The problem of an atom inside a cavity in an infinite isotropic medium

Abstract

The problem of a fluctuating atomic or molecular dipole inside a hollow spherical cavity in a homogeneous, isotropic, linear but non-local medium is examined. The difficulty due to the infinite extension of the medium is overcome by solving first, by use of an adequate basis set, the case of a medium limited by a concentric outer sphere of large radius (respecting the symmetry of the problem). It is then shown that when this radius tends to infinity, the results obtained in the quasi-static approximation, and in particular the reflection factors involved in the response field, take definite limits. These results, similar to but different from those obtained with a dipole outside a filled sphere, give a rigorous background to further extend the efficient ‘propagator method’ to the case of atomic or molecular systems confined in hollow cavities, or bubbles of finite thickness, of a micro- or nanometer size.