Temporal and spatiotemporal soliton molecules in ultrafast fibre lasers

Abstract

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.

Keywords: bound states; fibre lasers; nonlinear dynamics; soliton molecules; stability; ultrafast nonlinear optics.

Figure 1:

The roadmap for the studies of SMs.

Figure 2:

Simulated spectra of two-soliton SMs with φ = π (a); 0 (b); −π/2 (c); and π/2 (d), according to Eq. (3). In all figures, 0.8-ps chirp-free, sech-shaped pulses with a central wavelength of 1,560 nm and a temporal separation of 6 ps are used.

Figure 3:

Classification and manipulation of SMs with the multidimensional parameter space.

Figure 4:

Various scenarios of the formation and evolution dynamics of SMs. (a, b) The formation of SMs from a transient bound state and corresponding field autocorrelations (Herink et al. [89] © AAAS 2017). (c, d) The formation and evolution of SMs featuring beating dynamics (Liu et al. [90] © American Physical Society 2018). (e) The formation dynamics of ground-state SMs; (f) the build-up dynamics of excited-state SMs (Peng et al. [142] © Wiley-VCH Verlag 2018).

Figure 5:

Various dynamical scenarios of pulsation SMs. (a) SM featuring an oscillating time separation and phase (Herink et al. [89] © AAAS 2017). (b, c) SM featuring vibration and sliding phases (Krupa et al. [33] © American Physical Society 2017). (d–g) The experimental observation of subharmonic, modulated subharmonic, and non-subharmonic diatomic breathing SMs (Wu et al. [97] © American Physical Society 2023).

Figure 6:

Various scenarios of the SM interactions. (a, b) The formation of a dissipative SM by colliding free solitons (Zhang et al. [157] © Elsevier Ltd 2022). (c–g) Close-up of the collision, the subsequent partial spectral collapse of SM and numerical simulations of the collision between the SM and a free soliton (Liu et al. [183] © The Optical Society 2024). (h, i) The indirect and direct interactions of SMs (He et al. [184] © The Optical Society 2023).

Figure 7:

Linear dispersion relations and the corresponding numerical solutions for polychromatic SMs, as per Ref. [76] (© Springer Nature 2022).

Figure 8:

Two different mechanisms for the formation of dichromatic SMs: (a, b) The experimental setup and output spectra for the formation of dichromatic SMs through the dispersion management (Mao et al. [77] © Springer Nature 2021). (c, d) The experimental setup and output spectra for the formation of dichromatic SMs by the XPM effect (Cui et al. [192] © American Physical Society 2023).

Figure 9:

The experimental setup and spectral output characteristics for different cavity structures. (a, b) The formation of STSMs in the annular cavity, including a fully multimode fibre (Ding et al. [204] © The Optical Society 2019). (c, d) The formation of STSMs in the all-fibre hybrid annular cavity (Guo et al. [205] © Elsevier Ltd 2022). (e, f) The formation of STSMs in the ring cavity, including a few-mode fibre (Wu et al. [206] © Elsevier Ltd 2022.

Figure 10:

Various dynamics of different types of SM complexes. (a–d) The spectral evolution and interaction plane of sliding-phase and oscillatory-phase 2 + 2 SM complexes, as per Ref. [73] (© Wang et al., Springer Nature 2019); (e) the dynamics of various breather SM complexes, as per Peng et al. [212] (© Wiley-VCH Verlag 2021); (f–h) the spectral evolution of (2 + 1) and (2 + 2) breather dichromatic SM complexes, as shown by Cui et al. [195] (© Wiley-VCH Verlag 2024).

Figure 11:

The experimental setup and evolution dynamics of soliton “supramolecules”. (a–d) The experimental setup and evolution dynamics of soliton “supramolecules”, together with the schematic of the optomechanical effect, as per He et al. [75] (© Springer Nature 2019). (e, f) The synthesis and dissociation of SMs in soliton “supramolecules” as per He et al. [34] (© Springer Nature 2021).

Figure 12:

Two managing ways of SMs by polarization control. (a, b) The experimental setup, and the output spectrum of the SMs, realized by adjusting the polarization state (Wang et al. [52] © The Optical Society 2016). (c, d) The experimental setup and spectra for the intelligent generation of breathing SMs in ultrafast fibre lasers (Wu et al. [101] © Wiley-VCH Verlag 2022).

Figure 13:

Various dispersion control methods of SMs. (a, b) The experimental setup and results of on-demand generated SMs by adjusting the dispersion loss (Liu et al. [99] © OSA publishing 2022). (c, d) The experimental setup and measured spectra of SMs for adjusting the high even order dispersion (Han et al. [105] © Springer Nature 2024).

Figure 14:

The management of SMs is achieved by quickly changing the pump power and adjusting the frequency. (a, b) Two schemes for optical manipulations of SMs and transitions between different SM states (Kurtz et al. [95] © Springer Nature 2020). (c) The periodic switching of various SM complexes (Zhou et al. [223] © Springer Nature 2022).

Figure 15:

The control of SM by the external light injection. (a, b) Synchronization of internal vibrations in SMs through injection of optically modulated CW. Direct observation of the synchronization process using the BOC technique (Zou et al. [96] © OSA Publishing 2022). (c, d) Synthesis and dissociation dynamics of SMs with the help of addressing pulses (He et al. [34] © Springer Nature 2021). (e, f) Spontaneous collapse and rebuilding-up of SMs triggered by injected CWs (Chang et al. [225] © Elsevier Ltd 2022).

Figure 16:

Various ways of data encoding based on SMs. (a) The coding realized in terms of different SM temporal separations (Liu et al. [99] © OSA Publishing 2022). (b) The programmable phase modulation based on the phase-customized quaternary of internally assembled dissipative SMs (Liu et al. [100] © Springer Nature 2023). (c, d) The programmable phase-coded modulation of loosely bound SMs by means of the gain control (Yang et al. [224] © AIP Publishing LLC 2024).