We show that optical Bloch oscillations can emerge in waveguide arrays
with Linearly varying propagation constants. The existence of localiz
ed modes (Wannier-Stark. states) with equidistant wave-number spacing
(Wannier-Stark ladder) that do not undergo diffraction is analytically
proved. The evolution of arbitrary initial excitations is described,
and potential applications are suggested. (C) 1998 Optical Society of
America.