  We demonstrate the strong coupling of direct transition excitons in tungsten
disulfide (WS2) with collective plasmonic resonances at room temperature. We
use open plasmonic cavities formed by periodic arrays of metallic
nanoparticles. We show clear anti-crossings with monolayer, bilayer and thicker
multilayer WS2 on top of the nanoparticle array. The Rabi energy of such hybrid
system varies from 50 to 110 meV from monolayer to sixteen layers, while it
does not scale with the square root of the number of layers as expected for
collective strong coupling. We prove that out-of-plane coupling components can
be disregarded since the normal field is screened due to the high refractive
index contrast of the dielectric layers. Even though the in-plane dipole
moments of the excitons decrease beyond monolayers, the strong in-plane field
distributed in the flake can still enhance the coupling strength with
multilayers. However, the screened out-of-plane field leads to the saturation
of the Rabi energy. The achieved coherent coupling of TMD multilayers with open
cavities could be exploited for manipulating the dynamics and transport of
excitons in 2D semiconductors and developing ultrafast valley/spintronic
devices.
