We measure the Casimir force between a gold sphere and a silicon plate with nanoscale, rectangular corrugations with a depth comparable to the separation between the surfaces. In the proximity force approximation (PFA), both the top and bottom surfaces of the corrugations contribute to the force, leading to a distance dependence that is distinct from a flat surface. The measured Casimir force is found to deviate from the PFA by up to 10%, in good agreement with calculations based on scattering theory that includes both geometry effects and the optical properties of the material.

We compute the radiative heat transfer between nanostructured gold plates in the framework of the scattering theory. We predict an enhancement of the heat transfer as we increase the depth of the corrugations while keeping the distance of closest approach fixed. We interpret this effect in terms of the evolution of plasmonic and guided modes as a function of the grating's geometry.