We show that it is possible to confine light in a volume of order 10^-3 cubic wavelengths using only dielectric material. Low-index (air) cavities are simulated in high index rod-connected diamond (RCD) photonic crystals. These cavities show long storage times (Q-factors >10^6) even at the lowest volumes. Fabrication of such structures could open up a new field of photon level interactions.
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