Casimir energy in spherical cavities

We calculate the Casimir energy at spherical cavities within a host made up of an arbitrary material described by a possibly dispersive and lossy dielectric response. To that end, we add to the coherent optical response a contribution that takes account of the incoherent radiation emitted by the host in order to guarantee the detailed balance required to keep the system at thermodynamic equilibrium in the presence of dissipation. The resulting boundary conditions allow a conventional quantum mechanical treatment of the radiation within the cavity from which we obtain the contribution of the cavity walls to the density of states, and from it, the thermodynamic properties of the system. The contribution of the cavity to the energy diverges as it incorporates the interaction energy between neighbor atoms in a continuum description. The change in the energy of an atom situated at the center of the cavity due to its interaction with the fluctuating cavity field is however finite. We evaluate the latter for a simple case.Comment: 9 pages, 4 figures, Proceedings of QFEXT07. To be published in J. Phys.

Effective Dielectric Response of Metamaterials

We use a homogenization procedure for Maxwell's equations in order to obtain in the local limit the frequency ($\omega$) dependent macroscopic dielectric response $\epsilon^M(\omega)$ of metamaterials made of natural constituents with any geometrical shape repeated periodically with any structure. We illustrate the formalism calculating $\epsilon^M(\omega)$ for several structures. For dielectric rectangular inclusions within a conducting material we obtained a very anisotropic response which changes along one direction from conductor-like at low $\omega$ to a resonant dielectric-like at large $\omega$, attaining a very small reflectance at intermediate frequencies unrelated to surface plasmon excitation and which can be tuned through geometrycal tayloring. A similar behavior is obtained for other shapes close to the percolation threshold.Comment: 16 pages 7 figures. Accepted in Phys. Rev. B (2009-06-08