Optimization of the Q factor in photonic crystal microcavities

We express the quality factor of a mode in terms of the Fourier transforms of its field components and prove that the reduction in radiation loss can be achieved by suppressing the mode's wavevector components within the light cone. Although this is intuitively clear, our analytical proof gives us insight into how to achieve the Q factor optimization, without the mode delocalization. We focus on the dipole defect mode in free-standing membranes and achieve Q > 10^4, while preserving the mode volume of the order of one half of the cubic wavelength of light in the material. The derived expressions and conclusions can be used in the optimization of the Q factor for any type of defect in planar photonic crystals