  Design of a doubly-clamped beam structure capable of localizing mechanical
and optical energy at the nanoscale is presented. The optical design is based
upon photonic crystal concepts in which patterning of a nanoscale-cross-section
beam can result in strong optical localization to an effective optical mode
volume of 0.2 cubic wavelengths ((\lambda_{c})^3). By placing two identical
nanobeams within the near field of each other, strong optomechanical coupling
can be realized for differential motion between the beams. Current designs for
thin film silicon nitride beams at a wavelength of 1.5 microns indicate that
such structures can simultaneously realize an optical Q-factor of 7x10^6,
motional mass m~40 picograms, mechanical mode frequency ~170 MHz, and an
optomechanical coupling factor (g_{OM}=d\omega_{c}/dx = \omega_{c}/L_{OM}) with
effective length L_{OM} ~ \lambda = 1.5 microns.
