Role of Coherence in Polarization Response of Hybrid Monolayer MoS$_2$-Gold Nanoparticle Systems
Monolayers of transition metal dichacogenides show strong second-order nonlinearity and symmetry-driven selection rules from their three-fold lattice symmetry. This process resembles the valley-contrasting selection rules for photoluminescence in these materials. However, the underlying physical mechanisms fundamentally differ since second harmonic generation is a coherent process, whereas photoluminescence is incoherent, leading to distinct interactions with photonic nanoresonators. In this study, we investigate the far-field circular polarization properties of second harmonic generation from MoS$_2$ monolayers resonantly interacting with spherical gold nanoparticles. Our results indicate that the coherence of the second harmonic allows its polarization to be mostly preserved, unlike in an incoherent process, where the polarization is scrambled. These findings provide important insights for future applications in valleytronics and quantum nanooptics, where both coherent and incoherent processes can be probed in such hybrid systems without altering sample geometry or operational wavelength.