FDTD Simulation of Inverse 3-D Face-Centered Cubic Photonic Crystal Cavities

We present the modeling and simulation of 3-D face-centered cubic photonic crystal (PhC) cavities with various defects. We use the plane-wave expansion method to map the allowed modes and photonic bandgaps. Having determined the photonic bands we design specific defects and input-output waveguides and model the coupling between defects and waveguides using the 3-D finite-difference time-domain method. We have calculated the Q-factors and modal volumes (Veff) of the resonant cavity modes for the PhC structures made of materials including germanium (Ge), silicon (Si), gallium phosphide (GaP), titanium dioxide (TiO₂), and silica (SiO₂). We then use our estimates of Q and Veff to quantify the enhancement of spontaneous emission and possibility of achieving strong coupling with color centers and quantum dots.