Nonlocal lattice solitons in thermal media

We study the properties of solitons in thermal nonlocal media (media having an infinite range of nonlocality) with a periodic refractive index modulation. Such self-localized solutions exist for both signs of the nonlinearity and exhibit a host of features that have no counterpart in local or nonlocal media with finite range nonlocality. Perhaps the most intriguing property is that families of bright solitary pulses can exist inside the bands of the band structure. This property is attributed to the infinite range of nonlocality as well as to the boundary conditions applied to the system. Families of solitons bifurcating from higher-order band edges, otherwise unstable in local media, are found to be stable.