  We recently described a general solution to the phase matching problem that
arises when one wishes to perform an arbitrary number of nonlinear optical
processes in a single medium [PRL 95 (2005) 133901]. Here we outline in detail
the implementation of the solution for a one dimensional photonic quasicrystal
which acts as a simultaneous frequency doubler for three independent optical
beams. We confirm this solution experimentally using an electric field poled
KTiOPO$_4$ crystal. In optimizing the device, we find - contrary to common
practice - that simple duty cycles of 100% and 0% may yield the highest
efficiencies, and show that our device is more efficient than a comparable
device based on periodic quasi-phase-matching.
