General recipe for designing photonic crystal cavities

We describe a general recipe for designing high-quality factor (Q) photonic crystal cavities with small mode volumes. We first derive a simple expression for out-of-plane losses in terms of the k-space distribution of the cavity mode. Using this, we select a field that will result in a high Q. We then derive an analytical relation between the cavity field and the dielectric constant along a high symmetry direction, and use it to confine our desired mode. By employing this inverse problem approach, we are able to design photonic crystal cavities with Q > 4 ? 10(6) and mode volumes V ~ (lambda/n)(3). Our approach completely eliminates parameter space searches in photonic crystal cavity design, and allows rapid optimization of a large range of photonic crystal cavities. Finally, we study the limit of the out-of-plane cavity Q and mode volume ratio.