  A detailed treatment of an electro-optical trap for polar molecules, realized
by embedding an optical trap within a uniform electrostatic field, is presented
and the trap's properties analyzed and discussed. The electro-optical trap
offers significant advantages over an optical trap that include an increased
trap depth and conversion of alignment of the trapped molecules to marked
orientation. Tilting the polarization plane of the optical field with respect
to the electrostatic field diminishes both the trap depth and orientation and
lifts the degeneracy of the $\pm M$ states of the trapped molecules. These and
other features of the electro-optical trap are explained in terms of the
eigenproperties of the polar and polarizable molecules subject to the combined
permanent and induced electric dipole interactions at play.
