Fig. 4: Experimental observation of all-optical DTCs.

a Experimental setup; WGMR: whispering gallery mode resonator, OSA: optical spectrum analyser, RFSA: radio frequency spectrum analyser, BS: beam splitter, PD: photodetector. b RF signal ensuring stable pulse train generation. For the two pumps locked to two adjacent cavity modes, a narrow RF signal is generated (blue, 32.8 GHz carrier frequency). When locking to non-adjacent modes, the generation of frequency harmonics between the pumps (subharmonics) and hence solitons trapped in the background lattice further narrows the RF signal peak. An example is the red curve (32.8 GHz carrier frequency), corresponding to the experimental spectrum plotted in f in which M = 3. c, f Spectra corresponding, respectively, to period-quadrupling (M = 4) and period-tripling (M = 3) DTCs. Pumps are marked by red arrows, and red dashed curves show soliton envelopes. The stronger pump was at 1545 nm in c and 1544.8 nm in f. d, g Numerical modeling spectra matching c and f. e, h Time-domain pulse trains per round-trip time (numerical), with snapshots of pulses revolving around the resonator circumference as insets.