Genetic-Algorithm-Driven Intelligent Spatiotemporal Mode-Locking in All-Fiber Laser with Hysteresis

Abstract

We demonstrate a robust intelligent spatiotemporal mode-locked fiber laser with large modal dispersion, based on the nonlinear polarization rotation mechanism and an electric polarization controller (EPC). The hysteresis phenomenon induced by the polarization controller poses a substantial challenge to achieving stable intelligent spatiotemporal mode-locking (STML). To address this, we propose and implement a memory-diffusion genetic algorithm to achieve stable STML operation with a single-pulse energy of 8.6 nJ via automatic EPC optimization. Thus, understanding and coping with hysteresis is crucial for realizing robust intelligent STML fiber lasers. To the best of our knowledge, this is the first demonstration of an intelligent all-fiber STML laser operating under large modal dispersion. This work provides a new pathway toward achieving stable and intelligent spatiotemporal mode locking in fiber lasers.

1. Introduction

Ultrafast fiber lasers hold significant application value in precision machining, precision measurement, nonlinear optics research, biomedical engineering, and terahertz wave generation [1,2]. Single-mode fiber lasers offer advantages such as compact design, low cost, and high beam quality. However, their small core sizes inherently limit the enhancement of both communication capacity and mode-locked pulse energy [3,4]. In 2017, Wright et al. proposed spatiotemporal mode-locking (STML) based on multimode fibers, offering a new approach for realizing mode-locked fiber lasers with high bandwidth and high pulse energy [5]. Since then, significant progress has been made in areas such as the evolutionary dynamics of STML [6,7,8,9,10,11,12,13,14], beam self-cleaning effects [4,15,16,17,18], and mode-field control [19,20,21,22]. In 2021, Ding et al. achieved STML in large-core gain fibers with large modal dispersion [7]. Subsequently, Zhang et al. carried out a series of outstanding studies on all-fiber STML lasers with large modal dispersion [14,15,23]. Large modal dispersion refers to the transverse-mode dispersion in step-index (STIN) multimode fibers, which is significantly larger than that in graded-index multimode fibers traditionally used for STML [7,23]. While large-core fibers offer the potential to achieve higher pulse energy and bandwidth in STML systems by supporting multiple transverse modes, they also significantly increase intracavity modal dispersion, making it more challenging to balance modal dispersion with chromatic dispersion, nonlinearity, filtering, gain, and loss [7,23]. As a result, achieving stable STML becomes substantially more difficult. At present, the lack of efficient and robust parameter control strategies remains a major limitation for the practical implementation of high-energy and high-bandwidth STML.

The application of intelligent algorithms to mode-locked fiber lasers significantly reduces the reliance on manual intervention for parameter adjustment and mode-locking maintenance, thereby lowering operational costs and enhancing the practicality and deployment potential of these laser systems [24,25,26,27,28,29,30,31,32]. In recent years, evolutionary algorithms (EAs) and their key branch genetic algorithms (GAs) have been widely applied to intelligent mode-locked fiber lasers due to their strong global optimization capabilities. Promising results have been achieved in single-mode fiber mode-locking systems such as nonlinear polarization rotation (NPR) fiber lasers [27], Figure-8 fiber lasers [28], and thulium-doped fiber lasers [29,30]. However, research on applying intelligent algorithms to STML in fibers with large modal dispersion remains relatively limited. In spatiotemporal mode-locked lasers, which represent complex nonlinear systems involving multidimensional information, intelligent algorithms such as GAs offer significant advantages for multidimensional parameter optimization, integration, and analysis [21,22]. To further advance the application capabilities of STML fiber lasers, it is imperative to utilize algorithmic assistance to achieve robust and stable STML operation. Moreover, multimode fiber lasers, as complex nonlinear multimode systems, also exhibit a hysteresis phenomenon induced by the polarization controller. Hysteresis in mode-locked fiber lasers has been reported previously [32,33,34,35,36], and the inconsistency in laser output under identical intracavity parameters caused by hysteresis imposes more stringent requirements on the stability of intelligent STML. Kokhanovskiy et al. employed reinforcement learning to achieve stable mode locking at the minimum pump power under pump hysteresis [32]. However, reinforcement learning requires collecting large amounts of data for model training, which leads to high implementation costs and poor generalizability, thereby limiting its applicability. Yan et al. developed a two-stage genetic algorithm to overcome hysteresis and realize dual-wavelength mode locking [31]. Nevertheless, the two-stage approach compromises the global optimization capability of GA, making it prone to local optima or even convergence failure.

