Casimir Energies of Periodic Dielectric Gratings

Abstract

Reflection of electromagnetic waves from a periodic grating can be described in terms of a discrete coupled multichannel scattering problem. By modeling the grating as a space- and frequency-dependent dielectric, it is possible to use a variable phase method, applied to a generalized Helmholtz equation incorporating both transverse and longitudinal modes, to efficiently compute the scattering $S$-matrix. The projection onto transverse modes of this result, evaluated for imaginary wave vector, provides the information necessary for a Casimir energy calculation. This approach is of particular interest for gratings with deep corrugations, which can limit the applicability of techniques based on the Rayleigh expansion. We demonstrate the method by calculating the Casimir interaction energy between sinusoidal grating profiles as a function of separation and lateral displacement.

6 pages, 2 figures; v2: added clarifications and references

References in corpus (11)

• Casimir forces between arbitrary compact objects
• The Casimir effect within scattering theory
• Measurement of the Casimir force between a gold sphere and silicon surface with nanoscale trench arrays
• Casimir forces in a T operator approach
• Casimir interaction of dielectric gratings
• Lateral Casimir force beyond the Proximity Force Approximation
• The lateral Casimir force beyond the proximity force approximation: a nontrivial interplay between geometry and quantum vacuum
• Comment on ``Lateral Casimir force beyond the proximity-force approximation''
• A quasi-analytical modal approach for computing Casimir interactions in periodic nanostructures
• Variable Phase S-Matrix Calculations for Asymmetric Potentials and Dielectrics
• Calculating Casimir interactions for Periodic Surface Relief Gratings using the C-Method

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