  Light emitters in vicinity of a hyperbolic metamaterial (HMM) show a range of
quantum optical phenomena from spontaneous decay rate enhancement to strong
coupling. In this study, we integrate monolayer Molybdenum disulfide (MoS$_2$)
emitter in near field region of HMM. The MoS$_2$ monolayer has A and B
excitons, which emit in the red region of visible spectrum. We find that the B
excitons couple to HMM differently compared to A excitons. The fabricated HMM
transforms to a hyperbolic dispersive medium at 2.13 eV, from an elliptical
dispersive medium. The selective coupling of B Excitons to the HMM modes is
attributed to the inbuilt field gradient of the transition. The B exciton
energy lies close to the transition point of the HMM, relative to A Exciton.
So, the HMM modes couple more to the B excitons and the metamaterial functions
as selective coupler. The coupling strength calculations show that coupling is
2.5 times stronger for B excitons relative to A excitons. High near field of
HMM, large magnitude and the in-plane transition dipole moment of MoS$_2$
Excitons, result in strong coupling of B excitons and formation of hybrid
light-matter states. The measured differential Reflection and Photoluminescence
spectra indicate the presence of hybrid light-matter states i.e.
Exciton-Polaritons. Rabi splitting of at least 129 meV at room temperature is
observed. The low temperature Photoluminescence measurement shows mode
anticrossing, which is characteristic feature of hybrid states. Our results
show that the HMM works as a energy selective coupler for multi-excitonic
systems as MoS$_2$.
