Enhanced Second-Order Nonlinearity for THz Generation by Resonant Interaction of Exciton-Polariton Rabi Oscillations with Optical Phonons

Semiconductor microcavities in the strong-coupling regime exhibit an energy scale in the terahertz (THz) frequency range, which is fixed by the Rabi splitting between the upper and lower exciton-polariton states. While this range can be tuned by several orders of magnitude using different excitonic media, the transition between both polaritonic states is dipole forbidden. In this work, we show that, in cadmium telluride microcavities, the Rabi-oscillation-driven THz radiation is actually active without the need for any change in the microcavity design. This feature results from the unique resonance condition which is achieved between the Rabi splitting and the phonon-polariton states and leads to a giant enhancement of the second-order nonlinearity.

Figure 1

(a) Sketch of the conversion mechanism: Left, upper (green curve, ${\omega }_{+}$) and lower (blue curve, ${\omega }_{-}$) exciton-polariton dispersion branches along the $x$ axis; right, upper (yellow curve, ${\omega }_z$) and lower (red curve, ${\omega }_W$) phonon-polariton branches vs wave vector $|\mathit{q}|$. Dots in exciton-polariton branches indicate an example of laser-pumped states with intensity ${\mathcal{R}}_{+}$ and ${\mathcal{R}}_{-}$, respectively, with frequency difference $\tilde{\mathrm{\Omega }}$. The dot in the lower phonon-polariton branch shows the state emitting THz radiation at frequency $\tilde{\mathrm{\Omega }}/2\pi$. (b) Pump scheme: The excitation laser beams impinges the cavity surface each with an angle such that $\sin ({\theta }_{\pm })=c{k}_{\pm }/{\omega }_{\pm }$. The generated phonon polaritons propagate in the cavity plane with $\mathit{q}={\mathit{k}}_{+}-{\mathit{k}}_{-}$ and decay at the interface into THz radiation. (c) Elementary interaction mechanisms: An upper exciton polariton (UXP) is annihilated to create a lower exciton polariton (LXP) plus a phonon polariton (upper or lower depending on $\tilde{\mathrm{\Omega }}$).

Figure 2

Power conversion efficiency of THz photons (in the logarithmic scale) as a function of frequency $\tilde{\mathrm{\Omega }}$ (in units of $\mathrm{\Omega }$) and in-plane wave vector $q_{\parallel }=|{\mathit{q}}_{\parallel }|$ (in units of $\mu {\mathrm{m}}^{-1}$) for resonant pumping ${\omega }_{-}={\omega }_p$ and ${\omega }_{+}={\omega }_u$. We take $\kappa =0.1\mathrm{THz}$, ${\gamma }_b=0.35\mathrm{THz}$, ${\gamma }_l=0.6\mathrm{THz}$, and ${\gamma }_w={\gamma }_z\simeq 0.6\mathrm{THz}$ [21], assuming for simplicity a momentum-independent value. The decay rate of the exciton is neglected, since ${\gamma }_x\sim 0.01\mathrm{THz}$. The white dashed line is the light cone ${\omega }_{\mathrm{ir}}(q_{\parallel })=(c/n_{\mathrm{ir}})|{\mathit{q}}_{\parallel }$. Inset: Cavity detuning $|\delta |$ in units of $\mathrm{\Omega }$ as a function of $q_{\parallel }$ for $\tilde{\mathrm{\Omega }}={\omega }_w$ (red curve) and $\tilde{\mathrm{\Omega }}={\omega }_z$ (yellow curve).