Photon density of states for deformed surfaces

TL;DR

This paper introduces a novel method to analyze the electromagnetic density of states for arbitrarily shaped surfaces, enabling accurate calculations of Casimir forces for complex geometries with both perturbative and non-perturbative results.

Contribution

A new approach to the Helmholtz spectrum for deformed surfaces that allows for comprehensive Casimir interaction calculations across various geometries and boundary conditions.

Findings

Derived boundary-induced density of states change using Green's functions

Computed lateral Casimir force for corrugated surfaces over wide parameters

Identified universal behavior at large separations based on surface wavelength

Abstract

A new approach to the Helmholtz spectrum for arbitrarily shaped boundaries and a rather general class of boundary conditions is introduced. We derive the boundary induced change of the density of states in terms of the free Green's function from which we obtain both perturbative and non-perturbative results for the Casimir interaction between deformed surfaces. As an example, we compute the lateral electrodynamic Casimir force between two corrugated surfaces over a wide parameter range. Universal behavior, fixed only by the largest wavelength component of the surface shape, is identified at large surface separations. This complements known short distance expansions which are also reproduced.