Research On The Effect Factor Of Two-dimensional Photonic Crystal Band Gap

The band gap is one of the most fundamental characteristics of photonic crystal. The frequency band of light falling into the band gap will be the prohibition of propagation. Defect states may appear when defects are added to the crystal. Most photonic crystals are artificial structure. Main methods of making photonic crystal are precision machining, colloidal self-organization method, inverse opal structure method, layer by layer stacking method and so on. At present, the photonic crystal is mainly applied to microwave antennas, photonic crystal mirror, photonic crystal filters, photonic crystal waveguides, photonic crystal fibers etc. According to the spatial structure of photonic crystals can be divided into one-dimensional, two-dimensional and three-dimensional photonic crystals. Photonic crystal research methods are mainly plane wave expansion method, the time-domain finite difference method, transfer matrix method. In this paper, the effect of main effect factors on photonic band gap was investigated for the two-dimensional photonic crystal by means of plane wave expansion method.Firstly, the effect of space structure, medium shape, dielectric coefficient and packing ratio on photonic band gap were studied. The result shows that it is easier for TE wave to have band gap than TM wave. Band gap appearing in triangular photonic crystal is easier than that of in square photonic crystals. Honeycomb-shaped photonic crystals are most likely to produce photonic band gap and produced a complete band gap. Medium shape has an effect on width, number, and central location of band gap. Under certain conditions, band gap width increases with the increasing of dielectric coefficient and central location of band gap shifts down with the increasing of dielectric coefficient and packing ratio. Besides, the band gap width of the TE wave increases firstly and then reduces with the increasing of the packing ratio.Secondly, the effect of cylindrical point defect on two-dimensional photonic band gap was investigated. It is found that the point defect affects slightly for band gap width, central location and number of band gap. It is important that defect mode appears in the band gap, and central location of defect mode moves to low frequency with the increasing of dielectric coefficient and the increasing of radius of the defect cylinders, while it moves to high frequency with the increasing of location coordinate of the defect cylinders. Finally, the effect of line defects on photonic band gap was investigated on the two-dimensional photonic crystal. The result shows that both the radius and the width of defect layer in photonic crystal have an obvious effect on photonic band gap. The first band gap width of the TE wave increases firstly and then reduces with increasing of radius of the defect cylinders. The centre of the band gap shifts down and the numbers of band gap are changed with increasing the radius of the defect cylinders. In addition, the band gap width is reduced as the difference between the width of defect layer and the width of normal layer increases. These results have an important guiding significance for us to research the nature of photonic crystals and to produce the ideal photonic crystal devices.