  Room-temperature strong coupling between plasmonic nanocavities and monolayer
semiconductors is a prominent path towards efficient, integrated light-matter
interactions. However, designing such systems is challenging due to the
nontrivial dependence of the strong coupling on various properties of the
cavity and emitter, as well as the subwavelength scale of the interaction. In
this work, we develop a methodology for obtaining hybrid nanostructures
consisting of plasmonic metasurfaces coupled to atomically thin WS2 layers,
exhibiting extreme values of Rabi splitting, by inverse design of the
near-field plasmonic response. Contrary to common measures such as the quality
factor or the mode volume, our method relies on an overlap-integral-based
metric. We experimentally measure large values of Rabi splitting for our
nanoantenna designs, while providing theoretically optimal configurations for
several additional types of nanostructures. Our results open a path to
maximizing light-matter interactions in integrated platforms, for classical and
quantum-optical applications.
