Long-Tail Statistics of the Purcell Factor in Disordered Media Driven by Near-Field Interactions

In this Letter, we study the Purcell effect in a 3D disordered dielectric medium through fluorescence decay rates of nanosized light sources. We report distributions of Purcell factor with non-Gaussian long-tailed statistics and an enhancement of up to 8 times the average value. We attribute this large enhancement to strong fluctuations of the local density of states induced by near-field scattering sustained by more than one particle. Our findings go beyond standard diagrammatic and single-scattering models and can be explained only by taking into account the full near-field interaction.

Figure 1

Left panel: Schematic of the experiment showing a scanning electron microscopy image of the sample and the illumination or collection geometry. Right panel: Decay curves (colored lines) and their fit (white line) for different emitters, two different beads inside the ZnO disordered sample, and in air, on the glass surface.

Figure 2

Decay rates statistics for different experimental geometries (a) for beads on a glass-air and glass-PVA interface, (b) for beads in the $\mathrm{ZnO}+\mathrm{EG}$ sample, and (c),(d) for beads in ZnO. Note that (d) is a zoom out of (c) in log scale that shows the asymmetric tail and several extremely high rates. The symbols identify the decay curve plotted in Fig. 1: The black triangle and the blue square identify a bead in the pure ZnO sample, while the red pentagon represents the bead in air on glass in Fig. 1.

Figure 3

Numerical distribution of the decay rate $\Gamma$ for ZnO particles normalized by the decay rate in vacuum ${\Gamma }_0$ for $R_0=0.07\mu \mathrm{m}$ and $R=1.25\mu \mathrm{m}$. (b) is a logarithmic plot of (a). Inset: Schematic view of the system.

Figure 4

Numerical distributions of the decay rate for four different systems with the same value $k\ell =9.4$ and $R=0.63\mu \mathrm{m}$. Curves (a) and (c) correspond to an excluded radius $R_0=0.07\mu \mathrm{m}$ while (b) and (d) to $R_0=0.14\mu \mathrm{m}$. Curves (c) and (d) are the same as (a) and (b) but with a doubled density of scatterers.