Nonlinear force dependence on optically bound micro-particle arrays in the eva-nescent fields of fundamental and higher order microfibre modes

Particles trapped in the evanescent field of an ultrathin optical fibre inter-act over very long distances via multiple scattering of the fibre-guided fields. In ultrathin fibres that support higher order modes, these interac-tions are stronger and exhibit qualitatively new behaviour due to the cou-pling of different fibre modes, which have different propagation wave-vectors, by the particles. Here, we study one dimensional longitudinal opti-cal binding interactions of chains of 3 {\mu}m polystyrene spheres under the influence of the evanescent fields of a two-mode microfibre. The observa-tion of long-range interactions, self-ordering and speed variation of parti-cle chains reveals strong optical binding effects between the particles that can be modelled well by a tritter scattering-matrix approach. The optical forces, optical binding interactions and the velocity of bounded particle chains are calculated using this method. Results show good agreement with finite element numerical simulations. Experimental data and theoreti-cal analysis show that higher order modes in a microfibre offer a promis-ing method to not only obtain stable, multiple particle trapping or faster particle propulsion speeds, but that they also allow for better control over each individual trapped object in particle ensembles near the microfibre surface.