Dynamic gain driven mode-locking in GHz fiber laser

Ultrafast lasers with unique advantages in generating ultrashort pulses have drawn widespread interest in scientific and industrial areas, such as material processing, bioimaging, laser metrology, and spectroscopy. Despite intensive studies on ultrafast lasers with kHz–MHz repetition rates, there are strong motivations to explore multi-GHz fundamental repetition rates for applications including astronomical observations, photonic microwave generation, radar, and coherent optical communications. Approaches such as semiconductor microring lasers, microresonator-filtered fiber lasers, and microresonator-based ultrashort pulses have been investigated. Passive mode-locking, a mainstay for generating dissipative solitons supporting femtosecond pulses, is promising for forming solitons with GHz fundamental repetition rates in ultra-short solid-state cavities, but theoretical and technical questions remain for mode-locked fiber lasers above 10 GHz. The pioneer theory of passive mode-locking based on master equations interpreted soliton generation using fast and slow saturable absorbers, and was improved to establish a criterion distinguishing continuous-wave mode-locking (CWML) from Q-switched mode-locking (QSML). These have been successful when the gain relaxation time is slow. For materials with fast gain relaxation comparable to the cavity roundtrip time (T_G/T_R → 1), these theories fail to fully capture soliton shaping. Coherent master equations retaining light-matter coherence were proposed for fast-gain materials (e.g., semiconductors), but existing frameworks struggle with complex gain dynamics spanning multiple time scales. At multi-GHz rates, passively mode-locked fiber lasers face weakened balancing effects, and reported pulse energies are far below existing criteria. In this paper, the authors establish a new theoretical model for passively mode-locked GHz fiber lasers by exploring dynamic gain depletion and recovery (GDR) in dual time scales. They show that GDR-mediated collective behavior effectively reduces the gain saturation energy needed for stable mode-locking, aligning predicted pulse energies with experiments—orders of magnitude lower than prior theory. They introduce quasi-single solitons (QSSs) defined by a strongly correlated length to reconcile the new model with classical theory, observe diverse dynamics via simulation and real-time measurements, and demonstrate a mode-locked fiber laser at 21 GHz fundamental repetition rate.

Prior work established master-equation-based theories of passive mode-locking with fast and slow saturable absorbers and derived criteria distinguishing CWML from QSML for systems with slow gain relaxation times. For materials where the gain relaxation time approaches the cavity roundtrip time (T_G/T_R → 1), classical theories fail to explain soliton shaping, prompting development of coherent master equations that include light-matter coherence, suitable for fast-gain media such as semiconductors. However, these frameworks are not adequate for systems with complex, multi-timescale gain dynamics. Experimentally, at multi-GHz repetition rates, effects enabling balance in mode-locked fiber lasers are weakened, and observed pulse energies violate existing CWML criteria. This motivates a new framework that incorporates dynamic gain depletion and recovery across dual time scales to explain GHz fiber laser mode-locking.

The authors develop a theoretical framework emphasizing dynamic gain depletion and recovery (GDR) operating over dual time scales to explain passive mode-locking in GHz fiber lasers. They model the gain fiber as a quasi-four-level system (e.g., Er3+/Yb3+ co-doped fiber) with upper-level lifetime τ_G on the order of 1–10 ms. The gain rate equation includes effective lifetime, saturation energy, small-signal gain, overlap factor, effective mode area, pump absorption cross-section, pump power, and instantaneous pulse power. A multiscale approach introduces slow time τ (crystal-to-crystal evolution) and fast time T (soliton-to-soliton evolution), expanding the gain as g = g0(τ) + g1(T). They derive coupled rate equations describing slow-time evolution of the average gain and soliton crystal energy and fast-time gain variations between neighboring solitons. The concept of soliton crystals (multi-soliton trains separated by the cavity roundtrip time) is used to characterize pre-CWML QSML dynamics, where gain is depleted across a crystal and recovers between crystals. The GDR effect binds neighboring GHz solitons, forming quasi-single solitons (QSSs) within a strongly correlated (SC) length T_sc comprising N_sc solitons. Using linear stability analysis of the coupled equations, they derive a new CWML criterion expressed in terms of the soliton crystal energy, saturable absorber parameters (modulation depth q0, saturable energy E_a), gain saturation energy E_G, crystal duration ΔT, and crystal repetition rate f. In the strongly saturated absorber limit, the criterion reduces to E_c^2 > q0 f E_a E_G, contrasting with the classical E_c^2 > q0 E_a E_G and highlighting the role of collective dynamics (E_c = N_sc E_p). They also outline an experimental platform: a short Fabry–Pérot fiber cavity comprising a saturable absorber (SA), gain fiber (GF) pumped by a single-mode laser diode, and a dielectric film (DF) output coupler. Real-time diagnostics include a standard oscilloscope and time-lens magnification to resolve GHz pulse-train envelopes. Experimental evolution of a 4.6 GHz laser from rectangular-shape QSML to CWML with increasing pump power is used to validate the model, along with demonstrations up to 21 GHz.

• Dynamic gain depletion and recovery (GDR) produces an effective interaction that binds GHz solitons into soliton crystals during QSML, transitioning to CWML as pump power increases.
• The collective behavior within a strongly correlated (SC) length permits a reduced CWML threshold: in the strong saturation limit, the CWML criterion becomes E_c^2 > q0 f E_a E_G, effectively lowering the required pulse energy compared to the classical E_c^2 > q0 E_a E_G.
• Introducing quasi-single solitons (QSSs) comprising N_sc bound pulses provides a bridge between the proposed model and classical theory, with (N_sc E_p)^2 > q0 E_a E_G capturing the collective threshold.
• Two distinct QSML dynamics are identified and verified: rectangular-shape and Gaussian-shape pulse-train envelopes.
• Experimental observations (e.g., a 4.6 GHz cavity) show evolution from rectangular-shape QSML to CWML with pump increase, consistent with the model’s gain dynamics and Δg → 0 condition in CWML.
• A GDR-mediated mode-locked fiber laser with a record-high fundamental repetition rate of 21 GHz and signal-to-noise ratio of 85.9 dB is demonstrated.

The work addresses why previous CWML criteria underestimate the feasibility of GHz mode-locking at the low pulse energies observed experimentally. By treating mode-locking as a collective phenomenon governed by dual-timescale gain dynamics, the model shows that bound soliton ensembles (soliton crystals/QSSs) reduce the effective energy requirement for stable CWML. This reconciles experimental reports of multi-GHz mode-locking with theoretical expectations and clarifies transitions from QSML to CWML as pump power increases and Δg between adjacent pulses vanishes. The QSS concept provides a unifying picture that recovers classical criteria in the appropriate limits while explaining new GHz-regime behaviors. The experimental validations, including the observation of distinct QSML envelope shapes and the attainment of 21 GHz with high SNR, underscore the model’s relevance and potential impact on designing robust, ultra-high-repetition-rate fiber lasers.

The authors present a dual-timescale gain-dynamics model for passive mode-locking in GHz fiber lasers, introducing soliton crystals and quasi-single solitons to capture collective effects that lower CWML thresholds relative to classical theory. They derive a generalized CWML criterion that matches experimental observations and demonstrate record-high 21 GHz fundamental repetition rate with 85.9 dB SNR. The framework bridges existing master-equation approaches and coherent models, offering a comprehensive understanding of GHz soliton formation and stability. Potential future work includes applying the framework to diverse gain media and cavity designs, exploring transitions between QSML types, and leveraging time-resolved diagnostics to further elucidate collective soliton dynamics.