  Based on the dyadic Green's function (DGF) method, we present a formalism to
study the propagation of electromagnetic fields with slowly varying amplitude
(EMFSVA) in dispersive anisotropic media with two dyadic constitutive
parameters, the dielectric permittivity and the magnetic permeability. We find
the matrix elements of the envelope DGFs by applying the formalism for uniaxial
anisotropic metamaterials. We present the relations for the velocity of the
EMFSVA envelopes which agree with the known definition of the group velocity in
dispersive media. We consider examples of propagation of the EMFSVA passing
through active and passive media with the Lorentz and the Drude type
dispersions, demonstrating beam focusing in hyperbolic media and superluminal
propagation in media with inverted population. The results of this paper are
applicable to the propagation of modulated electromagnetic fields and slowly
varying amplitude fluctuations of such fields through dispersive and
dissipative (or active) anisotropic metamaterials. The developed approach can
be also used for the analysis of metamaterial-based waveguides, filters, and
delay lines.
