Fig. 2: Floquet solitons and incommensurate combs in the AF phase, for θ_A =  0.45π, θ_B = 0.05π.

a Band structure, b absorption spectrum of the lattice, in the linear regime, showing edge and bulk bands. The band structure shown in a. is a zoom-in of Fig. 1c within a single FSR. The absorption spectrum in b. is calculated as (1-Tx), with the transmission (Tx) shown in Fig. 1b, and is zoomed-in within a single FSR. The pumped edge mode is highlighted in blue. c Comb power (normalized) in the input-output ring as a function of pump frequency detuning in the non-linear regime. The pump frequency where we observe coherent incommensurate combs soliton molecules is indicated. d Intensity distribution in the lattice showing phase-locked super-soliton molecules. The super-solitons circulate the edge in the CCW direction as time evolves (here time interval δt = 8τ_R). Insets show the positions of solitons in the individual rings. To show the location of the rings, we have added a constant intensity (normalized) background of 0.01. e Output of the floquet topological comb in the time domain, showing super-soliton pulses repeating after round trip time in the super-ring resonator. The inset shows a zoom-in of the temporal output where relative intensity variations in the output pulses are clearly visible. f Output comb spectrum. g Comb spectrum reorganized as a function of frequency detuning δω/Ω_R and FSR index μ. h Comb spectrum showing oscillation of edge modes in a single FSR (here μ = 50). The incommensurate nature of the comb is evident in g, h where the oscillating edge mode frequencies are not all equidistant.