Supersolid behavior of nonlinear light

We present a formal demonstration that light can simultaneously exhibit a superfluid behavior and spatial long-range order when propagating in a photonic crystal with self-focussing nonlinearity. In this way, light presents the distinguishing features of matter in a "supersolid" phase. We show that this supersolid phase provides the stability conditions for nonlinear Bloch waves and, at the same time, permits the existence of topological solitons or defects for the envelope of these waves. We use a condensed matter analysis instead of a standard nonlinear optics approach and provide numerical evidence of these theoretical findings.