Homogenization of Maxwell's equations in a layered system beyond the static approximation

The propagation of electromagnetic waves through a disordered layered system is considered in the paradigm of the homogenization of Maxwell's equations. Although the accuracy of the effective dielectric permittivity and/or magnetic permeability is still unclear outside the static approximation, we show that the effective wave vector can be correctly introduced even in high-frequency cases. It is demonstrated that both the real and imaginary parts of the effective wave vector are self-averaging quantities connected by the Kramers-Kronig relations. We provide a unified approach to describe the propagation and localization of electromagnetic waves in terms of the effective wave vector. We show that the effective wave vector plays the same role in describing composite materials in electrodynamics as the effective dielectric permittivity does in statics.