In this work, we demonstrate a compact, all-fiber intelligent STML laser based on the NPR mechanism, without the use of additional spatial or spectral filters. To address the above challenges, we propose a memory-diffusion genetic algorithm (MDGA) for intelligent STML. Unlike reinforcement learning, MDGA does not require large-scale experimental data for model training, offering low deployment costs and strong generalizability while enhancing the stability of intelligent STML in the presence of hysteresis. By automatically optimizing the electric polarization controller (EPC), our system achieves stable STML operation, delivering a single-pulse energy of 8.6 nJ. To the best of our knowledge, this work represents the first demonstration of an all-fiber, intelligent STML laser operating under large modal dispersion. By achieving automated, hysteresis-resilient control with competitive output performance, this work opens a new pathway toward practical, high-energy, and high-bandwidth multimode STML fiber lasers.

2. Experimental Setup and Methods

2.1. Experimental Setup

Figure 1 shows the schematic diagram of the intelligent STML fiber laser, with multiple measurement instruments. A 976 nm multimode semiconductor laser (DILAS, Mainz, Germany) serving as the pump source is coupled into the cavity through a multimode pump combiner (MPC, DKPHOTONICS, Shenzhen, China). The gain medium is a 1 m STIN multimode ytterbium-doped gain fiber (LMA-YDF-20/130-HI-8, Nufern, East Granby, CT, USA; 6 modes are supported, with a group velocity dispersion range of approximately 18.5–23.2 ${\mathrm{f}\mathrm{s}}^2/\mathrm{m}\mathrm{m}$ for the six lowest-order modes). A polarization-dependent isolator (PD-ISO, DKPHOTONICS, Shenzhen, China) not only ensures unidirectional operation of the cavity but also provides an NPR mechanism for STML. The 3 m few-mode pigtails (LMA-GDF-10/125-M) from both the ISO and the MPC provide strong spatial and spectral filtering within the multimode cavity, which is crucial for realizing STML. An optical coupler (OC1, AFR, Zhuhai, China) with a 20/80 splitting ratio, featuring the 3 m 50/125 μm pigtails (OM4) within the cavity, is used to extract part of the output power for measurements. An electric paddle fiber polarization controller (EPC, THORLABS, MPC320, Newton, NJ, USA) with 2 m OM4 fiber, serving as a key device for modifying intracavity parameters, is used to modify the state of polarization (SOP) within the cavity and to cooperate with the NPR mechanism to achieve different laser output states [24,25]. The total length of the cavity is approximately 12 m. After exiting from OC1, the laser is split into five channels by OC2, which is composed of multiple cascaded optical couplers. These channels are simultaneously measured by an optical spectrum analyzer (OSA, YOKOGOWA, AQ6370C, Tokyo, Japan), a charge-coupled device (CCD) camera (SPIRICON, SP620U, Beijing, China), an oscilloscope (RIGOL, DS4054, Suzhou, China) and a radio-frequency (RF) analyzer (RIGOL, DSA815, Suzhou, China), each paired with a photodetector (THORLABS, DET08CFC/M, Newton, NJ, USA), and a power meter (THORLABS, PM100D, Newton, NJ, USA) with a thermal power sensor (THORLABS, S425C, Newton, NJ, USA). After OC2, the branch directed to the power meter receives 30% of the total laser output. These measurement devices, the EPC, and a personal computer (PC) communicate in real time with each other, and together with the STML fiber laser, they form the hardware foundation of the intelligent STML system.

