The Simulation And Design Of Photonic Crystal Devices

Photonic crystal is a structure patterned with a periodicity in dielectric constant. The prime property of photonic crystal is the existence of gaps, which could prohibit the propagation of electromagnetic wave within a certain range of frequencies, so it can control the light transmission in the medium. For this reason, photonic crystal can offer a good approach to solve the problems of traditional fiber communication systems.In order to obtain good structure and device of photonic crystal, it's necessary to carry theoretical simulation for photonic crystal. In this thesis, methods of the plane wave expansion and the finite difference time domain have been used to simulate the structure and device of photonic crystal. We used the BandSOLVE and FullWAVE software designed by the Rsoft company of America.The so-called two-dimensional photonic crystal means that in two dimensions the refractive index of the medium has a periodicity. However, the other direction unchanged. In this thesis, we investigated the band structures of the square-lattice and triangular-lattice photonic crystal, photonic crystal defect cavity and waveguide in two-dimensional. Firstly, gaps of two dimensional square and triangular lattice photonic crystals with the structure of air rods and dielectric (Si) rods were calculated. The influences of rods radius lattice constant ratio on gap were analyzed in detail and some useful conclusions were received. Then we investigated the 2D air holes photonic crystal cavities. The TE mode bandgap of triangular lattice photonic crystal with point defect was simulated with the plane wave expansion. And we obtained the cavity wavelength and cavity mode profile of the point defect photonic crystal cavity with the finite difference time domain method. The cavity's quality factor was calculated. And we found that the quality factor of 2D photonic crystal cavity was changed by photonic crystal wall thickness with the relation of Index. We simulated the quality factor and cavity wavelength of the cavity structure created by displacing the air holes at both edges, and we found quality factor deceased when the air holes displaced at both edges. The cavity wavelength created by displacing the air holes at both edges was first more than normal point defect's situation, then less than normal point defect. At last we investigated the 2D photonic crystal line-defect waveguides with the structure of dielectric (Si) rods. We obtained the dispersion relation of TM guide mode of square-lattice photonic crystal defect waveguides, and the curve of Group velocity as a function of frequency. We found that Group velocity is small when defect's frequency is near 0.3. This feature can be used to design the optical delay line. The TM guide mode profile of line-defect waveguide was obtained by the plane wave expansion method. And we simulated the field pattern of this line-defect photonic crystal waveguide with the finite difference time domain method.Photonic crystal slab is regarded as a 2D photonic crystal with a finite length in z direction. It's a composite structure of planar waveguide and 2D photonic crystal. Photonic crystal slab can be viewed as a 3D structure with the optical limitation of two-dimensional photonic crystal plane and optical confinement of the vertical direction of the planar waveguide. In this paper, we investigated the band structures of the 2D triangular-lattice photonic crystal slab, the defect cavity and waveguide of photonic crystal slab. Firstly, gaps of photonic crystal slab were calculated by 3D plane wave expansion method. At the same time, we simulated the transmission spectrum of photonic crystal slab with the finite difference time domain method. And we found that band gaps were very similar under these two methods. We discussed two key factors which affect the band gap photonic crystal slab. That is the symmetry about the central plane and slab thickness. Then we investigated the cavities in 2D photonic crystal slab. And we obtained the cavity wavelength and quality factor of the point defect triangular lattice SiO2 hole photonic crystal slab cavity. We analyzed the reason why quality factor of photonic crystal slab is relatively low. We considered the method of displacing the air holes at both edges in order to increase quality factor, and found that cavity wavelength and quality factor will increase with an increase of displacing the air holes at both edges. We investigated the line-defect waveguides of photonic crystal slab later. We obtained the dispersion relation of guide mode of triangular-lattice SiO2 holes photonic crystal slab defect waveguide, and we simulated the field pattern of this line-defect photonic crystal slab waveguide. In order to simulate transmission efficiency we considered the size of the monitor. We obtained a photonic crystal waveguide, the transmission efficiency of whose is over 98%. At last we designed a directional coupler which can split the optical wavelength into 1.617um and 1.606um on two-dimensional triangular-lattice SiO2 holes photonic crystal slab.In addition to periodic photonic crystal, photonic quasi-crystal also possessed photonic bandgap. The structure of photonic quasi-crystal lattices possessed the symmetry of circumrotation and string but not translational symmetry. Compared with periodic photonic crystal, a omnidirectional isotropy bandgap of photonic quasi-crystal was more apparent even for small values of filling factor. Owing to the different effect of every lattice spot in quasi-crystal, defect modes are quite abundance. It's favorable to form photonic crystal resonant cavity. Transmission efficiency of photonic quasi-crystal line-defect waveguide is also relatively high. In this thesis, we designed the 2D structure of 12-fold photonic quasi-crystal, and investigated the transmission character of this 12-fold photonic quasi-crystal. Firstly, we calculated the transmission and reflection spectrum of 2D 12-fold photonic quasi-crystal slab of air holes with the finite difference time domain method. Consequently we obtained the bandgap of this photonic quasi-crystal slab. In order to understand the gap of quasi-crystal better, we simulated the band structure of the slab composed of four super-cells from the 12-fold photonic quasi-crystal. We found that the bigger super-cell we chosen the more similar the bandgap of quasi-crystal slab. Then we calculated the transmission and reflection spectrum of point defect quasi-crystal slab of air holes, and in the meantime we found the cavity wavelength compared with integrated quasi-crystal. At last we designed two photonic quasi-crystal slab waveguides whose transmission efficiency is relatively high.