maximal force when $k$ is varied. It corresponds to $k=9\times 10^{-3}$nm$^{-1}$ with the other length scales corresponding to the experiment. The ratio $L / \lambda_{\rm C} = 1 / \pi$ is thus falling outside the PFA sector which confirms that a lateral force measurement is an excellent candidate for probing deviations from the PFA.

Torque {#sec:9}
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Another interesting observable for exploring the non-trivial geometry dependence of the Casimir energy is the torque arising when the corrugations of the two plates are misaligned. With this angular mismatch between the corrugations, rotational symmetry is broken and induces a restoring torque between the plates.

The calculations are quite similar to those which were done for aligned corrugated surfaces, in particular because the same non-specular reflection coefficients are used to describe each plate. The second-order correction is still given by the sensitivity function $G_{\rm C}[{\bf k}]$ which does only depend on the modulus of the corrugation wavevector ${\bf k}$. The difference with the lateral force case lies only in the fact that the corrugation profiles $h_{i=1,2}({\bf r})=a_{i}\cos ({\bf k}_{i}\cdot {\bf r} - kb_{i})$ corresponds to different corrugation wavevectors ${\bf k}_{i=1,2}$ having however the same modulus $k=2\pi /\lambda_{\rm C}$. The angular mismatch between ${\bf 