2.2. Hysteresis

The EPC utilized in our experimental setup is a motorized paddle-type device featuring three individual paddles. Each paddle provides a rotational range from 0° to 160°, and our experiments demonstrate that a rotational precision of 1° is sufficient to achieve stable automatic mode-locking. In this work, the orientation angles of the three EPC paddles are denoted as $({\theta }_1, {\theta }_2, {\theta }_3)$. These paddles function as waveplates within the cavity, altering the polarization state evolution of the intracavity laser beam through rotation and thereby providing the necessary control for the NPR effect.

The hysteresis phenomenon observed in the experiment, induced by the EPC, is shown in Figure 2. Figure 2 illustrates the evolution of the laser’s output power, pulse train, and optical spectrum as the paddle angle is adjusted. Specifically, the orientations of two EPC paddles were kept fixed, while the third paddle was rotated from 0° to 160° and then reversed back to 0°. The laser operated in a continuous wave (CW) state when the paddle started rotating from 0°. As the rotation angle increased and reached 115°, the output power abruptly rose, pulses appeared in the temporal waveform, the optical spectrum broadened, and the beam profile changed from a speckle pattern to a relatively uniform distribution, indicating the onset of STML. This STML state was maintained as the paddle angle continued to increase beyond 115°, until it was lost at around 135°. When the angle reached 160°, the paddle was rotated back in the reverse direction. In this process, STML reappeared but vanished again at 152°. STML did not re-emerge until the angle decreased to 116°, and it persisted until the angle reached 99°, where it was ultimately lost. It is noteworthy that the hysteresis curve shown in Figure 2, obtained by rotating one specific paddle, is unique to that paddle’s role in the polarization evolution. Similar hysteresis phenomena were observed when individually rotating the other two paddles, but with distinct power variation profiles and switching thresholds. This is expected, as each paddle imparts a different and sequential transformation on the intracavity polarization state, leading to non-identical responses. The phenomenon demonstrated in Figure 2 is representative of the hysteresis effect, which exists across the entire three-dimensional parameter space of the EPC.

The hysteresis phenomenon induced by the polarization controllers (PCs) originates physically from the modulation of nonlinear transmission characteristics by the polarization state evolution within the NPR mechanism [33]. This modulation leads to path-dependent alterations in the intracavity gain-loss balance. Specifically, adjusting the PCs angles directly alters the trajectory of polarization state evolution inside the laser cavity. Combined with the polarizing selection effect of the PD-ISO, changes in the PCs state effectively reshape the intracavity nonlinear transmission curve—that is, the relationship between light intensity and nonlinear loss. This alteration directly influences the operating range of the nonlinear feedback mechanism. Under certain PCs configurations, the system can enter a bistable state where positive and negative feedback coexist within a certain intensity interval. This bistable state consequently causes the thresholds for pulse formation and disappearance to differ during the upward and downward sweeping of the pump power, thereby forming a hysteresis loop.

To the best of our knowledge, this is the first experimental observation of polarization-controller-induced hysteresis in a spatiotemporal mode-locked fiber laser. The overlapping parameter range of the EPC, within which STML is obtained during both clockwise and counterclockwise rotations, constitutes the stable mode-locking (ML) region. In this region, the STML state remains robust against perturbations in the EPC orientation, whether tuned in the increasing or decreasing direction. This robustness suggests that STML within the stable ML region exhibits significantly enhanced tolerance to environmental disturbances. This concept of a stable ML region can be extended from the one-dimensional parameter space of a single EPC angle to a three-dimensional parameter space encompassing all three EPC angles. This approach provides a foundational framework for future research into stable spatiotemporal mode-locking in even higher-dimensional parameter spaces. It is worth noting that this initial investigation focused on hysteresis in a one-dimensional parameter subspace. The hysteresis behavior in the full three-dimensional parameter space, where all three EPC paddles are adjusted simultaneously, is expected to be more complex and constitutes an important topic for future research.

