  We study the lateral Casimir force between corrugated dielectric plates. We
use the dielectric contrast perturbation theory [R. Golestanian, {\it Phys.
Rev. Lett.} {\bf 95}, 230601, (2005)], which allows us to consider arbitrary
deformations with large amplitudes. We consider sinusoidal, rectangular, and
sawtooth corrugations, for samples made of silicon and gold. We use the plasma
and Drude-Lorentz models for the permittivity of gold and silicon,
respectively. For these geometries and materials, the lateral Casimir force is
{\it not} a sinusoidal function of the relative lateral displacement of plates
when the gap between the plates in comparable with the depth of the
corrugations. Our results facilitate the design of miniaturized devices based
on lateral Casimir forces.
