Talbot Effect for Exciton Polaritons

We demonstrate, experimentally and theoretically, a Talbot effect for hybrid light-matter waves—an exciton-polariton condensate formed in a semiconductor microcavity with embedded quantum wells. The characteristic “Talbot carpet” is produced by loading the exciton-polariton condensate into a microstructured one-dimensional periodic array of mesa traps, which creates an array of phase-locked sources for coherent polariton flow in the plane of the quantum wells. The spatial distribution of the Talbot fringes outside the mesas mimics the near-field diffraction of a monochromatic wave on a periodic amplitude and phase grating with the grating period comparable to the wavelength. Despite the lossy nature of the polariton system, the Talbot pattern persists for distances exceeding the size of the mesas by an order of magnitude. Thus, our experiment demonstrates efficient shaping of the two-dimensional flow of coherent exciton polaritons by a one-dimensional “flat lens.”

Figure 1

Schematics of (a) an elliptical optical pump illuminating a 1D array of mesa traps in a microcavity and (b) the polariton flows (arrows) responsible for the Talbot effect in panel (d). Real space images of the exciton-polariton emission (c) at low excitation power, below the condensation threshold and (d) at high excitation power, above the condensation threshold. The Talbot effect is visible in panel (d).

Figure 2

(a),(b) Dispersion measurement of the polariton emission from the mesa traps (a) below and (b) above the condensation threshold. Both localized and extended energy states are seen in panel (a). Condensation in two gap states in the first ($G1$) and the third ($G3$) spectral gaps are visible in panel (b). The dashed yellow lines correspond to $\pm k_B/2$ and mark the first Brillouin zone of the array. The solid lines in panel (a) show the first four extended Bloch bands calculated from Eq. (1). (c),(d) Energy filtered reciprocal space image of the condensate emission from the $G3$ state (c) measured in the experiment, and (d) calculated theoretically from the field distribution $f_T(\mathit{r})$ (see text).

Figure 3

(a) Experimental spatial distribution of the polariton emission intensity corresponding to the Bloch mode and the Talbot pattern [energy filtered at the $G3$ position in Fig. 2]. (b),(c) Talbot pattern calculated (b) numerically using the full nonlinear 2D mean-field model and (c) theoretically using the Huygens-Fresnel superposition. The “$+$” and “$-$” signs in panel (c) indicate the relative $\pi$ phase difference between the adjacent sources of the polariton flow located between the mesas (black circles), and $L$ marks the Talbot length. (d) Comparison between $|{\varphi }_B(x){|}^2$ calculated using Eq. (1) (solid line) and the experimental real-space profile (circles) taken along the line $y=0$ in panel (a).