Generation of Periodic Pulsating Soliton Packet Train in Differential Time-Delayed Feedback Broadband Optoelectronic Oscillator

The time-delayed fast-slow dynamics in broadband optoelectronics oscillators (OEOs) have given birth to many important nonlinear phenomena and promising applications. In this paper, we numerically and experimentally demonstrate a late-model compound dissipative soliton dynamic phenomenon, i.e., periodic pulsating soliton packets, in a dual-time-delayed feedback broadband OEO. The dual-time-delayed feedback module is constructed by inserting a dual-branch electrical differential module into the broadband OEO loop. The pulsating dissipative solitons (DSs) are excited by injecting a perturbation signal into the OEO. With the increasing of cycles, the soliton energy is gradually coupled from the short delay loop to the long delay loop, which leads to the energy dissipation of the solitons at the front of the soliton packet. Meanwhile, the soliton energy at the back of the soliton packet is enhanced. In addition, the DSs are subjected to the amplitude attenuation induced by the spiking-DS refractory period. The total energy loss is compensated by the loop gain. Finally, the OEO system reaches nonlinear equilibrium regime, and undergoes regular pulsation in the time domain. The pulsating characteristics are analyzed in detail. This finding not only paves the way for the compound soliton dynamic research in time-delayed OEOs, but also is valuable for applications such as multi-band dense coherent microwave frequency comb generation, radar and anti-interference.