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

Abstract: The propagation of electromagnetic waves through disordered layered system is considered in the paradigm of Maxwell's equations homogenization. In spite of the impossibility to describe the system in terms of effective dielectric permittivity and/or magnetic permeability the unified way to describe the propagation and Anderson localization of electromagnetic waves is proposed in terms of the introduced effective wave vector (effective refractive index). It is demonstrated that both real and imaginary parts of the effective wave vector (contrary to effective dielectric permittivity and/or magnetic permeability) are the self-averaging quantities at any frequency. The introduced effective wave vector is analytical function of frequency; corresponding Kramers-Kronig relation generalizes the Jones-Herbert-Thouless formula.