  We investigate different ground-state phases of attractive spin-imbalanced
populations of fermions in 3-dimensional optical lattices. Detailed numerical
calculations are performed using Hartree-Fock-Bogoliubov theory to determine
the ground-state properties systematically for different values of density,
spin polarization and interaction strength. We first consider the high density
and low polarization regime, in which the effect of the optical lattice is most
evident. We then proceed to the low density and high polarization regime where
the effects of the underlying lattice are less significant and the system
begins to resemble a continuum Fermi gas. We explore the effects of density,
polarization and interaction on the character of the phases in each regime and
highlight the qualitative differences between the two regimes. In the
high-density regime, the order is found to be of Larkin-Ovchinnikov type,
linearly oriented with one characteristic wave vector but varying in its
direction with the parameters. At lower densities the order parameter develops
more structures involving multiple wave vectors.
