Bound states of solitons in fiber lasers

Bound states of solitons, alias “soliton molecules”, in fiber-laser cavities is one of central topics in the ongoing experimental and theoretical work in nonlinear optics. This topic has drawn much interest as a unique platform for the studies of dynamics of dissipative solitons, and also due to its vast potential for various applications in optics and photonics. This article presents a systematic review of theoretical and experimental findings for bound states of two and several dissipative solitons in fiber lasers. The theoretical basis underlying the formation and stabilization of soliton molecules in the fibers, which is provided by the complex Ginzburg–Landau equations and bound states of such equations, is presented in necessary detail, which is followed by a detailed presentation of experimental findings, including very recent ones. In particular, included are the results for the multi-soliton bound states in the fibers, as well as for the bound states in the temporal and frequency domains, single-component (scalar) and two-component (vector), two- and multi-soliton modes, as well as for bound states of spatiotemporal dissipative solitons in the lasers based on multimode fibers.