Transition from strong to ultra-strong coupling regime in mid-infrared metal-dielectric-metal cavities

We have investigated the transition from strong to ultra-strong coupling regime between a mid-infrared intersubband excitation and the fundamental mode of a metal-dielectric-metal microcavity. The ultra-strong coupling regime is demonstrated up to room temperature for a wavelength of $11.7 \mu$m by using 260 nm thick cavities, which impose an extreme sub-wavelength confinement. By varying the doping of our structures we show that the experimental signature of the transition to the ultra-strong coupling regime is the opening of a photonic gap in the polariton dispersion. The width of this gap depends quadratically on the ratio between the Rabi and intersubband transition energies.