Investigations on diverse dynamics of soliton triplets in mode-locked fiber lasers.

Optical soliton molecules exhibiting behaviors analogous to matter molecules have been the hotspot in the dissipative system for decades. Based on the dispersion Fourier transformation technique, the real-time spectral interferometry has become the popular method to reveal the internal dynamics of soliton molecules. The rising degrees of freedom in pace with the increased constitutes of soliton molecules yield more intriguing sights into the internal motions. Yet the soliton molecules with three or more pulses are rarely investigated owing to the exponentially growing complexity. Here, we present both experimental and theoretical studies on the soliton molecules containing three solitons. Different assemblies of the constitutes are categorized as different types of soliton triplet akin to the geometric isomer, including equally-spaced triplet and unequally-spaced triplet. Typical soliton triplets with different dynamics including regular internal motions, hybrid phase dynamics and complex dynamics involving separation evolution are experimentally analyzed and theoretically simulated. Specifically, the energy difference which remains elusive in experiments are uncovered through the simulation of diverse triplets with plentiful dynamics. Moreover, the multi-dimensional interaction space is proposed to visualize the internal motions in connection with the energy exchange, which play significant roles in the interplays among the solitons. Both the experimental and numerical simulations on the isomeric soliton triplets would release a larger number of degrees of freedom and motivate the potentially artificial configuration of soliton molecules for various ultrafast applications, such as all-optical buffering and multiple encoding for telecommunications.