Temporal and spatiotemporal soliton molecules in ultrafast fibre lasers.

Ultrafast fibre lasers, characterized by ultrashort pulse duration and broad spectral bandwidth, have drawn significant attention due to their vast potential across a wide range of applications, from fundamental scientific to industrial processing and beyond. As dissipative nonlinear systems, ultrafast fibre lasers not only generate single solitons, but also exhibit various forms of spatiotemporal soliton bunching. Analogous to molecules composed of multiple atoms in chemistry, soliton molecules (SMs) - alias bound states - in ultrafast fibre lasers are a key concept for gaining a deeper understanding of nonlinear interaction and hold a promise for advancing high-capacity fibre-optic communications. SMs are particularly notable for their high degree of controllability, including their internal temporal separation, and relative phase differences, thereby suggesting new possibilities for manipulating multi-pulse systems. In this review, we provide a comprehensive overview of recent advancements in the studies of SMs with the multidimensional parameter space in ultrafast fibre lasers. Owing to the flexibility afforded by mode-locking techniques and dispersion management, various types of SMs - with diverse values of the soliton number, relative phase, pulse separation, carrier frequencies, and even modal dispersion - have been experimentally demonstrated. We also discuss other basic nonlinear optical phenomena observed in fibre lasers, including the formation, spatiotemporal pulsations, and interaction dynamics of SMs. Furthermore, we explore the multidimensional control of SMs through approaches such as gain modulation, polarization control, dispersion management, and photomechanical effects, along with their applications to optical data encoding. Finally, we discuss challenges and future development of multidimensional technologies for the manipulation of SMs.