Photonic systems acting as magnetic solids

In this contribution we present theoretical results, confirmed by numerical simulations, showing how a periodic distribution of solitons completely filling an optical lattice or a photonic crystal presents identical dynamics than that of a magnetic crystalline solid. We show that the optical Hamiltonian of a soliton lattice is given, to lowest order, by a typical model of magnetism; namely, the X-Y model. Following this equivalence, it is possible to reproduce all the photonic counterparts of magnetic systems. In this way, we have been able to prove that a soliton array supported by a photonic crystal in the presence of a Kerr self-focusing nonlinearity is the photonic equivalent of an antiferromagnetic crystalline solid.