We investigate the interaction of light in gain-enhanced multilayered hyperbolic
metamaterials in the strong interaction regime. Pumping the dye in the dielectric
layers from inside the light cone, while emission occurs into the lower hyperbolic band
outside the light cone, eases the problem of light incoupling. In the strong coupling
regime both emission and absorption lines cause a distortion of the plasmonic modes
due to Rabi splitting and a
PT
-symmetry broken phase, with generation of exceptional
points at loss-gain compensation frequencies. We derive a semi-classical model that
describes these phenomena for finite and infinite devices in detail, requiring only the
overlap factor and the complex frequencies of the dye transition and the optical mode.