Modulation The Dirac Point Of Photonic Crystal

In 2004, Novoselov successfully produced a single layer of graphite crystals. In the band structure of graphene,Some conical structures with linear dispersion relation exists in the high symmetry points of the Brillouin zone boundary. The central point of those conical structures is called the Dirac point. The Dirac point of the relativistic particle theory has received more and more attention. Because of the similar microstructure between the photonic crystal and the electronic crystal, the Dirac point can be realized the high symmetry point of the photonic crystal’s Brillouin zone.In this paper, we mainly study the modulation of Dirac points in photonic crystals. The specific Dirac point is modulated by introducing anisotropic material or changing the parameters of the column, And use the plane wave expansion method to carry out theoretical analysis and numerical calculation. The main content is below:1. The first chapter briefly introduces: the concept of photonic crystal and Dirac point;Commonly used numerical methods and the advantages of plane wave expansion method; Current status of research on Dirac point in photonic crystals; Derive the matrix form eigen equation of TE wave and TM wave in two-dimensional photonic crystals;and have a briefly introduce to the k·p perturbation theory; Study of Dirac points in photonic crystals by Rsoft simulation software, and use a novel structure or special material to modulate the normalized frequency of the Dirac point and its position in the Brillouin zone, to meet the needs of scientific research and Application.2. Here present a study on the character of Dirac cones in two-dimensional anisotropic photonic crystals which are made of anisotropic material. In these photonic crystals, it can find three different main dielectric constant: εxx, εyy ,εzz . From Maxwell’s equations, the Dirac point in TE wave will be affected by εxx≠εyy. So, it is possible to modulate the main refractive index of the X, Y direction in anisotropic materials, and get a Dirac velocity (△ω/△k) in TE wave. It means researcher can change the Dirac frequency and shifts the k-point in a wide range. Meanwhile, the existence of the Dirac point also has a close relationship with them. Then, researcher start from the photonic crystals made of regular hexagonal rods arranged in a hexagonal lattice for the simulation experiment to prove above points. The features of this new characteristics will add new capabilities and more flexibility to the design techniques of novel photonic components and photonic chip architectures.3. Dirac point in photonic crystals is affected by three primary dielectric constants:εxx,εyy,εzz. In transverse electric (TE) wave,Dirac point realized in some non high symmetry point of Brillouin zone by modulate εxx and εyy. The cylindrical rods arranged in a square lattice anisotropic photonic crystals using bi-axial materials are presented. If εxx=εyy, Dirac point A realized in Brillouin zone center, and Dirac point B realized in Brillouin zone corner. It is investigated that the shifts of Dirac points (△k)are affected by primary dielectric constants difference |△1-△2|.When Dirac point exists,△k and |△1-△2| satisfies a constant relationship. Then Dirac point is realized in a number of non high symmetry points of Brillouin zone. Meanwhile, Dirac point B has high stability, even if εxx and εyy are very different, B still exists.4. In this chapter,elliptical rods arranged in a hexagonal lattice photonic crystal to explore the formation of the photonic Dirac cone by the accidental degeneracy method.The results show that this system can provide a Dirac point at the corner of the Brillouin-zone if the semi-major axis a、semi-minor axis b and the refractive index n of each rod are chosen to be appreciate values. It is also found that within a confined region of a, b, n (2.5≤n≤4, 0.1≤a≤0.5, 0.1≤b≤0.6), when a Dirac point is realized,a, b, n are all inversely proportional to the normalized frequency of Dirac point. The above relationship can be expressed by a series of specific functions, this allows us to be more flexible in the design and modulate of Dirac points. Especially, the refractive index of elliptical rods can influence the existence of Dirac point. This is very rare in other photonic crystals which are made of isotropic materials.