The solutions showed that waves are best transmitted when their frequency matches a "resonance" value for the nonlinear layers, but as with many nonlinear systems, this frequency depends on the wave's amplitude. However, the dependence is different for oppositely-directed waves because of the asymmetric set-up. So for some amplitudes, if identical waves come from opposite directions, only one of them can have the right combination of frequency and amplitude to be fully transmitted, while the other is largely reflected. They found similar results with larger numbers of nonlinear layers.
Because Lepri's system doesn't rely on harmonics, as the photonic crystal system did, it can transmit light much more efficiently, says Panayotis Kevrekidis of the University of Massachusetts at Amherst. The amount of light that makes it through depends on the properties of the nonlinear material, which means you can tune the system to block some or all of the light. "What the nonlinear medium allows you to do is create perfect transmission," Kevrekidis says.
And it appears from this article that the test to show this isn't going to be too complicated. So it shouldn't be too long for us to hear the first experiment on such a system.