Nonlinear relaxation and selective polychromatic lasing of confined polaritons

Polaritons have often been proposed as promising candidates for the realization of all-optical devices due to the easy manipulation and control of their density and spin. In this paper we present a relaxation mechanism for confined polaritons and its application in a device based on polariton lasing in which the incoming monochromatic beam can be channeled into several polariton lasers at different wavelengths. Polaritons are injected in a 3 $\mu$m diameter trap by an incoming beam slightly detuned with respect to a confined state, and the resulting optical bistability is then imprinted on the lower confined states through an efficient relaxation mechanism which combines phonon interaction and bosonic stimulation. Above threshold, all the confined states behave like lasers and the onset of coherence is demonstrated by spectral narrowing. Moreover, the initial polarization of the laser is conserved during the relaxation process allowing for spin logic operations. In this paper we demonstrate that, due to the nonlinear behavior, it is possible to switch ON and OFF the lasing from the confined states of the trap by tailoring the input beam. All the experimental findings are validated and very well reproduced in the framework of the generalized Gross-Pitaevskii equation.

Figure 1

(a) Detailed structure of the semiconductor microcavity and the engineered photonic potential (mesa). (b) Numerical simulation of the confined photonic modes $(CS0\text{−}CS4)$ inside the mesa. The blue lines are a guide for the eyes representing the energy of the confining potential. (c) Experimental dispersion for nonresonant excitation. The dispersion shows the upper and lower polariton branches at strong positive detuning $({\delta }_{2D}=4$ meV) and the lower confined states of a 3 $\mu$m diameter mesa. The states considered in the working principle of the device are labeled as $S_j$ with $j=0,1,2,3$. (d) Polariton emission (right axis) as a function of the excitation energy (bottom axis) for $P=100$ $\mu$W.

Figure 2

(a) Spectrally resolved intensity of the mesa emission as a function of the pump power (left axis in log scale) when excited 0.3 meV above $S3$. The sample is excited with ${\sigma }^{+}$ polarization and the emission is detected for cocircular polarization. The color scale is saturated in order to make the low power zone visible. (b) Integrated and normalized density for the confined states of the mesa as a function of the increasing (solid lines) and decreasing (dashed lines) power.

Figure 3

The plot shows the linewidth of all the confined states as a function of the pump power. A narrowing is observed at the onset of the bistability.

Figure 4

(a) Sketch of the energy levels with the relaxation process ($R_{jl}$) and the loss (${\gamma }_j$). (b) Result of the numerical simulations of the density of the confined states coupled through polariton relaxation.

Figure 5

(a) Spectrally resolved intensity map of the mesa emission as a function of the pump power. The sample is excited with ${\sigma }^{+}$ and only ${\sigma }^{-}$ is detected. The color scale of the map is $\sim 400$ times more intense with respect to the case of cocircular polarization detection (Fig. 2). Nevertheless, the emission of ${\sigma }^{-}$ is so weak compared to the one of ${\sigma }^{+}$ that the latter is still visible in the map. (b) Linewidth of the ${\sigma }^{-}$ emission of the confined states as a function of the pump power.

Figure 6

Spectral emission of the mesa for counter-polarized (solid line) and copolarized (dotted line) detection at $P=20$ mW (a) and $P=45$ mW (b). The spectra for copolarized emission are corrected considering the extinction rate of the polarization optics and the different detection configuration.

Figure 7

The plot on the top shows the integrated intensity of the confined states. The intensity threshold for the switch ($I_{th}$) and the powers at which this occurs for the different states are stressed by dashed and vertical dotted lines. The panels in the bottom show the experimental dispersion of the mesa for different powers of the control beam. The emission of three states can be controlled (0–1) by tailoring the input power. A color scale minimum is set in order to simulate an intensity threshold for the switch.