A quasi-analytical modal approach for computing Casimir interactions in periodic nanostructures

Abstract

We present an almost fully analytical technique for computing Casimir interactions between periodic lamellar gratings based on a modal approach. Our method improves on previous work on Casimir modal approaches for nanostructures by using the exact form of the eigenvectors of such structures, and computing eigenvalues by solving numerically a simple transcendental equation. In some cases eigenvalues can be solved for exactly, such as the zero frequency limit of gratings modeled by a Drude permittivity. Our technique also allows us to predict analytically the behavior of the Casimir interaction in limiting cases, such as the large separation asymptotics. The method can be generalized to more complex grating structures, and may provide a deeper understanding of the geometry-composition-temperature interplay in Casimir forces between nanostructures.

16 pages, 7 figures

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• Finite temperature Casimir effect for charged massless scalars in a magnetic field
• Thermal effects on the Casimir energy of a Lorentz-violating scalar in magnetic field
• Nonequilibrium atom-surface interaction with lossy multi-layer structures
• Spoof polariton enhanced modal density of states in planar nanostructured metallic cavities
• Tunable non-additivity in Casimir-Lifshitz force between graphene gratings
• Casimir Energies of Periodic Dielectric Gratings
• Perturbative Roughness Corrections to Electromagnetic Casimir Energies
• Polaritonic Contribution to the Casimir Energy between two Graphene Layers
• Mode structure and polaritonic contributions to the Casimir effect in a magneto-dielectric cavity
• How modes shape Casimir Physics
• Calculating Casimir interactions for Periodic Surface Relief Gratings using the C-Method