Casimir interaction between a sphere and a grating

We derive the explicit expression for the Casimir energy between a sphere and a 1D grating, in terms of the sphere and grating reflection matrices, and valid for arbitrary materials, sphere radius, and grating geometric parameters. We then numerically calculate the Casimir energy between a metallic (gold) sphere and a dielectric (fused silica) lamellar grating at room temperature, and explore its dependence on the sphere radius, grating-sphere separation, and lateral displacement. We quantitatively investigate the geometrical dependence of the interaction, which is sensitive to the grating height and filling factor, and show how the sphere can be used as a local sensor of the Casimir force geometric features. To this purpose we mostly concentrate on separations and sphere radii of the same order of the grating parameters (here of the order of one micrometer). We also investigate the lateral component of the Casimir force, resulting from the absence of translational invariance. We compare our results with those obtained within the proximity force approximation (PFA). When applied to the sphere only, PFA overestimates the strength of the attractive interaction, and we find that the discrepancy is larger in the sphere-grating than in the sphere-plane geometry. On the other hand, when PFA is applied to both sphere and grating, it provides a better estimate of the exact results, simply because the effect of a single grating is underestimated, thus leading to a partial compensation of errors.Comment: 16 pages, 7 figure

The Casimir effect in the sphere-plane geometry

We present calculations of the Casimir interaction between a sphere and a plane, using a multipolar expansion of the scattering formula. This configuration enables us to study the nontrivial dependence of the Casimir force on the geometry, and its correlations with the effects of imperfect reflection and temperature. The accuracy of the Proximity Force Approximation (PFA) is assessed, and is shown to be affected by imperfect reflexion. Our analytical and numerical results at ambient temperature show a rich variety of interplays between the effects of curvature, temperature, finite conductivity, and dissipation.Comment: Proceedings of the 10th International Conference "Quantum Field Theory Under the Influence of External Conditions" (Benasque, Spain, 2011); 10 pages and 6 figure

Reply to ``Comment on ``Lateral Casimir Force beyond the Proximity Force Approximation'' ''

We reply to the comment arXiv:quant-ph/0702060 on our letter arXiv:quant-ph/0603120 [Phys. Rev. Lett. 96, 100402 (2006)]Comment: 1 pag

Advancing numerics for the Casimir effect to experimentally relevant aspect ratios

Within the scattering theoretical approach, the Casimir force is obtained numerically by an evaluation of the round trip of an electromagnetic wave between the objects involved. Recently [Hartmann M et al. 2017, Phys. Rev. Lett. 119 043901] it was shown that a symmetrization of the scattering operator provides significant advantages for the numerical evaluation of the Casimir force in the experimentally relevant sphere-plane geometry. Here, we discuss in more detail how the symmetrization modifies the scattering matrix in the multipole basis and how computational time is reduced. As an application, we discuss how the Casimir force in the sphere-plane geometry deviates from the proximity force approximation as a function of the geometric parameters.Comment: 9 pages, 8 figure