  The nonlinear properties of quasiperiodic photonic crystals based on the
Thue-Morse sequence are investigated. The intrinsic spatial asymmetry of these
one-dimensional structures for odd generation numbers results in bistability
thresholds which are sensitive to the propagation direction. Along with
resonances of perfect transmission, this feature allows to achieve strongly
non-reciprocal propagation and to create an all-optical diode. The salient
qualitative features of such optical diode action is readily explained through
a simple coupled resonator model. The efficiency of a passive scheme, which
does not necessitate of an additional short pump signal, is compared to an
active scheme, where such a signal is required.
