Theoretical Research On Bandgap Characteristic Of2D Photonic Crystals With Compound Lattices

Photonic crystals, whose applications are based on photonic band gaps, are different dielectric materials with different dielectric constant in the structure of spatial periodic arrangement. Researching theoretically the effect of the structure parameters of photonic crystals on bandgap properties, and designing a photonic crystal structure with as large complete band gaps as possible is of great importance for improving the performance of optical devices, like reflector, filter and so on.Decreasing the symmetry of photonic crystal structure can relieve the restriction coming from the photonic band gaps degeneracy in Brillouin for bandgap to get wider effectively. In the paper, lower symmetric compound lattice structure Archimedes (32,4,3,4)、A13are proposed. By means of plan wave expansion method, the bandgap properties of different types of the two kinds of2-D Archimedes compound lattice photonic crystal are simulated under a wide range of refractive index respectively.The effect of scattering body shape, refractive index, packing ratio and rotation symmetry on complete forbidden band are researched,and corresponding physical mechanism are also discussed.The main research contents and conclusions are as follows:(1)As to four common semiconductor materials of high and low refractive index(GaN,GaAs,Si,Ge),we study the relationship between the bandgaps and the filling ratio for different kinds of2-D Archimedes (32,4,3,4)、A13compound lattice photonic crystal.(2)For different kinds of2-D Archimedes (32,4,3,4)、A13compound lattice photonic crystal,what does the bandgap properties have to do with the filling ratio under a wide range of refractive index,and how dose the rotation operation influence on bandgap are studied. The results found that, with smaller refractive index difference, Archimedes (32,4,3,4). A13compound lattice structure can get complete photonic bandgap, and the maximum band width is not continue to increase but has a peak value with the adding of the d-value between two refractive indexes. Moreover, the range of the filling ratio making wide bandgaps are very large. The complete forbidden bandwidth coming from air rods is apparently higher than that from dielectric rods,but the former kind needs lager refractive index materials as its background. Rotation operation can also effect bandgap properties, especially for Archimedes (32,4,3,4) lattice of air square column photonic crystal, it can increase forbidden bandwidth by2.60times and the relative width of band gap by3.00times.(3)In theory, due to the special low cycle symmetry in structure, Archimedes A13compound lattice can produce rather wide complete photonic bandgap, meanwhile, the rotation operation also have a great influence on bandgap, and the simulation results verified the theory:forbidden bandwidth and the relative width of band gap can reach0.13306(ωa/2πc) and33.65%for air circular column,0.07206(ωa/2π c) and23.21%for air square column.If rotate air square column, forbidden bandwidth will be0.77times greater.