Two-dimensional Triangular Lattice Photonic Crystal Band Gap And Waveguide Properties Of Numerical Study

In this paper, we introduce the general characteristics, applications and theoretical research methods of photonic crystals, systematically . Then, we study respectively the relations of photonic band-gap and structure parameters of two dimensional tri-angular lattice photonic crystals by using plain wave expanding methods (PWE methods) and the transmission properties of linear waveguide of two dimensional tri-angular lattice photonic crystals composed of air holes by using the Finite Difference Time Domain methods (FDTD methods) under TE polarization. The main topics of this thesis are listed as follows:Firstly, we study the relations of band-gap and structure parameters of two dimensional photonic crystals by using PWE methods. The results is below:For two dimensional tri-angular lattice photonic crystals composed of air holes: Big photonic band-gap appears more easily under TE polarization than under TM polarization. The central frequency of photonic band-gap will move towards to higher frequency zone when we enlarge filling ratio (r/α) and it will move towards to lower frequency zone when we increase dielectric constants(ε)For two dimensional tri-angular lattice photonic crystals composed of dielectric poles: Big photonic band-gap appears more easily under TM polarization than under TE polarization. The central frequency of band-gap will move towards to lower frequency zone when we increase filling ratio (r/α) or dielectric constants (ε).Secondly, we study transmission properties of linear waveguide of two dimensional tri-angular lattice photonic crystals composed of air holes under TE polarization by using FDTD methods for the first time. We found:When we change r, the radius of air holes that form linear defect, the larger the r varies, the wider the frequency band width of waveguide turns. When we minish r, the central frequency of waveguide move towards to the lower frequency zone of photonic band-gap. When we enlarge r , The central frequency of waveguide move towards to the higher frequency zone of photonic band-gap.When we enlargeε, the dielectric constant of air holes that form linear waveguide, the frequency band width of waveguide augment rapidly at first, then it minish gradually, so there is a maximum; The central frequency of waveguide always move monotonously towards to the lower frequency zone of band-gap, when we enlargeε.