Investigating Josephson plasmons in layered cuprates via nonlinear terahertz spectroscopy

Josephson plasmons in layered superconductors represent a natural source of optical non-linearity, thanks to their intrinsically anharmonic nature. Here we derive the selection rules behind non-linear plasmonics showing its dependence on plasmonic branches hidden to other spectroscopies, like RIXS. We benchmark our results for the case of layered cuprates, showing how in a layered system the combined effect of plasmon dispersion and light polarization can move the resonance of the bilayer system away from the plasma edge measured in linear spectroscopy. Our results demonstrate the dependence of the non-linear THz response on the convoluted plasmon dispersion in a momentum region complementary to RIXS, and offer a possible perspective for the generation of THz pulses by artificially designed Josephson heterostructures.