Theoretical Research On Bandgap Characteristic Of Archimedean Lattices Photonic Crystals

Photonic crystals are new man-made materials with periodic variation in their electromagnetic properties, which are especially of interest owing to the possibility of having complete photonic band gaps (PBGs), a range of frequencies for which the propagation of any kinds of electromagnetic waves in any directions is prohibited. Large numbers of applications of photonic crystals are based on this characteristic. For different photonic crystal structures, the refractive index, dielectric filling ratio, lattice structure, rods shape, lattice symmetry and other parameters will affect the band structure of photonic crystals, but only certain conditions met it will have a complete photonic band gap in the periodic structure, therefore, seeking for the ideal structure parameters is one of the main theoretical researches.Because of symmetry of the compound lattice structures decreasing, photonic band gaps degeneracy was partly eliminated. That lattice structures will produce or increase photonic band gaps. Based on this principle, plane wave expansion method was used to study on the band gap characteristics of two-dimensional Archimedes A7,(4,82),(33,42) compound lattices photonic crystals. The thesis includes the following contents:(1). Plane wave expansion method was used to research on the band characteristics of two-dimensional Archimedes A7,(4,82),(33,42) compound lattices photonic crystals composed of the four semiconductor materials GaN, GaAs, Si, Ge. The four materials were studied separately as a function of the filling ratio, dielectric rods shape and so on as the background materials and the medium rods, respectively. and further optimize the structure to get the optimization parameters of the three lattices.(2). Research the two dimensional circular and square rods respectively of the three kinds of Archimedes compound lattice photonic crystals on the largest complete photonic band gaps (PBGs) as the index of refraction of the relationship changes. It is showed that the three lattices can produce complete photonic bandgap when the refractive index is as low as2.60, and in certain refractive index (or dielectric constant) range, the complete photonic band gap presents monotony change that caused by the refractive index changing; however, with the refractive index range further expanding, the relationship between complete photonic band gaps and refractive index is varied:Some lattices appear one peak, for example, the Archimedes(4,82) lattice of dielectric circular rods in the air, the Archimedes(3,4) lattice of square or circular rods and the Archimedes A7lattice of air rods in the dielectric; but also some have two peaks, for example, the Archimedes(4,82) lattice of dielectric square rods in the air and the Archimedes A7lattice of dielectric rods in air.(3). In the paper, we take two dimensional Archimedes A7,(4,82) lattices photonic crystal as examples to research on the complete photonic band gaps(PBGs) by changing of the rotation angles. It is founded that rotation some angle has little influence on the complete photonic band gaps of the Archimedes A7lattice and Archimedes (4,82) lattice (n=4.4), however, the PBGs of the Archimedes (4,82) lattice can increase by50%or so through rotation some angle.