  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.
