Unified description of saturation and bistability of intersubband transitions in the weak and strong light-matter coupling regimes

We propose a unified description of intersubband absorption saturation for quantum wells inserted in a resonator, both in the weak and strong light-matter coupling regimes. We demonstrate how absorption saturation can be engineered. In particular we show that the saturation intensity increases linearly with the doping in the strong coupling regime, while it remains doping independent in weak coupling. Hence, countering intuition, the most suitable region to exploit low saturation intensities is not the ultra-strong coupling regime, but is instead at the onset of the strong light-matter coupling. We further derive explicit conditions for the emergence of bistability. This work sets the path towards yet unexisting ultrafast mid-infrared semiconductor saturable absorption mirrors (SESAMs) and bistable systems. As an example, we show how to design a mid-infrared SESAM with a three orders of magnitude reduction in saturation intensity, down to about 5 kW/cm2.