Percolation of light through whispering gallery modes in 3D lattices of coupled microspheres

Using techniques of flow-assisted self-assembly we synthesized three-dimensional (3D) lattices of dye-doped fluorescent (FL) 5 mum polystyrene spheres with 3% size dispersion with well controlled thickness from one monolayer up to 43 monolayers. In FL transmission spectra of such lattices we observed signatures of coupling between multiple spheres with nearly resonant whispering gallery modes (WGMs). These include (i) splitting of the WGM-related peaks with the magnitude 4.0-5.3 nm at the average wavelength 535 nm, (ii) pump dependence of FL transmission showing that the splitting is seen only above the threshold for lasing WGMs, and (iii) anomalously high transmission at the WGM peak wavelengths compared to the background for samples with thickness around 25 mum. We propose a qualitative interpretation of the observed WGM transport based on an analogy with percolation theory where the sites of the lattice (spheres) are connected with optical "bonds" which are present with probability depending on the spheres' size dispersion. We predict that the WGM percolation threshold should be achievable in close packed 3D lattices formed by cavities with ~10(3) quality factors of WGMs and with ~1% size dispersion. Such systems can be used for developing next generation of resonant sensors and arrayed-resonator light emitting devices.