Purcell-Factor-Enhanced Scattering from Si Nanocrystals in an Optical Microcavity

Scattering processes in an optical microcavity are investigated for the case of silicon nanocrystals embedded in an ultra-high-$Q$ toroid microcavity. Using a novel measurement technique based on the observable mode splitting, we demonstrate that light scattering is highly preferential: more than 99.8% of the photon flux is scattered into the original doubly degenerate cavity modes. The large capture efficiency is shown to result from the Purcell enhancement of the optical density of states over the free space value, an effect that is more typically associated with spontaneous emission. The experimentally determined Purcell factor has a lower bound of 171.

Figure 1

Left: Modal coupling parameter (or doublet “visibility”) $\Gamma$ as a function of $Q$ for several fundamental modes of a ${\mathrm{SiO}}_2$ toroid microcavity. A scanning electron micrograph of a toroid microcavity is shown as the inset. Upper right-hand panel: Characteristic spectral scan, showing a typical mode splitting of $\sim 10\mathrm{MHz}$ and $\Gamma \sim 30$. Lower right-hand panel: Splitting $Q_{\mathrm{split}}$ ($=\omega /\gamma$) as a function of $Q$, which is nearly identical for all modes of the resonator.

Figure 2

Cross-sectional confocal PL images taken on a $72\mathrm{\text{−}}\mu \mathrm{m}$-diameter Si NC doped ${\mathrm{SiO}}_2$ toroidal microcavity. Photoluminescence is collected in 650–690 nm band. (a) $x\mathrm{\text{−}}y$ cross section. (b) $y\mathrm{\text{−}}z$ cross section. Both images are taken with the toroid immersed into index-matching oil doped with rhodamine. The insets show PL spectra taken at characteristic locations in the toroid. The outer bright line in both images is attributed to the PL of the rhodamine dye and serves to determine the cavity’s outer contour.

Figure 3

Normalized splitting parameter ($\Gamma$) as a function of $Q$ for the microcavity from Fig. 2. The solid line is a linear fit to Eq. (3) in the scattering-limited regime (closed circles), yielding ${\tau }_0=115.2\pm 3\mathrm{ns}$, and $\eta =99.42\pm 0.04\%$. The low $Q$ data (stars), fitted with the dashed line, correspond to higher-order (absorption-limited) radial modes [Eq. (2)]. The extrapolated intercept of the data with the vertical axis yields a lower bound for the scattering efficiency (${\Gamma }_x$).