Topological dipole Floquet solitons

We theoretically introduce a type of topological dipole soliton propagating in a Floquet topological insulator based on a kagome array of helical waveguides. Such solitons bifurcate from two edge states belonging to different topological gaps and have bright envelopes of different symmetries: fundamental for one component, and dipole for the other. The formation of dipole solitons is enabled by unique spectral features of the kagome array which allow the simultaneous coexistence of two topological edge states from different gaps at the same boundary. Notably, these states have equal and nearly vanishing group velocities as well as the same sign of the effective dispersion coefficients. We derive envelope equations describing the components of dipole solitons and demonstrate in full continuous simulations that such states indeed can survive over hundreds of helix periods without any noticeable radiation into the bulk.Y.V.K. and S.K.I. acknowledge funding of this study by RFBR and DFG according to Research Project No. 18- 502-12080. A.S. acknowledges funding from the Deutsche Forschungsgemeinschaft (Grants No. BL 574/13-1, No. SZ 276/19-1, and No. SZ 276/20-1). Y.V.K. and L.T. acknowledge support from the Government of Spain (Severo Ochoa CEX2019-000910-S), Fundació Cellex, Fundació Mir-Puig, Generalitat de Catalunya (CERCA). V.V.K. acknowledges financial support from the Portuguese Foundation for Science and Technology (FCT) under Contract No. UIDB/00618/2020.Peer ReviewedPostprint (author's final draft

Floquet edge multicolor solitons

Topological insulators are unique physical structures that are insulators in their bulk, but support currents at their edges which can be unidirectional and topologically protected from scattering on disorder and inhomogeneities. Photonic topological insulators can be crafted in materials that exhibit a strong nonlinear response, thus opening the door to the exploration of the interplay between nonlinearity and topological effects. Among the fascinating new phenomena arising from this interplay is the formation of topological edge solitons — hybrid asymmetric states localized across and along the interface due to different physical mechanisms. Such solitons have so far been studied only in materials with Kerr-type, or cubic, nonlinearity. Here the first example of the topological edge soliton supported by parametric interactions in χ(2) nonlinear media is presented. Such solitons exist in Floquet topological insulators realized in arrays of helical waveguides made of a phase-matchable χ(2) material. Floquet edge solitons bifurcate from topological edge states in the spectrum of the fundamental frequency wave and remain localized over propagation distances drastically exceeding the helix period, while travelling along the edge of the structure. A theory of such states is developed. It is shown that multicolor solitons in a Floquet system exists in the vicinity of (formally infinite) set of linear resonances determined by the Floquet phase matching conditions. Away from resonance, soliton envelopes can be described by a period-averaged single nonlinear Schr¨odinger equation with an effective cubic nonlinear coefficient whose magnitude and sign depend on the overall phase-mismatch between the fundamental frequency and second harmonic waves. Such total phase-mismatch includes the intrinsic mismatch and the geometrically-induced mismatch introduced by the array, and its value reveals one of the genuine effects exhibited by the Floquet quadratic solitons. Our results open fundamental new prospects for the exploration of a range of parametric frequency-mixing phenomena in photonic Floquet quadratic nonlinear media.Y.V.K., A.S., and S.K.I. acknowledge funding of this study by RFBR and DFG according to the research project no. 18-502-12080 and SZ 276/19-1. V.V.K.acknowledges financial support from the Portuguese Foundation for Science and Technology (FCT) under Contract no. UIDB/00618/2020. Y.V.K.and L.T. acknowledge support from the Government of Spain (Severo Ochoa CEX2019-000910-S), Fundació Cellex, Fundació Mir-Puig, Generalitat de Catalunya (CERCA program), and NEPA: PGC2018-097035-B-I00 project funded by MCIN/ AEI /10.13039/501100011033/ FEDER “A way tomake Europe".Peer ReviewedPostprint (author's final draft