Two-dimensional Photonic Crystal Band-gap Structure And Defect States

Photonic crystal is a kind of manufactural composite material withperiodic arrangement of dielectric constant. Either light-wave orelectromagnetic wave can appear photonic band gap when they propagatein the photonic crystal. The propagation of light-wave can be controlledby using the characteristic of band gap. And many potential applicationsin photonic communications can be expected. So the research of photoniccrystals becomes the worldwide hotspot and foreland.In this paper, based on the particular introduction of the plane waveexpansion and FDTD method, the influences on photonic crystal bandgap and propagation of electromagnetic wave were investigated in 2Dphotonic crystal by the dielectric medium parameter, structure of crystallattice, material component, defect and so on.Firstly, the influence on photonic crystal band gap was investigatedby the ratio of dielectric medium constant, the filling fraction, the shapeof insertion and the manner of arrangement. It was shown that the biggerthe ratio of dielectric medium constant, the easier the band gap appeared.The band gap became wider at first and narrower later with theaugmentation of filling fraction. And the band gap of PC was closelyrelated with the shape of insertion and the manner of arrangement. Theresearch of 2D three-component GaAs/glass/air envelope-system showedthat three-component system got the wide band gap more easily thantwo-component system in same arrangement of crystal lattice. And thelowest band gap of the third component GaAs with column core waswider than with square core in the three-component system, but thechange trend of band gap with filling fraction was the same. The bandgap of optional design of the three components' filling-fraction in columncore system reached△ω=0.1848.Secondly, the transmission and the distribution of electric field of 2Dtwo-component system with point cavity defect/linear defects wereinvestigated. And the influence of defect rods filling fraction on band gapstructure was also studied. The results showed that the band gap structures in glass/air system is obviously different from that in GaAs/airsystem, but the defect states were produced in formerly band gap of thetwo integrated system, and these defect states were all localized. So thepropagation of electromagnetic wave will be localized in the defectposition. Therefore, some special filter states/guided states would beformed. The position and width of defect bands were modulated by thefilling fraction of defect rods.Finally, the defect states and the distribution of electric field werestudied in 2D three-component heterogeneous pole system andthree-component envelope-system. It was shown that the third componentmaterial was introduced into two-component system as defect, theposition and with of band gap would be perhaps changed and produceddefect states. The defect states/bands frequency was affected by the thirdcomponent material's physical parameter. And their defect states hadgood wave-guide character. In three-component envelope-system, themodulation of defect states became easier by introducing defects in wideband gap. Owing to the coupling effects among defects which light-wavepropagated in, light-wave with different frequency had differentpropagation behavior, and light propagating of wanted frequency can beallowed by designing suitable combined defects.