  A photonic crystal nanocavity with a Quality (Q) factor of 2.3 x 10^5, a mode
volume of 0.55($\lambda/n$)^3, and an operating wavelength of 637 nm is
designed in a silicon nitride (SiN_x) ridge waveguide with refractive index of
2.0. The effect on the cavity Q factor and mode volume of single diamond
nanocrystals of various sizes and locations embedded in the center and on top
of the nanocavity is simulated, demonstrating that Q > 2 x 10^5 is achievable
for realistic parameters. An analysis of the figures of merit for cavity
quantum electrodynamics reveals that strong coupling between an embedded
diamond nitrogen-vacancy center and the cavity mode is achievable for a range
of cavity dimensions.
