Study On Bandgap Properties And Defective States Of Two Dimensional Complex Periodic Photonic Crystals

Photonic crystal is a periodic artificial crystals with forbidden band characteristics.It can control the transmission of light at different frequencies.Because of its unique optical properties and unique applications in optical devices,it has attracted wide attention from researchers.Compared with simple photonic crystal,complex periodic photonic crystals have better optical controllability.Therefore,two-dimensional complex periodic photonic crystals and defect characteristics are one of the important directions in photonic crystal research.In this paper,two-dimensional complex periodic photonic crystals with triangular lattice and quadrate lattice are constructed,and point defect,line defect,windmill defect and ?-type defects are set up.Then,the effect of defect state on photonic crystal band gap is studied.The main research contents and innovations of this paper are as follows:First,the PWE(Plane wave expand method)is used to calculate the relationbetween the radius size,dielectric constant,and the total forbidden band width and number of photonic crystal for single/recycled triangular lattices and tetragonal lattice photonic crystals.The results show that the complex periodic structure destroys the symmetry of the lattice,and the reduction of the symmetry of the lattice structure can increase the width of the band gap.The width of the complete band gap of the single/complex lattice photonic crystal is greater than the complete band gap of the four square lattice photonic crystals under the same condition;In the case of large and small dielectric cylinders with a radius of 0.48 ?m and 0.01 ?m respectively,the most wide and complete forbidden band of the complex periodic triangular lattice photonic crystal is obtained,its size is 0.08396(?a/2?c).Under the condition of no complete band gap,the dielectric constant of the large and small dielectric columns can be changed to produce complete band gap.And when the radius of the large dielectric column of the triangular lattice photonic crystal is 0.48?m,the dielectric constant is 1,the radius of the small dielectric column is 0.08 ?m and the dielectric constant is 22.8,the width of the band gap is the most wide and the width is up to 0.13448(?a/2?c).Secondly,by using the hyper cell theory of plane wave expansion method,the optical transmission characteristics of the photonic crystal point and line defect stateof the complex periodic triangular lattice with the most wide band gap are studied.The results show that compared with linear defect complex periodic triangular lattice photonic crystals,point defect complex periodic triangular lattice photonic crystals have larger forbidden band width.This is because the point defect photonic crystal can form a flat local mode and limit the light wave to the point defect,so that the light wave can't propagate in the photonic crystal and can only pass the light wave of the specific frequency;However,due to linear defect photonic crystals can't produce flat localized modes,which lead the light waves to propagate directly through defects.Therefore,the requirement to adjust the forbidden band width of photonic crystals can be achieved through artificial defects.Finally,the "windmill" and " ? " type complex defects were innovatively introduced to the single-cycle tetragonal lattice photonic crystals.The influence of the structural parameters of the defect states on the photonic crystal TM band gap was investigated.The results show that the rotation of the odd-window windmill defect and ?-type defects photonic crystal dramatically destroys the symmetry of the defect and improves the width of TM band gap.The increase in the TM band gap width of the even-numbered blade photonic crystal is not significant.However,the windmill defects of even blades are wider than the TM blowbands of windmill defects of odd blades.The TM band gap is the widest at the fault of the four-bladed windmill,reaching 0.05382(?a/2?c).Based on the method of changing the lattice structure of the photonic crystal and the symmetry of the defect structure,we studied the effects of different points,lines and complex defects on the properties of the photonic crystals aiming at the forbidden band and optical transmission characteristics of two-dimensional complex periodic photonic crystals.These will provide a basis for further understanding of the forbidden band characteristics of two-dimensional complex periodic photonic crystals,and provides a theoretical basis and a design method for the artificial modulation of optical transmission properties.