时空耗散孤子（时空锁模）光纤激光器，即实现横模和纵模同时锁定的多模光纤激光器，具备产生高时空相干性的时空超快脉冲的能力。自2017年报道以来，这一技术备受关注，其空间模式增加有望进一步提高锁模脉冲的输出能量，同时，时空耗散孤子光纤激光器为高维非线性光学研究提供了新的实验平台。时空耗散孤子光纤激光器主要朝着实现输出锁模稳定、能量高、光斑可控的超快脉冲发展，未来可在激光加工、精密测量、散射介质成像、非线性光谱学和光镊等领域应用。但目前学者对其的研究依旧处于初步发展阶段，许多关键基础问题尚待解决，如模间色散的补偿原理、时空锁模的时空稳定性表征等，这些问题阻碍了时空耗散孤子光纤激光器的进一步发展。因此，本论文旨在深入研究时空耗散光纤激光器中稳定和呼吸的时空耗散孤子的锁模机理和稳定性，以完善多模光纤激光器中的时空耗散孤子锁模理论，为该技术的进一步发展提供理论支持。具体研究内容包括：实现全阶跃时空锁模光纤激光器，探究其中大模间色散的补偿原理。在具有大模间色散的全阶跃多模光纤激光器中产生了内部存在皮秒级走离的模式分辨锁模脉冲，并揭示空间耦合补偿皮秒级的模式走离，以保证脉冲的自洽传播。最后，提出母子耦合理论解释大模间色散下的锁模机理。观测时空锁模光纤激光器抵御时空扰动保证时空锁模稳定的机制。时空锁模状态下，通过在空间光调制器上加载空间相位模拟时空扰动，并利用基于深度学习的模式分解方法对其输出光斑进行分解，证明了时空稳定子的存在。吸引子剖析法被用于理解时空稳定子，并揭示激光器抵御时空扰动的机制。最后，通过观测不同锁模状态下承受的最大随机相位扰动的变化，指出时空耗散孤子抵抗时空扰动的能力，随着腔内能量以及低阶模比例的增加而增加。探究时空锁模光纤激光器中呼吸的时空耗散孤子的内部特征。一方面借助空间采样和色散傅里叶变换技术表征时空呼吸子的空间比例变化；另一方面借助空间采样和平衡光互相关技术对时空呼吸子的时域内部变化进行观测。最后，使用将增益速率方程考虑至多模增益光纤的仿真模型，成功模拟时空锁模光纤激光器中的时空呼吸子，验证实验观测的结果。
The spatiotemporal dissipative solitons (spatiotemporal mode-locking) fiber laser, which achieves simultaneous locking of transverse and longitudinal modes in a multimode fiber laser, possesses the capability to generate highly spatiotemporally coherent spatiotemporal ultrafast pulse. Since its introduction in 2017, this technology has garnered significant attention. Its spatial mode reuse holds promise for further enhancing the energy output of mode-locked pulses, while multimode fiber mode-locked lasers provide a critical experimental platform for high-dimensional nonlinear optics research. The development direction of spatiotemporal dissipative solitons fiber lasers primarily focuses on achieving stable, high-energy and beam-controllable ultrafast pulse, promising significant applications in laser processing, precision ranging, scattering medium imaging, nonlinear spectroscopy and optical tweezers. However, current scholarly research on this technology remains in its initial stages, with many key issues yet to be addressed, such as the compensation principles for intermode dispersion and characterization of spatiotemporal stability in spatiotemporal mode-locking, hindering further advancement of spatiotemporal dissipative solitons fiber lasers. Therefore, this thesis aims to delve into the mode-locking mechanism and stability of stable and breathing spatiotemporal dissipative solitons in spatiotemporal mode-locked fiber lasers, aiming to establish a spatiotemporal dissipative soliton mode-locking mechanism in multimode fiber lasers and provide theoretical support for the future applications of this technology. Specific research endeavours include: Exploring the compensation principles of intermode dispersion in spatiotemporal mode-locked fiber lasers. Mode-resolved locked pulses with picosecond-level departures were generated in an all-step-index-fiber laser with large intermodal dispersion, revealing the mechanism of spatial coupling compensation for picosecond-level modal departures to ensure the self-consistent propagation of pulses. Finally, the mother-child coupling theory was proposed to explain the mode-locking mechanism under large intermode dispersion. Investigating the mechanisms for resisting spatiotemporal disturbances to ensure the stability of spatiotemporal mode-locking in spatiotemporal mode-locked fiber lasers. Under spatiotemporal mode-locked states, the existence of spatiotemporal stabilizers was demonstrated by loading spatiotemporal disturbances simulated by spatial phase modulation on a spatial light modulator and decomposing the output beam profile using deep learning-based pattern decomposition methods. The attractor dissection theory was employed to understand spatiotemporal stabilizers and reveal the mechanism by which lasers resist spatiotemporal disturbances. Finally, by observing the changes in maximum random phase disturbance endured under different mode-locking states, it was indicated that the ability of spatiotemporal dissipative soliton to resist random phase disturbances increases with the pulse energy and the proportion of the low-order modes. Exploring the internal characteristics of breathing spatiotemporal dissipative solitons in spatiotemporal mode-locked fiber lasers. On one hand, spatial proportion vibrations of spatiotemporal vibrations were characterized using spatial sampling and dispersion Fourier transform techniques. On the other hand, observations of temporal interval vibrations at different spatial positions were made using spatial sampling and balanced optical cross-correlation techniques. Finally, a simulation model incorporating gain rate equations into a multimode gain fiber successfully simulated spatiotemporal breather in spatiotemporal mode-locked fiber lasers, validating experimental observations.
