Optically bound arrays of microscopic particles in one dimension

We demonstrate that counter-propagating light fields have the ability to create self-organized one-dimensional optically bound arrays of microscopic particles, where the light fields adapt to the particle locations and vice versa. We are able to create chains of up to 9 particles with only modest laser power. We outline the experimental observation of this phenomenon examining the effect of laser wavelength (780nm and 1064nm) and particle size (1, 2.3 and 3 micron diameter sphere sizes) on the interparticle separation. We develop a theoretical model to describe this situation making use of the beam propagation method to calculate the fields. Using the fields we are able to calculate the gradient and scattering forces experienced by the particles. Equilibrium positions in these forces indicate the predicted positions of the spheres. We find good agreement between the theory and experimental data for two and three particles, if the scattering force is assumed to dominate the axial trapping of the particles. We discuss the limitation of the model when dealing with spheres size of the order of the wavelength of light involved and also the experimental uncertainties relating to the measurement of the laser beam waist separations. The extension of these ideas to two and three dimensional optically bound states is also discussed.