Strong Optical Confinement between Non-periodic Flat Dielectric Gratings

We present a novel design of optical micro-cavity where the optical energy resides primarily in free space, therefore is readily accessible to foreign objects such as atoms, molecules, mechanical resonators, etc. We describe the physics of these resonators, and propose a design method based on stochastic optimization. Cavity designs with diffraction-limited mode volumes and quality factors in the range of $10^4$--$10^6$ are presented. With a purely planar geometry, the cavity can be easily integrated on-chip using conventional micro- and nano- fabrication processes.