Research On The Effect Of Symmetry And Defect For Effection In The Width Of The Band Gap And The Location Of The Defect Mode

Photonic crystals are materials patterned with a periodicity in dielectric constant, which can create a range of 'forbidden' frequencies called a photonic band gap. Photonic crystal cannot only be used to inhibit the spontaneous emission and redistribute the energy into useful forms, but also can be designed to control and confine photons. And The most importantly is that it can be used in the applications of LED and the resonance oscillation and mode selection of chip lasers. There are so many similar properties between photonic crystals and semiconducting crystals. And the ideas, where the photonic crystals were regarded as analogies of semiconducting crystals, also promoted the work of theory and experiment researching of photonic crystals. Following these ideas, comparing the photonic crystals with the semiconducting crystals, the effect of symmetry and defect on the width of the band gap and the location of the defect mode is researched.Based on the calculation result, the cooperation between the symmetry effect and the quantum confinement effect is discussed further. The work is mainly committed to assisting us in designing and creating all-silicon photonic crystal laser. And finally some results were obtained from two aspect below.?1?The calculation results suggest that the reason for the variation of the width of bandbaps is the competition between the symmetry and the quantum confinement effects.?2?The evolution of the localized photonic states in different symmetrical photonic crystal super-cells was investigated. On the one hand, the radius of some dielectric rods at or near the defect H1 are changed simultaneously,to transform the symmetry of the super-cell involving the defect to that of the point group of C_6v,C_3v or C_2v;On the other hand, the evolution of the localized photonic states is studied.The stimulated calculation results demonstrate that the location of the localized photonic states in the photonic band gap?PBG? depends on the radius of the rods,that the evolution of the localized photonic states has its periods and that the amount of the localized photonic states increases with the degree of the relaxation of symmetry increasing. The calculation result suggest that, compared to other super-cells the C2 v super-cell has its superiority where the C2 v super-cell has lower change rate of the radius and slower evolution velocity of the defect mode.