  We report on a study of a one-dimensional linear photonic lattice hosting,
simultaneously, fundamental and dipolar modes at every site. We show how,
thanks to the interaction between the different orbital modes, this minimal
model exhibits rich transport and topological properties. By varying the
detuning coefficient we find a regime where bands become flatter (with reduced
transport) and, a second regime, where both bands connect on at a gap-closing
transition (with enhanced transport). We detect an asymmetric transport due to
the asymmetric inter-mode coupling and a linear energy exchange mechanism
between modes. Further analysis show that the bands have a topological
transition with a non-trivial Zak phase which leads to the appeareance of edge
states in a finite system. Finally, for zero detuning, we found a symmetric
condition for coupling constants, where the linear spectrum becomes completely
flat, with states fully localized in space occupying only two lattice sites.
