  We study the propagation of electromagnetic waves in one-dimensional chirped
periodic structures composed of alternating layers of negative-index (or
left-handed) metamaterial and conventional dielectric, under the condition of
the zero average refractive index. We consider the case when the periodic
structure has a linear chirp, and the chirp is introduced by varying linearly
the thickness of the layers across the structure. We apply an asymptotic
analytical method for the analysis of the Bloch oscillations and find that, in
a sharp contrast to ordinary periodic dielectric structures, the energy flow in
multi-layered stacks with metamaterials may have the opposite direction at the
band edges, thus providing novel possibilities for the beam steering in the
transmission band.
