Two-dimensional Photonic Crystal Applied Research

Photonic crystals are periodic nanostructures with photonic band gap (PBG) that forbids the propagation of electromagnetic wave. Due to their potential applications and the unique capability, photonic crystals have been widely investigated both theoretically and practically. Since the theoretical study and the fabrication technology of the two-dimensional photonic crystals have been developed sufficiently, their potential applications in communication field have attracted much attention of research groups from all over, the world, so the study of the two-dimensional photonic crystal is of great importance.We applied both plane-wave expansion(PWE) method and finite difference time domain(FDTD) method in our numerical calculations of two-dimensional photonic crystals, the main work of this paper is listed as follow:1. We introduce the concepts and properties of photonic crystals, as well as current progress in their theoretical, experimental and practical studies. The fundamental theory of PWE and FDTD methods and their applications in the study of two-dimensional photonic crystals are also presented.2. The simulations and analysis of two-dimensional photonic crystals are performed with PWE method, which is programmed in MATLAB. The results have been compared with other methods to confirm the validity of our programs and the Fourier transform approach. We proposed a two-dimensional hexagonal array of cylinders filtrated with EIT atomic vapor, whose complete band gap can vanish by simply tuning the Rabi frequency of the controlling light.3. The point defect modes in two-dimensional square array of anisotropic tellurium cylinders have been calculated with FDTD method, when the radius of the central point defect is tuned., Our numerical results show that the frequencies of the H-polarized defect modes are insensitive to the variation of the radius of point defect. Moreover, we obtain the relationship between the frequency of the defect mode and the radius of the point defect (in or around the center).4. We design some two-dimensional photonic crystal filters, and compared our simulation results with those in other references. Meanwhile, the validity of our design is confirmed. Besides, we design a tunable photon-controlled two-dimensional photonic crystal filter, and study the relationship between the coupling wavelengths and the defect size, as well as the connection between the filter efficiency and the positions of the point defect. The results show that the coupling wavelength is redshift as the radius of the defect grows; and the coupling efficiency dropss when the point defect is away from the waveguide. In conclusion, we investigate the main applications of two-dimensional photonic crystal, and the results could be significant to the design of photonic switches, micro cavities and photonic crystal filters.