  A one-dimensional discrete lattice of dimers is known to possess
topologically protected edge states when interdimer coupling is stronger than
intradimer coupling. Here, we address richer topological properties of photonic
superlattices having arbitrary number of elements in each unit cell. It is
shown that the superlattice provides tunable number of topologically protected
edge and interface states depending on certain restrictions on intra- and
intercell couplings maintaining inversion symmetry of the lattice. Simultaneous
and stable propagation of multiple topological interface states, their
interference pattern, and stable oscillation are reported. The superlattice
configuration can be relevant for topologically protected mode-division
multiplexing through a narrow route in photonic devices.
