  Two well-known methods for the design of quasicrystal models are used to
create novel nonlinear optical devices. These devices are useful for efficient
three-wave mixing of several different processes, and therefore offer greater
flexibility with respect to the more common periodic nonlinear photonic
crystals. We demonstrate applications for polarization switching as well as
multi-wavelength and multi-directional frequency doubling. The generalized dual
grid method is proven to be efficient for designing photonic quasicrystals for
one-dimensional collinear devices as well as elaborate two-dimensional
multi-directional devices. The cut and project method is physically realized by
sending finite-width optical beams at an irrational angle through a periodic
two-dimensional nonlinear photonic crystal. This enables two simultaneous
collinear optical processes that can be varied by changing the angle of the
beams.
