  It was recently demonstrated that, in deep subwavelength gap resonators
coupled to two-dimensional electron gases, coupling to propagating plasmons can
lead to energy leakage and prevent the formation of polaritonic resonances.
This process, akin to Landau damping, limits the achievable field confinement
and thus the value of light-matter coupling strength. In this work, we show how
plasmonic subwavelength reflectors can be used to create an artificial energy
stopband in the plasmon dispersion, confining them and enabling the recovery of
the polaritonic resonances. Using this approach we demonstrate a normalized
light-matter coupling ratio of {\Omega}/{\omega} = 0.35 employing a single
quantum well with a gap size of {\lambda}/2400 in vacuum.
