Nonlocal nature of the electrodynamic response of colloidal systems

In this paper we describe the propagation of the coherent component of an electromagnetic wave in a colloidal system with large inclusions using an effective-medium approach. We show that the effective medium is nonlocal (spatially dispersive) and derive expressions for the nonlocal longitudinal and transverse components of the dielectric response, ϵL and ϵT. Numerical calculations of the wave-vector dependence of these response functions are displayed. The dispersion relation for the transverse modes is calculated and compared with the results obtained using well-known approximations for the effective index of refraction. It is also shown that some of these approximations have actually a nonlocal nature, explaining why it is not possible to use them to calculate, for example, the reflection properties of the colloidal system using conventional continuum electrodynamics. We also calculate the effective nonlocal electric permittivity $ϵ$ and effective nonlocal magnetic susceptibility μ and show that this more traditional description is equivalent to the one using ϵL and ϵT.