Analysis and design of single-defect cavities in a three-dimensional photonic crystal

We theoretically investigate the properties of a single-defect cavity, which is created by adding dielectric material to a three-dimensional (3D) photonic crystal, by utilizing the plane-wave expansion method and the 3D finite-difference time-domain method. We show that the resonant frequency can be controlled well by changing the defect size, and a large frequency separation of the defect modes can be achieved by adjusting the defect shape and position appropriately. We calculate the time response of each defect mode in order to examine the dependence of the quality factor on the number of stacked stripes and on the resonant frequency. The quality factor increases exponentially with the number of stacked stripes. Furthermore, a large quality factor can be obtained with relatively small number of stacked stripes and can be kept very large over a wide frequency range. These results provide significant design rules for developing a single-mode high-Q cavity in a 3D photonic crystal.