Floquet Edge Multicolor Solitons

Topological insulators are unique physical structures that in their bulk, but support currents at edges which can be unidirectional and topologically protected from scattering on disorder inhomogeneities. Photonic topological crafted materials exhibit a strong nonlinear response, thus opening the door to exploration of interplay between nonlinearity effects. Among fascinating new phenomena arising this is formation edge solitons -- hybrid asymmetric states localized across along interface due different mechanisms. Such have so far been studied only with Kerr-type, or cubic, nonlinearity. Here first example soliton supported by parametric interactions $\chi^{(2)}$ media presented. exist Floquet realized arrays helical waveguides made phase-matchable material. bifurcate spectrum fundamental frequency wave remain over propagation distances drastically exceeding helix period, while travelling structure. A theory such developed. It shown multicolor system exists vicinity (formally infinite) set linear resonances determined phase matching conditions. Away resonance, envelopes described period-averaged single Schr\"odinger equation an effective cubic coefficient whose magnitude sign depend overall phase-mismatch second harmonic waves.