respect to the chiral aspect of the coupling between the excitonic valleys and the plasmonic OSO modes [@LiACS2016; @Gong2017], resulting in the strongly coupled energy diagram shown in Fig. \[fig:1\](c).

![(a) Absorbance spectrum of a WS$_2$ monolayer as obtained from its transmission spectrum. (b) Crystal packing of a tungsten disulfide (WS$_2$) monolayer, and sketch of its electronic band structure around the points $K$ and $K'$ of the Brillouin zone, with the corresponding optical selection rules for band-edge excitons formation under left ($\sigma^+$) and right ($\sigma^-$) circular excitation. (c) Energy level diagram of the $K$ and $K'$ excitons of WS$_2$ strongly coupled to an OSO plasmonic mode at energy $\hbar\omega_{\rm OSO}$ and wavevector $\pm k_{\textrm{\tiny SP}}$. \[fig:1\]](Figure1rev.png){width="1\columnwidth"}

Experimentally, our system, shown in Fig. \[fig:2\](a), consists of a mechanically exfoliated monolayer of WS$_2$ covering a plasmonic OSO hole array, with a $5$ nm thick dielectric spacer (polymethyl methacrylate). The array, imaged in Fig. \[fig:2\](b), is designed on a $(x,y)$ square lattice with a grating period $\Lambda$, and consists of rectangular nano-apertures $(160\times90$ nm$^2)$ rotated stepwise along the $x$-axis by an angle $\phi=\pi/6$. The associated orbital period $6\times\Lambda$ sets a rotation vector $\boldsymbol{\Omega}=(\phi /
\Lambda)\hat{z}$, which combines with the spin $\sigma$ of the 