  We show theoretically that, in the limit of weak dispersion, one-dimensional
(1D) binary centrosymmetric photonic crystals can support topological edge
modes in all photonic band gaps. By analyzing their bulk band topology, these
"harmonic" topological edge modes can be designed in a way that they exist at
all photonic band gaps opened at the center of the Brillouin Zone, or at all
gaps opened at the zone boundaries, or both. The results may suggest a new
approach to achieve robust multi-frequency coupled modes for applications in
nonlinear photonics, such as frequency up-conversion.
