Simultaneous multi-frequency topological edge modes between one-dimensional photonic crystals

We show theoretically that, in the limit of weak dispersion, one-dimensional binary centrosymmetric photonic crystals can support topological edge modes in all photonic bandgaps. By analyzing their bulk band topology, these "harmonic" topological edge modes can be designed in a way that they exist at all photonic bandgaps opened at the center of the Brillouin zone, 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 upconversion.