  Light propagation in asymmetric Kerr-nonlinear multilayers with perfect
transmission resonances is theoretically investigated. It is found that hybrid
Fabry-P\'erot/photonic-crystal structures of the type (BA)^k(AB)^k(AABB)^m
exhibit both pronounced unidirectionality (due to strong spatial asymmetry of
the resonant mode) and high transmission (due to the existence of a perfect
transmission resonance). This results in nonlinear optical diode action with
low reflection losses without need for a pumping beam or input pulse
modulation. By slightly perturbing the perfect transmission resonance
condition, the operating regime of the optical diode can be tuned, with a
trade-off between minimizing the reflection losses and maximizing the frequency
bandwidth where unidirectional transmission exists. Optical diode action is
demonstrated in direct numerical simulation, showing >92% transmittance in one
direction and about 22% in the other. The effect of perfect transmission
resonance restoration induced by nonlinearity was observed analytically and
numerically. The proposed geometry is shown to have advantages over previously
reported designs based on photonic quasicrystals.
