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We investigate optical Bloch oscillation, Zener tunneling and breathing modesin arrays of optical waveguides. We perform a new method of calculation basedon the multiple scattering formalism. To demonstrate Bloch oscillation andbreathing modes, we consider a planar array of parallel cylindrical waveguideswith the refractive index gradually varying across the array. We demonstratethat the form of Bloch oscillation may be predicted by means of dispersion lawanalysis. To demonstrate Zener tunneling, we consider a planar array ofcylindrical waveguides of two types situated by turn. The band structure ofthis array contains two bands separated by a narrow gap. If the refractiveindices of waveguides gradually vary across the array, the Zener tunnelingleads to the Bloch-Zener oscillation.

Optical Bloch oscillation and Zener tunneling in an array of cylindrical waveguides. Numerical simulation