We study the dynamics of excitations in general two-dimensional (2D) lattices with an external spatial linear potential. Analytical expressions for the energy eigenspectrum (Wannier–Stark ladder) and the eigenstates (Wannier–Stark states) of the lattice Schrödinger equation are given, and the resulting periodic motion of localized excitations (Bloch oscillations) is investigated for arbitrary excitation, including single site and broad beam excitation.
© 2007 Optical Society of America
Original Manuscript: June 14, 2007
Revised Manuscript: July 10, 2007
Manuscript Accepted: July 25, 2007
Published: September 19, 2007
Alexander Szameit, Thomas Pertsch, Stefan Nolte, Andreas Tünnermann, Ulf Peschel, and Falk Lederer, "Optical Bloch oscillations in general waveguide lattices," J. Opt. Soc. Am. B 24, 2632-2639 (2007)