>\lambda_{\rm C} / L_{y}$, its subsequent motion is a combination of rotation and lateral displacements. Rotation is favored over lateral displacements for $\theta <\lambda_{\rm C} / L_{y}$ (see Fig.(1) in [@RodriguesEPL2006]). The torque $\tau = - \partial \delta E_{\rm PP} / \partial\theta $ is evaluated in [@RodriguesEPL2006] for corrugated Au mirrors, with corrugation amplitudes $a_{1}=a_{2}=14$nm, corrugation length $L_{y}=24\mu$m and separated by a distance of $L=1\mu$m. It is maximum at $\theta = 0.66 \lambda_{\rm C} / L$ and is plotted in Fig.(\[fig:6\]) as a function of $k$. It starts increasing linearly with $k$ in the $k\rightarrow 0$ PFA sector and for the same reason as the lateral force, it decreases exponentially in the high-$k$ limit.

As is clear on Fig.(\[fig:6\]), the PFA overestimates the magnitude of the torque by a factor of the order of $2$ at the peak value of the torque. The discrepancy even increases with $k$, since smaller values of $k$ correspond to smoother surfaces. The conditions are gathered up towards a direct experimental evidence of a non-trivial effect of geometry.

Fig.(\[fig:6\]) also displays the torque when evaluated between perfect metallic corrugated mirrors [@EmigPRA03]. The corresponding deviation with respect to the calculation given by Eq.(\[torque\]) stresses that at 