Arbitrary Shape Of The Two-dimensional Photonic Crystal Properties Study

In recent years there has been a fast development in the research of photonic crystals, and much work has done both theoretically and experimentally.Photonic crystals have the properties of photonic band gaps and photanic localization, and many potential applications in communications can be expected. To find a photonic crystal structure with a larger absolute gap is still one of the research directions in this field.This paper discussed two kind geometry structure of medium PBG triangle lattice and square lattice using the plane-wave expanded method. I used MATLAB to programme and calculate two-dimensional medium photonic crystal triangle lattice and square lattice two kinds of arrangements'band gap structures. Through calculated band gap structures many times, I drew the global PBG-bands of two-dimensional medium photonic and found the quite obvious band gap from the chart,and several valuable achievements are listed as the followings:1. First, we calculated the expanded Fourier expansion coefficient of dielectric distributed functoion by methods of numerical integration and Monte Carlo. As method of numerical integration, we divided the region of integration into some triangles and added these results that integration in each triangle. Monte Carlo is a statistical method and judge the relationship of points and the region of integration to be a committed step. When the region of integration has much more points, the result is very accurate.2. With dielectric constant distribution function of Fourier coefficients as a foundation, we calculated the arbitrary shape two-dimensional photonic crystals'bandgap structures by PWM (Plane Wave Expansion Method). The main method of solving bandgap structure is to calculate the eigenvalues of the intrinsic equation.3. The results by the methods of this paper were accorded with the results of CST(Computer Simulation Technology)and Ref[39] very well and analysed PBG-bands'some regular rules when photonic crystals's structure, filling ratio and dielectric constant were changed.4.Through theoretical analysis and numerical calcuation , the obtained band-structures of photonic crystals structures in this paper demonstrated some rules when the dielectric constant of filling area is small and the dielectric constant of background area is large, the PBG-bands of the H polarization are extraordinary wide when the filling ratio is 0.65. When the dielectric constant of filling area is large and the dielectric constant of background area is samll, the obtained PBG-bands of the E polarization are comparatively wide when filling ratio is small.5.We applyed photonic crystals to slow-wave structure and used CST(Computer Simulation Technology)to emulate photonic crystal dielectric pillar's helix. Then, we analysed their dispersion characteristics and the coupling impedance.