ABSTRACT
Nonlinear optical effects in silicon nanocrystal structures and their
device applications are receiving widespread attention. The reason
is that the optical nonlinearities of the nanocrystals are much
greater than in bulk silicon, and it is feasible to engineer the
nonlinear optical response of nanocrystal structures by controlling
the size, shape, and orientation of the nanocrystals. Exploiting
these effects will require an understanding of the fundamental
physics behind the associated nonlinear propagation, and accurate
prediction of propagation outcomes through numerical simulations.
Since numerically solving Maxwell equations for structures con-
taining hundreds of thousands of nanocrystals is not practicable,
one must resort to semi-analytical theories that deal with effective
(homogenized) macroscopic parameters of the structures. This
chapter reviews a unified theoretical approach to the modeling
of nonlinear optical phenomena in silicon nanocrystal structures,
based on the effective-medium approximation and the slowly varying amplitude approximation.
