  We investigate optical Bloch oscillation, Zener tunneling and breathing modes
in arrays of optical waveguides. We perform a new method of calculation based
on the multiple scattering formalism. To demonstrate Bloch oscillation and
breathing modes, we consider a planar array of parallel cylindrical waveguides
with the refractive index gradually varying across the array. We demonstrate
that the form of Bloch oscillation may be predicted by means of dispersion law
analysis. To demonstrate Zener tunneling, we consider a planar array of
cylindrical waveguides of two types situated by turn. The band structure of
this array contains two bands separated by a narrow gap. If the refractive
indices of waveguides gradually vary across the array, the Zener tunneling
leads to the Bloch-Zener oscillation.
