Interactions between spherical nanoparticles optically trapped in Laguerre-Gaussian modes

When a Laguerre-Gaussian (LG) laser mode is used to trap nanoparticles, the spatial disposition of the particles about the beam axis is determined by a secondary mechanism that engages the input radiation with the interparticle potential. This analysis, based on the identification of a range-dependent laser-induced energy shift, elicits and details features that arise for spherical nanoparticles irradiated by a LG mode. Calculations of the absolute minima are performed for LG beams of variable topological charge, and the results are displayed graphically. It is shown that more complex ordered structures emerge on extension to three- and four-particle systems and that similar principles will apply to other kinds of radially structured optical mode.