Discrete periodic structures play an important role in physics, and
have opened up an exciting new area of investigation in recent
years. Questions relating to the control of light in such
structures still represent a major challenge. It is this highly
active field that is addressed in the present thesis. Using the
model system of a photorefractive nonlinearity that allows one to
simultaneously create and control photonic lattices by light, the
author obtains a comprehensive picture of the control of nonlinear
and quantum optics phenomena in photonic lattices. He describes and
demonstrates experimentally for the first time resonant transitions
in two-dimensional hexagonal lattices, including Rabi oscillations
and Landau-Zener tunneling, as well as the direct control and
exploitation of these transitions. A particular highlight of this
thesis is the study of soliton-cluster switching and control of
Zener tunneling.
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