Design of Photonic Crystal Nanocavity With $Q$ -Factor of ${{\sim}10^{9}}$

Photonic crystal nanocavities are expected to make great contributions in areas of physics and engineering such as the slowing and stopping of light and optical quantum information processing. We first review approaches to the goal of increasing the quality factor of two-dimensional photonic crystal nanocavities. Losses from a cavity can be suppressed, with a consequent increase of the quality factor, by containing the electromagnetic field in the form of a Gaussian envelope function. We then propose a new method of analytical cavity design, based on the detailed investigation of waveguide modes, in order to realize Gaussian cavity mode fields. This has enabled us to achieve a quality factor of while maintaining a cavity volume of one cubic wavelength.