Lifshitz Interaction between Dielectric Bodies of Arbitrary Geometry

A formulation is developed for the calculation of the electromagnetic-fluctuation forces for dielectric objects of arbitrary geometry at small separations, as a perturbative expansion in the dielectric contrast. The resulting Lifshitz energy automatically takes on the form of a series expansion of the different many-body contributions. The formulation has the advantage that the divergent contributions can be readily determined and subtracted off, and thus makes a convenient scheme for realistic numerical calculations, which could be useful in designing nanoscale mechanical devices.

Figure 1

Schematics of (a) the dielectric function profile and the many-body contributions to the electromagnetic-fluctuation forces, and (b) the two semi-infinite dielectric bodies with irregular surfaces.

Figure 2

Comparison of the expansion in Eq. (3) up to the second, fourth, and sixth order, as well as the Clausius-Mossotti (CM) approximation, with the exact Lifshitz result for a pair of parallel semi-infinite dielectrics, as a function of their separation $H$ in units of the plasma wavelength ${\lambda }_{\mathrm{p}}$. The dielectric constant of both objects is chosen as $ϵ(i\zeta )=1+{\omega }_{\mathrm{p}}^2/({\omega }_0^2+{\zeta }^2)$ with ${\omega }_0^2=2{\omega }_{\mathrm{p}}^2$.