  Optical refrigeration of solids holds tremendous promise for applications in
thermal management. It can be achieved through multiple mechanisms including
inelastic anti-Stokes Brillouin and Raman scattering. However, engineering of
these mechanisms remains relatively unexplored. The major challenge lies in the
natural unfavorable imbalance in transition rates for Stokes and anti-Stokes
scattering. We consider the influence of anisotropic photonic density of states
on Raman scattering and derive expressions for cooling in such systems. We
demonstrate optimization of the Raman cooling figure of merit considering all
possible orientations for the material crystal and two example photonic
crystals. We find that the anisotropic description of the photonic DoS and the
optimization process is necessary to obtain the best Raman cooling efficiency
for systems having lower symmetry. This general result applies to a wide array
of other laser cooling methods in the presence of anisotropy.
