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 ultrastrong 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 Letter sets the path toward, as yet, nonexistent ultrafast midinfrared semiconductor saturable absorption mirrors (SESAMs) and bistable systems. As an example, we show how to design a midinfrared SESAM with a 3 orders of magnitude reduction in saturation intensity, down to $\approx 5\mathrm{kW}{\mathrm{cm}}^{-2}$.

Figure 1

(a) Sketch of the QWs embedded in a microcavity array with relevant parameters. (b) Intersubband absorption ${\mathcal{A}}^{\mathrm{ISB}}(n_s,\omega )$ as a function of $n_s$. Inset: reflectivity of the system as a function of $n_s$. (c) Saturation intensity normalized to $I_{\mathrm{sat}}^{\mathrm{WC}}$ (left axis) or following our proposal (right axis) as a function of $n_s$. The black solid line is the asymptotic saturation intensity in the WCR $I_{\mathrm{sat}}^{\mathrm{WC}}$, and the two dashed lines are the asymptotic saturation intensity $I_{\mathrm{sat}}^{\mathrm{SC}}$ in the SCR corresponding to the lower (blue) and upper (green) polaritons. The red solid line is the analytical solution $I_{\mathrm{sat}}^{\pm ,\mathrm{CMT}}$. The black dotted line shows the proposed design for low saturation SESAMs. (d) Sketch of the two operating regimes and potential devices as a function of $n_s$.

Figure 2

(a) Bottom: FEM reflectivity simulations for two different doping densities. Blue, red: low incident power, the polaritonic states are present. Black: high incident power, only the cavity resonance is visible. The arrows indicate the pump frequency used in (b). (a) Top: differential reflectivity $\mathrm{\Delta }R$. (b) Reflectivity of the two design samples, SESAM (blue, $n_s=310^{11}{\mathrm{cm}}^{-2}$) and bistable (red, $n_s=210^{12}{\mathrm{cm}}^{-2}$) as a function of pump intensity obtained from TCMT at the frequencies shown with arrows in (a).