Phenomenological study of binding in optically trapped photonic crystals

We describe a phenomenological theory of the phenomenon of binding observed both experimentally and numerically when particles are trapped by an interference system in order to make a structure close to a photonic crystal. This theory leads to a very simple conclusion, which links the binding phenomenon to the bottom of the lowest bandgap of the trapped crystal in a given direction. The phenomenological theory allows one to calculate the period of the trapped crystal by using numerical tools on dispersion diagrams of photonic crystals. It emerges that the agreement of our theory with our rigorous numerical results given in a previous paper [J. Opt A8, 1059 (2006)] is better than 2% on the crystal period. Furthermore, it is shown that in two-dimensional problems and s polarization, all the optical forces derive from a scalar potential.