  Layered cuprates offer a preferential playground for optical non-linearity
thanks to the emergence, below Tc, of soft out-of-plane Josephson plasmons. The
hallmark of such a non-linearity is the observation of Third Harmonic
Generation, that has been theoretically understood as a sum-frequency process
involving a two-plasmon excitation. However, recent experiments in cuprates
with two planes per unit cell challenge this interpretation, due to the lack of
resonant response at the temperature where the driving frequency matches the
plasma energy scale, as observed instead in single-layer cuprates. Here we show
that such an apparent discrepancy in bilayer systems can be resolved by taking
into account the combined effect of light polarization and Josephson-coupling
anisotropy on setting the energy range where three-dimensional layered plasma
modes can be resonantly excited. Our results offer a novel perspective on the
possibility to tune on demand high-harmonic generation by artificially
designing Josephson heterostructures.
