Floquet topological dissipative Kerr solitons and incommensurate frequency combs.

Generating coherent optical frequency combs in micro-ring resonators with Kerr nonlinearity has remarkably advanced the fundamental understanding and applications of temporal dissipative solitons. However, the spectrum of such soliton combs is restricted to the conventional definition of combs as phase-locked, equidistant lines in frequency. Here, we introduce a new class of floquet topological soliton combs that emerge in two-dimensional arrays of strongly coupled resonators engineered using floquet topology. Specifically, we demonstrate incommensurate combs where the comb lines are not equidistant but remain phase-locked. These incommensurate combs are generated by self-organized, phase-locked floquet topological soliton molecules that circulate the edge of the array. We show that these floquet topological solitons are robust and they navigate around defects, allowing for agile tunability of the comb line spacing. Our results introduce a new paradigm in using floquet engineering to generate unconventional frequency combs beyond those achievable with single or weakly coupled resonators.