Engineering the spatial confinement of exciton polaritons in semiconductors

We demonstrate three-dimensional spatial confinement of exciton-polaritons in a semiconductor microcavity. Polaritons are confined within a micron-sized region of slightly larger cavity thickness, called mesa, through lateral trapping of their photon component. This results in a shallow potential well that allows the simultaneous existence of extended states above the barrier. Photoluminescence spectra were measured as a function of either the emission angle or the position on the sample. Striking signatures of confined states of lower and upper polaritons, together with the corresponding extended states at higher energy, were found. In particular, the confined states appear only within the mesa region, and are characterized by a discrete energy spectrum and a broad angular pattern. A theoretical model of polariton states, based on a realistic description of the confined photon modes, supports our observations.

Figure 1

(Color online) Sketch of the sample (cross-section view). For clarity, the various lengths are not represented to scale. In particular, the mesa pattern has a height $\Delta L=6\mathrm{nm}$, as indicated, while the cavity spacer is approximately $230\mathrm{nm}$ thick.

Figure 2

(Color online) (Left) Measured polariton PL intensity (linear color scale from blue to red) as a function of energy and emission angle for the $3\mu \mathrm{m}$ (a), $9\mu \mathrm{m}$ (b), and $19\mu \mathrm{m}$ (c) mesa. For clarity, the intensity above $1485\mathrm{meV}$ is multiplied by a constant factor, as indicated. Dashed: dispersion of the extended polariton modes, computed from a coupled oscillator model. (Right) Intensity plot of the simulated polariton spectral density for the $3\mu \mathrm{m}$ (d), $9\mu \mathrm{m}$ (e), and $19\mu \mathrm{m}$ (f) mesa (color log-scale, 4 decades from blue to red).

Figure 3

(Color online) Measured polariton PL intensity (color log-scale varying over 1.4 decades from blue to red) as a function of energy and position on the sample, for the $3\mu \mathrm{m}$ (a), $9\mu \mathrm{m}$ (b), and $19\mu \mathrm{m}$ (c) mesa. The horizontal lines to the right of the lowest levels in (a), as well as the faint darker vertical stripes, are experimental artifacts.

Figure 4

(Color online) (a) Computed energy eigenvalues for the photon modes of a circular mesa ($D=8.6\mu \mathrm{m}$, $\hslash \Delta {\omega }_c=-9\mathrm{meV}$). (b) Intensity plot of the photon spectral density (log scale, 4 decades from blue to red).

Figure 5

(Color online) (a) Computed polariton eigenvalues for $D=8.6\mu \mathrm{m}$. (b) Intensity plot of the polariton energy-momentum spectral function for $D=8.6\mu \mathrm{m}$ (log scale, 4 decades from blue to red). The dashed lines indicate the bare polariton dispersion of the planar MC corresponding to the mesa barrier.

Figure 6

(Color online) Simulated squared wave functions of the exciton component as a function of radius, for three selected lower polariton states. Polar numbers $(m,n)$ are indicated. Thin curve: lower polariton confinement potential, computed from the photon and exciton potentials (this latter being the zero energy reference). The curves are offset by the corresponding eigenenergies.

Figure 7

(Color online) (a) Measured PL intensity for the $9\mu \mathrm{m}$ mesa at low pump intensity $P_0$ in the linear regime [same data as in Fig. 2b]. Dashed: extended polariton dispersion from a coupled oscillator model. (b) Pump intensity ${10}^3\times P_0$. (c) Pump intensity ${10}^4\times P_0$. Log-scale covering a factor 30 (a), 30 (b), and 100 (c) from blue to red.