Discretized disorder in planar semiconductor microcavities: Mosaicity effect on resonant Rayleigh scattering and optical parametric oscillation

The features of resonant secondary emission by two-dimensional multiple semiconductor microcavities are experimentally investigated. The multiband photonic/polaritonic dispersion makes possible a normal laser incidence which represents an isotropic probe of the system defectivity. We show that the static disorder determines the final states of the resonant Rayleigh scattering in the high-symmetry axes of the GaAs matrix. Scanning transmission electron microscopy and x-ray-diffraction measurements reveal the origins of disorder: a small misfit dislocation density and step formation at the layer interfaces due to strain accumulation and relaxation. These mosaicity effects ruled by the symmetry of the underlying GaAs matrix are common features of thick and strained crystals and determine the scattering channels by selecting the crystallographic discretized directions. The structural characterization demonstrates that, while the presence of misfit dislocations plays a minor role, the principal source of disorder is due to the elastic relaxation of strain. Moreover, interband optical parametric oscillation of the intensity balanced signal and idler beams is seeded by the resonant Rayleigh scattering and takes place in the directions selected by the photonic disorder in the distributed Bragg reflector.

Figure 1

(a) HAADF-STEM image of sample A. (b) Magnified view of MC1 of sample A. The different layers are labeled, and the yellow arrows indicate the In${}_{0.07}$Ga${}_{0.93}$As QWs. (c) Scheme of 2D-MMC (the distributed Bragg reflectors are not represented) and of the experimental configuration of excitation/detection of the far field. The angles $\alpha$ and $\beta$ represent the cavity wedges. (d) Cavity modes/lower polariton state dispersions in energy-momentum space. The circle represents the possible final states of the RRS, while dots and arrows specify a particular scattering process $2(0,0)\to 1(+k,-k)$ labeled as R.

Figure 2

RRS ring from sample A (a) and sample B (b) and (c), as measured in the process $2(0,0)\to 1(+k,-k)$ for different $\delta$ and low incident power. The cross-shaped emission at $\phi \simeq$ 315 deg in graphs (b) and (c) is stray light entering in the system. (d) Symbols: intensity of the speckle at $\phi =90$ deg of graph (c) as a function of the incident power. The line is a linear fit to the data.

Figure 3

(a) 220 dark field TEM image of sample A at the first interface substrate/DBR. The white square indicates the area shown in graph (b). (b) High-resolution TEM image of the misfit dislocation shown in (a). (c) HAADF-STEM image of cavity A at the first interface substrate/DBR. The horizontal white lines indicate the areas shown in graphs (d) and (e). (d) and (e) Expanded view of the areas selected in graph (c). Vertical and horizontal axes have different scales in order to evidence the layer tilts. The inset shows a scheme of the layer arrangement. (f) High-resolution x-ray reciprocal space mapping of sample B around the 004 reflection.

Figure 4

(a) Far-field pattern for the interband scattering $2(0,0)\to 1(+k,-k)$ under high excitation power for sample A. (b) Symbols: $S$ intensity as a function of the incident power. The vertical dashed line labels the threshold power P${}_{\text{Th}}$.

Figure 5

(a): Far-field pattern for the interband scattering $2(0,0)\to 1(+k,-k)$ under high excitation power for sample B. Inset: real-space image of resonant transmission. (b) Symbols: S and I intensity as a function of the incident power. The vertical dashed line labels the threshold power $P_{\text{Th}}$. Inset: same as (b) in logarithmic scales. Lines are quadratic (below $P_{\text{Th}}$) and square-root (over $P_{\text{Th}}$) fit to the data.