The Optimizing For Two-dimensional Photonic Band Gap Geometrical Shape And Parameters By Finite Element Method

The photonic band gap, which could prevent electromagnetic wave with a range of frequency spreading in photonic crystals, is the basic character of photonic crystals. Basing on electromagnetic field theory and numerical algorithms, we mainly research on optimizing photonic band gaps for two-dimensional photonic crystals. We consider the geometric and parametric factors for two-dimensional square lattice photonic crystal band gap structure, including symmetry, rotation, radius and refractive index in the TE and TM modes. In this paper, by the method of numerical simulation, we study and analysis the geometric and parametric factors for two-dimensional square lattice photonic crystal band gap structure.The process, which the electromagnetic wave spreads in photonic crystals, is controlled by the Maxwell equations. In the TE and TM modes,this problem could be converted to the Helmholtz equation system. To this differential equation system, this paper respectively adopts the plane wave method and the finite element method to numerically solve it.Firstly, we use the plane wave method to explore and optimize the structures with simple shapes, such as the band gap of structures with square, circular and square-ring medium boundary. We can conclude that destroying symmetry can produce wider gaps. The process of changing the geometrical shape of medium has a certain gradualness and stability by observing the variation trend of the maximum gaps. Further, we use the high-precision finite element method to optimize the unit cell with a curve boundary, such as the new designed ellipse and 45° oblique ellipse structures. We can get the conclusion that damaging the geometrical symmetry and rotating the dielectric rod could produce a wider gap.This paper includes many numerical simulation experiments, designs several optimal structures of photonic crystals and shows effective new designed schemes in optimizing band gaps. By analyzing the results of numerical experiments operated on MATLAB and COMSOL software,we could see the new designed square-ring structure and the changing process from circular to ellipse, then to 45° oblique ellipse can both widen gaps, coming into the purpose of optimization. The experimental results indicate that the algorithm and designed process are effective.