  In liquid crystals, if flexoelectric couplings between polar order and
director gradients are strong enough, the uniform nematic phase can become
unstable to formation of a modulated polar phase. Previous theories have
predicted two types of modulation, twist-bend and splay-bend; the twist-bend
phase has been found in recent experiments. Here, we investigate other types of
modulation, using lattice simulations and Landau theory. In addition to
twist-bend and splay-bend, we also find polar blue phases, with 2D or 3D
modulations of both director and polar order. We compare polar blue phases with
chiral blue phases, and discuss opportunities for observing them
experimentally.
