Photonic Dirac Point Realized In Two Dimensional Annular Photonic Crystals

The acquisition of single-layer Graphene at finite temperature opened a new chapter in the field of physics and material science. After that, the research of Graphene-like Photonic Crystals uncovered a series of unique physical properties,such as zitterbewegung, pseudo scattering, unconventional edge states, etc. Moreover,the Graphene-like Photonic Crystals have been a research hotspot in the field of optical materials due to the application in cloaking as zero-refractive-index materials,which is acquired by accidental degeneracy. In this thesis, we show that by employing accidental degeneracy, dielectric annular photonic crystals can be designed to provide a Dirac point at the center of the Brillouin-zone at a finite frequency, and we explore the formation of the photonic Dirac point by accidental degeneracy in a two-dimensional square lattice dielectric annular photonic crystal, and the theoretical tool is the plane wave expansion method.Firstly, after constructing the structure of annular photonic crystal, we study the general formation process of Dirac point in a two-dimensional square lattice dielectric annular photonic crystal. The results show that this system can provide a Dirac point by accidental degeneracy at the center of the Brillouin-zone in the photonic band if both the outer radius and the inner radius of each scatterer are chosen as appropriate values when the refractive index of the annular rod is fixed. And the results have also showed the variation law, which is explained in the next chapters, of the second, third and fourth band during the formation process of the photonic Dirac point.Secondly, under the condition of air background, we use control variable method to explore the influence of the inner radius RI, outer radius RO and refractive index n on the formation of the photonic Dirac point. The results show that, within a confining region for RO(0.37a<RO<0.5a), when a Dirac point is realized in the annular photonic crystals, the inner radius RI and the outer radius RO obey an invariable relation which has no business with the refractive index n of the dielectric annular rod. If n is less than 1.4, this rule is invalid. At the same time, the normalized photonic frequency at the Dirac point f decreases with both the refractive index n and the outer radius RO.Thirdly, based on the general relation between the Dirac point frequency f and the outer radius RO for different refractive index, the relation between the Dirac point frequency f and the refractive index n for(RO, RI)=(0.45 a, 0.26a) and the invariable relation between the inner radius RI and the outer radius RO, we also do design andprediction for the structure of the annular photonic crystal with a Dirac point. The goal is to obtain the other relative parameters(the normalized photonic frequency f,outer radius RO and inner radius RI) of the photonic crystal system if the refractive index n(n∈[2.8, 4]) is fixed first. The values of the prediction agree very well with the values obtained by the rigid theoretical calculation with a maximum relative error of 4%.Finally, we give a simple summary and potential applications about our work.