Cross density of states and mode connectivity: Probing wave localization in complex media

We introduce the mode connectivity as a measure of the number of eigenmodes of a wave equation connecting two points at a given frequency. Based on numerical simulations of scattering of electromagnetic waves in disordered media, we show that the connectivity discriminates between the diffusive and the Anderson localized regimes. For practical measurements, the connectivity is encoded in the second-order coherence function characterizing the intensity emitted by two incoherent classical or quantum dipole sources. The analysis applies to all processes in which spatially localized modes build up, and to all kinds of waves

The viability of achieving chiral separation through the optical manipulation of molecules

Several different optical methods have recently been proposed for the potential separation of chiral molecules according to their intrinsic handedness. Applying fundamental symmetry and electrodynamical principles provides a perspective that casts doubt over the viability of some of the more extravagant claims. However there is a genuine basis for achieving chiral separation by using circularly polarized light to deliver chirally sensitive optical forces. The mechanism comes into play when molecules (or nanoscale particles) are optically trapped in a laser beam by forward Rayleigh scattering, as a result of trapping forces that depend on positioning within the beam profile. In such a setup, chiral molecules experience subtle additional forces associated with a combination of electric and magnetic transition dipoles; when circularly polarized light is used for the trapping, a discriminatory response can be identified that has the capacity to separate left- and right-handed molecular isomers. Here, clear differences can be observed between the behavior of isotropic liquids and poled solutions or liquid crystals. Detailed analysis provides an objective basis to assess new prospects for the recognition and differentiation of molecules with opposite chiral form, identifying and paving the way for future commercial applications

Pairwise summation approximation for Casimir potentials and its limitations

We investigate the error made by the pairwise summation (PWS) approximation in three geometries where the exact formula for the Casimir interaction is known: atom-slab, slab-slab and sphere-slab configurations. For each case the interactions are calculated analytically by summing the van der Waals interactions between the two objects. We show that the PWS result is incorrect even for an infinitely thin slab in the atom-slab configuration, because of local field effects, unless the material is infinitely dilute. In the experimentally relevant case of dielectric materials, in all considered geometries the error made by the PWS approximation is much higher than the well-known value obtained for perfect reflectors in the long-range regime. This error is maximized for permittivities close to the one of Silicon