  The interaction between arbitrary dielectric heterostructures is studied
within the framework of a recently developed dielectric contrast perturbation
theory. It is shown that periodically patterned dielectric or metallic
structures lead to oscillatory lateral Casimir-Lifshitz forces, as well as
modulations in the normal force as they are displaced with respect to one
another. The strength of these oscillatory contributions increases with
decreasing gap size and increasing contrast in the dielectric properties of the
materials used in the heterostructures.
