Ultrahigh Purcell factor in photonic crystal slab microcavities

The design of high Purcell factor optical photonic crystal slab microcavities by means of two techniques is presented. First, a combination of stochastic optimization algorithms is used to modify the position of the holes made in a dielectric membrane, breaking their periodic pattern. The combined algorithm is a mixture of a genetic algorithm and a simulated annealing algorithm that is shown to work better than if they were used separately. Secondly, the combined algorithm is used to transform a periodic microcavity where subwavelength sized high-index elements have been inserted. Although the optimization is performed over two dimensional structures with the help of the multiple scattering theory, we show that the optimized microcavities maintain their peculiarities when transformed to their three dimensional equivalent slab microcavities using the finite integration technique. We numerically prove the existence of modified microcavities with extremely small mode volumes of 0.086 91 in (lambda/n)(3) units and ultrahigh Purcell factor of 75 with an enhancement factor of 5.36 with respect to the unperturbed microcavity.