Casimir-Lifshitz force out of thermal equilibrium between dielectric gratings

We calculate the Casimir-Lifshitz pressure in a system consisting of two different one-dimensional dielectriclamellar gratings having two different temperatures and immersed in an environment having a third temperature.The calculation of the pressure is based on the knowledge of the scattering operators, deduced using the Fouriermodal method. The behavior of the pressure is characterized in detail as a function of the three temperaturesof the system as well as the geometrical parameters of the two gratings. We show that the interplay betweennonequilibrium effects and geometrical periodicity offers a rich scenario for the manipulation of the force. Inparticular, we find regimes where the force can be strongly reduced for large ranges of temperatures. Moreover,a repulsive pressure can be obtained, whose features can be tuned by controlling the degrees of freedom of thesystem. Remarkably, the transition distance between attraction and repulsion can be decreased with respect tothe case of two slabs, implying an experimental interest for the observation of repulsion.