Two columnar phases of bent-core molecules have been observed, with a two-dimensional (2D) structure modulated in the plane perpendicular to the direction of the spontaneous polarization vector. The phases are switchable under an applied electric field, contrary to the commonly observed 2D modulated B1 phase. These new phases are built from broken smectic layers with orthogonal or tilted molecules. The evidence for a 3D structure in which the density modulations along and perpendicular to the spontaneous polarization vector co-exists is also given.