Dynamic theory of nanophotonic control of two-dimensional semiconductor nonlinearities

We introduce a Maxwell-Bloch simulation approach which self-consistently combines a microscopic description of the carrier and polarization dynamics of a transition-metal-dichalcogenide (TMDC) monolayer with a spatiotemporal full-wave time-domain simulation of Maxwell's equations on the basis of a finite-difference time-domain (FDTD) method beyond the slowly varying amplitude or paraxial approximations. This offers a platform to realistically model, in particular, the typical ultrafast optical excitation experiments in micro- and nanocavities. Our simulations confirm that the weak screening of the Coulomb interaction in TMDC monolayers yields pronounced exciton lines in the linear spectrum and we uncover the second-order nonlinearity represented in the semiconductor Maxwell-Bloch equations by an intraband dipole moment. This allows us to calculate the spectral shape of the exceptionally strong second-harmonic generation around the exciton lines of TMDC monolayers. We demonstrate that the second-harmonic signal can remarkably be further enhanced by several orders of magnitude through a suitably designed (one-dimensional) photonic microcavity. Due to its self-consistency, flexibility, explicit spatio-temporal resolution on the nanoscale and the ready access to light field and electron dynamics, our theory and computational approach is an ideal platform to design and explore spatiotemporal nonlinear and quantum dynamics in complex photonic or plasmonic micro- and nanostructures for optoelectronic, nanophotonic and quantum applications of TMDC monolayers.