Stability of extended structures stabilized by light as governed by the competition of two length scales

Light-induced forces can bind dielectric spheres into extended structures through two mechanisms, each with its own length scale which can be adjusted by the configuration of the external light source. By manipulating the commensurability of the two length scales, these two mechanisms can cooperate to bind a large number of spheres. When the two length scales become incommensurate for some particular incident angle, the competition between the two mechanisms can lead to modulated structures and other complex phenomena such as reentrant stability.