  A theoretical study on the stimulated Brillouin scattering (SBS) in a
sub-wavelength anisotropic waveguide is conducted. The optical, photoelastic
and mechanical anisotropies of the waveguide materials are all taken into
account. First, the integral formulae for calculating the acousto-optical
coupling coefficients (AOCCs) due to the photoelastic and moving interface
effects in SBS are extended to an optically anisotropic waveguide. Then, with
the extended formulae, the SBSs in an elliptical nanowire with strong
transverse anisotropies are simulated. In the simulations, the elastic fields
are computed with the inclusion of mechanical anisotropy. Observable effects of
the strong transverse anisotropies are found in numerical results. Most
notably, the SBS gains of some elastic modes are found to be very sensitive to
the small misalignment between the waveguide axes and the principal material
axes. Detailed physical interpretations of this interesting phenomenon are
provided. This interesting phenomenon implies an attractive way for more
sensitive tuning of the SBS gain without significantly changing the phononic
frequency.
