Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal

The properties of the coupling between a point-defect cavity and a line-defect waveguide in three-dimensional (3D) photonic crystal are investigated theoretically using plane-wave expansion and 3D finite-difference time-domain methods. It is shown that for the symmetric structure where the point and line defects are on the same rod within the photonic crystal, a state is created in which the point- and line-defect modes are completely decoupled due to the mismatch in modal symmetry, while coupled states can be formed by introducing asymmetry. In these asymmetric structures, the strength of coupling between point- and line-defect modes is estimated as a function of the position of the end of the line-defect waveguide by estimating the quality factor of the point-defect cavity. The quality factor is found to oscillate with small changes in the position of the waveguide. For instance, the quality factor changes by a factor of up to $\sim 1.1\times {10}^4$ with small positional change. In addition, the quality factor and light extraction efficiency are estimated when the size of the photonic crystal is finite, as in experimental circumstances. These findings provide very useful design rules for controlling the transfer of light from the point-defect cavity to the line-defect waveguide. These coupling structures are thought to be an important component in 3D photonic crystal optical circuits.