Photonic (or electromagnetic) bandgap, in which the propagation of photon (electromagnetic wave) is forbidden is one of the characteristics of photonic crystals (PCs). Therefore, photonic crystal structures can be employed for the implementation of optical or microwave cavity by overlapping two finite photonic crystals with a predetermined inter-PC distance. Some PC based cavity structures with an extraordinary high quality (Q) factor have recently been reported. However, the mechanism of that high Q-factor has not been thoroughly investigated until now. In this thesis, we have investigated the mechanism that determines the center frequency and Q factor of resonant mode of the PC-based cavity.
We first investigate the resonant mode characteristics of a cavity with two-dimensional (2D) photonic crystal mirrors using the transfer matrix method and FDTD. The first studied PC resonant cavities are composed of a square array of dielectric rods in air. The examined characteristics are the dependence of resonant frequencies and Q factor of a resonant mode on the radius of the rods, and they are compared with the one-dimensional PC cavities studies by invariant embedding method. We also calculated the band structure of 1D and 2D PC cavity is much larger than that of a one-dimension PC cavity using average dielectric constant of that of 2D PC cavity. Between the results, we found that the Q factor depends on the ratio relative location of resonant frequency (ω0) within the absolute magnitude of bandgap and the resonant frequency, i.e Δω/ω0.
We also investigated the same things for the 2D square hole structure in 2D PC cavity and compared with those of 1D PC cavity using average dielectric constant of 2D PC cavity. In this case, Q-factor of 2D PC cavity is not always larger than that of 1D PC cavity. In order to look into that phenomenon in detail, we calculated the band structure and its field distribution. From this study, we find out that Q factor of 2D PC cavity is not always larger than that of 1D PC because of different field confinement effect. That means that the structural parameter plays very important role in enhancing the Q factor.