Observation of Spatial Fluctuations of the Local Density of States in Random Photonic Media

We experimentally study spatial fluctuations of the local density of states (LDOS) inside three-dimensional random photonic media. The LDOS is probed at many positions inside random photonic media by measuring emission rates of a large number of individual fluorescent nanospheres. The emission rates are observed to fluctuate spatially, and the variance of the fluctuations increases with the scattering strength. The measured variance of the emission rates agrees well with a model that takes into account the effect of the nearest scatterer only.

Figure 1

(a) Time-correlated single-photon counting setup with mode-locked supercontinuum fiber laser, CCD camera, and single-photon avalanche photodiode (SPAD). (b) Scanning electron micrographs (SEMs) of random photonic media made of polystyrene (PS) (top) and zinc oxide (ZnO) (bottom). (c) Fluorescence image of a single fluorescent nanosphere with a diameter of 22 nm embedded in a $7.4(5)\mu \mathrm{m}$-thick slab of PS random photonic medium at a depth $d=3.3\mu \mathrm{m}$.

Figure 2

(a) Time-resolved fluorescence from a single fluorescent nanosphere embedded in PS random photonic medium with a thickness of $7.4(5)\mu \mathrm{m}$. The slow (purple) and the fast (blue) decay curves were measured on two different single fluorescent nanospheres at the same depth $d=3.3\mu \mathrm{m}$. The white lines through the data are lognormal fits. The most-frequent decay rate ${\gamma }_{\mathrm{mf}}$ and the width of the distribution $\Delta \gamma$ are shown. (b) Time-resolved fluorescence of a single fluorescent nanosphere in a reference polymer sample (green) decays exponentially with a rate of $0.26{\mathrm{ns}}^{-1}$.

Figure 3

Distribution of the emission rates for materials with different scattering strengths ($1/k\ell$). Histograms of the emission rates from fluorescent nanospheres embedded in three different materials: (a) ZnO, (b) PS, and (c) nonscattering polymer layer. Dotted lines: width of the distribution $2\sigma$. Full lines: Gaussian fits to the histograms.

Figure 4

Relative variance of the mean decay rate ${\sigma }^2/⟨{\gamma }_{\mu }{⟩}^2$ versus scattering strength $1/k\ell$. The measured values are shown as filled circles with error bars indicating the statistical uncertainty for $N=48$ measurements. Full lines: single-sphere-scatterer model for PS and ZnO scatterers. Dotted line: calculated LDOS variance for pointlike scatterers [11]. Empty diamonds: upper bound to $C_0$ determined from the fluctuations of the emitted intensity.