Enhanced Resonant Backscattering of Excitons in Disordered Quantum Wells

A clear signature of enhanced backscattering of excitons is observed in the directional resonant Rayleigh scattering of light from localized two-dimensional excitons in disordered quantum wells. Its spectral dependence and time dynamics are measured and theoretically predicted in a quantitative way. The intensity enhancement has a large momentum span extending beyond the external light emission cone. This is a consequence of the small localization length of the exciton as a massive particle probed close to the band bottom. The localization length can be controlled by the photon kinetic energy. This constitutes a qualitative difference to backscattering phenomena in other branches of physics.

Figure 1

Top: sketch of the optical setup and the detection geometry, together with a gray-scale representation of the directionally resolved RRS intensity from a 15 nm SQW for cw excitation at $\hslash {\omega }_{\mathrm{e}}=1.5355\mathrm{e}\mathrm{V}$. Bottom: RRS intensity resolved along $k_x$ (left) and $k_y$ (right), speckle averaged in the orthogonal $k$ direction over $\pm 4\mu {\mathrm{m}}^{-1}$.

Figure 2

Spectrally resolved data for a 15 nm SQW and cw excitation. (a) EBS slope from experiment (circles) and the theoretical prediction for $\gamma =20\mu \mathrm{e}\mathrm{V}$ (dotted line). The experimental (squares) and computed (solid line) RRS spectra are also shown. (b) Solid line: optical density extracted from the measured SE for nonresonant excitation using a carrier temperature of 15 K. Dotted line: SE spectrum for $\hslash {\omega }_{\mathrm{e}}=1.53583\mathrm{e}\mathrm{V}$. Squares: coherent emission fraction $c$ versus $\hslash {\omega }_{\mathrm{e}}$.

Figure 3

(a)–(d) Calculated spectrally resolved RRS intensity in $\mathbf{k}$ space for $\gamma =20\mu \mathrm{e}\mathrm{V}$ and different relative energies $\Delta$, on a logarithmic gray scale covering 1.5 orders of magnitude and relative scaling factors as indicated. The narrow bright spot is the specular direction ${\mathbf{k}}_{\mathrm{e}}$. The white circle in (a) indicates the $\mathbf{k}$ range accessible by external light. (e),(f) RRS intensity at $k_x=0$ versus $k_y$. (e) Different $\Delta$ as indicated, to visualize the EBS slope in the optically accessible range. (f) $\Delta =0.3\mathrm{m}\mathrm{e}\mathrm{V}$ (dots), with fit curve to extract the EBS width. Inset: Characteristic length $\xi$ versus $\Delta$.

Figure 4

Time-resolved SE intensity after resonant pulsed excitation (dashed curve). Time-resolved backscattering slope $s(t)$ from the experiment (symbols and error bars) and the theory (solid curve).