Local density of photonic states calculation based on multipole expansion method is a powerful tool for studying spontaneous emission and calculation of photon confinement in photonic crystal cavities. Using multipole expansion method, we calculate local density of states and quality factor of a two-dimensional three angle photonic crystal cavity. We also compare this quality factor result with the one calculated using finite difference time domain of a pulse response. It turns out that the local density of states calculation is more accurate and computationally less expensive. It is shown that shifting and changing the size of neighboring cylinders in the vicinity of photonic crystal cavity has a large impact on the mode volume and confinement. It is also described how the increasing of quality factor can be split up into local optimization of neighboring rods and the effect of increasing the number of photonic crystal layers, which exponentially increases the quality factor. This finding strongly suggests that the number of layers can be excluded from an optimization procedure. We also present structural design rules and geometrical freedom contour plots for the neighboring cylinders. These design rules can be used in further optimization of photonic crystal cavities.
Non-Lorentzian Local Density of States in Coupled Photonic Crystal Cavities Probed by Near- and Far-Field Emission
