition,valley topological boundary states are built in TM mode and TE mode respectively,which show great advantages in immuning the defect and backscattering.