Non-reciprocal second harmonic generation in ferroelectric photonic structures

Second harmonic generation is a powerful tool directly connected to the symmetry of materials. Phase transitions, lattice rotations or electromagnetic coupling in multiferroic compounds can be revealed by using second harmonic generation.[1-4] Here we show that the sense of the spontaneous electric polarization Ps in trigonal ferroelectrics can lead to a pronounced spatial dependence of the second harmonic generation. By using a two-dimensional nonlinear photonic structure we demonstrate that counter-propagating beams along the polar axis generate non-reciprocal second harmonic patterns. In optics, with some exception,[5] non-reciprocal phenomena are generally related to the breaking of time-reversal symmetry involving a magnetic field.[6,7] Here, in contrast, the non-reciprocity is inherent to the quadratic nonlinear tensor being related to the inversion symmetry breaking at the ferroelectric phase. These findings provide novel routes to generate nonreciprocal light-matter interaction processes in two-dimensional structures assembled onto polar surfaces,[8,9] including metals for plasmonics or biological compounds.