Polaritonic Critical Coupling in a Hybrid Quasi-Bound States in the Continuum Cavity-WS$_2$ Monolayer System

We theoretically propose and numerically demonstrate that perfect feeding of a polaritonic system with full electromagnetic energy under one-port beam incidence, referred to as polaritonic critical coupling, can be achieved in a hybrid dielectric metasurface-WS$_2$ monolayer structure. Polaritonic critical coupling, where the critical coupling and strong coupling are simultaneously attained, is determined by the relative damping rates of the cavity resonance, $\rm \gamma_Q$, provided by a symmetry-protected quasi-bound states in the continuum, and excitonic resonance of WS$_2$ monolayer, $\rm \gamma_X$. We reveal that the population of the polariton states can be tuned by the asymmetric parameter of the quasi-bound states in the continuum. Furthermore, polaritonic critical coupling is achieved in the designed system while $\rm \gamma_Q=\gamma_X$ and only strong coupling is achieved while $\rm \gamma_Q
eq\gamma_X$. This work enriches the study of polaritonic physics with controlled absorbance and may guide the design and application of efficient polariton-based light-emitting or lasing devices.