k}_{1}$ and ${\bf k}_{2}$ is given by the angle $\theta$. The parameters $b_{i}$ represent lateral displacements with respect to the configuration with a line of maximum height at the origin. We assume that the corrugation $h_{2}$ is restricted to a rectangular section of area $L_{x}L_{y}$ centered at $x=b_{2},y=0$ and much larger than $L^{2}$ so that diffraction at the borders can be neglected. With these assumptions, and in the limit of long corrugation lines $kL_{y}\gg 1$ with $L_{x}$ smaller or of the order of $L_{y}$, the energy correction per unit area is given in [@RodriguesEPL2006] as $$\begin{aligned}
\frac{\delta E_{\rm PP}}{L_{x}L_{y}}=\frac{a_{1}a_{2}}{2}G_{\rm C}[k]\cos (kb)\frac{\sin (kL_{y}\theta /2)}{kL_{y}\theta /2}.  
\label{torque}\end{aligned}$$ The spatial coefficient $b=b_{2}\cos \theta -b_{1}$ is the relative lateral displacement along the direction ${\bf k}_{1}$. As expected by symmetry, this correction is invariant under the transformation $\theta \rightarrow - \theta$ and $\theta\rightarrow \pi -\theta$ due to the fact that the corrugation lines have no orientation. The case $\theta =0$ corresponds to the result of pure lateral displacement discussed in the preceding section.

The scale of the energy variation with $b$ and $\theta$ is set by the parameter $ \lambda_{\rm C} / L_{y}$. In fact, if plate $2$ is released after a rotation of $\theta 