Abstract
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.
Highlights
Light localization [1,2] and various interference effects [3,4] have been studied in structures formed by scatterers, such as powders [5,6] of dielectric or semiconductor materials, with dimensions comparable to the wavelength of light
The light is tightly confined in such cavities due to whispering gallery modes (WGMs) [28,29] with extremely high quality resonances (Q>103 for 4 μm spheres and up to ~109 for submillimeter spheres)
In the low-intensity (Iav
Summary
Light localization [1,2] and various interference effects [3,4] have been studied in structures formed by scatterers, such as powders [5,6] of dielectric or semiconductor materials, with dimensions comparable to the wavelength of light. In the case of microspheres, the cavities can be micromanipulated and sorted individually which opens a possibility to select much more uniform resonators [10,12,15,16,17] on the basis of spectroscopic characterization of their WGM peak positions These techniques allow selecting spheres with the size uniformity ~0.03%. The optical transport in disordered mesoscopic systems of coupled cavities can be compared with the case of random waveguides [3,4] formed by wavelength scale scatterers. We observed an unusual dependence of the WGM-related transmitted intensity on the thickness of the structure We explain these results by the presence of localized clusters or configurations of nearly uniform spheres inside our 3D structures well connected at the WGM wavelengths
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