2.3. Memory-Diffusion Genetic Algorithm

One major limitation of the conventional GA in handling the hysteresis phenomenon is its lack of memory. After the GA reaches a ML parameter point, it may fail to recover ML when returning to the same point due to hysteresis. Consequently, the algorithm can lose focus on this region and drift away from the stable mode-locking domain, ultimately preventing convergence. Another limitation is that the fitness evaluation of individuals in a conventional GA is completely independent, lacking awareness of the neighborhood structure in the parameter space. As a result, the algorithm cannot recognize when it is operating near the boundary of the STML parameter region, where even slight perturbations may cause the loss of the STML state, leading to instability.

To enable the GA to achieve stable STML output and correctly converge into the stable ML region, we introduce a value space (VS) into the conventional GA framework to record the entire discrete and finite parameter space. The purpose of this VS is to quantify the temporal stability of the laser output and the robustness of parameters against drift, while simultaneously serving as a memory mechanism that guides the algorithm back to promising regions in the parameter space. The simplified flowchart of the algorithm is shown in Figure 3. The VS is represented as a three-dimensional matrix, where the three coordinates correspond to the discrete step angles $({\theta }_1, {\theta }_2, {\theta }_3)$ of the EPC, each with 1° resolution. The value at a given position, $V({\theta }_1, {\theta }_2, {\theta }_3)$, denotes the fitness associated with the EPC angles $({\theta }_1, {\theta }_2, {\theta }_3)$. With the introduction of the VS, the fitness of individuals in the GA is no longer obtained directly from the merit function $F_{merit}$ based on the laser output parameters. Instead, the value computed by $F_{merit}$ is first stored in the VS, which acts as an intermediate evaluation layer. By incorporating both temporal stability and the neighborhood structure of the parameter space, the VS refines the raw evaluation and provides a more robust fitness measure for guiding the evolutionary process.

The main workflow of the algorithm is illustrated in Figure 3a. It begins with the initialization of a population consisting of n individuals (in our experiments, n = 20). Each individual is characterized by a set of EPC angles $({\theta }_1, {\theta }_2, {\theta }_3)$, which define its genetic representation. The optimization process involves evaluating each individual by configuring the EPC according to its gene (angle set) and measuring the corresponding laser output. The measured laser output parameters are then assessed by a merit function, $F_{merit}$, to yield a performance score for the individual. This score is subsequently processed within the VS to determine the final fitness value of the individual. The transition between individuals requires the EPC motors to rotate to new angles. During this rotation process, we are able to monitor the laser output state in real time. In conjunction with our experimental setup, we introduced an acceptance mechanism into the algorithm optimization process to enhance the effectiveness of the value space. The acceptance mechanism means that if a ML state (corresponding to the $F_{merit}>0$ in the following text) emerges during the EPC rotation, the VS is updated synchronously, and the corresponding parameter angles are directly incorporated into the next round of selection and iterative optimization. Although this operation sacrifices part of the optimization time, it allows the VS to take fuller effect, thereby helping the algorithm to locate the stable ML region, enhancing its stability, and accelerating convergence. After evaluating all individuals by rotating the EPC through the corresponding parameter sets, we employ an elitism strategy to expedite convergence. Specifically, the individual with the highest fitness is preserved unchanged and directly added to the new generation population. Random selection is then performed based on fitness, with individuals of higher fitness having a higher probability of being selected. In each operation, two individuals are chosen. Their genes then undergo crossover and mutation to generate new offspring, which are added to the new population. This process of selection, crossover, and mutation is repeated until the new population size reaches the predefined number n. The algorithm then proceeds to optimize the next generation. This generational cycle continues iteratively until either the fitness score meets a predefined convergence criterion or the maximum number of iterations is reached.

The fitness update within the VS occurs in two steps: memory time decay and spatial diffusion. A schematic illustration in a two-dimensional VS, for ease of understanding, is shown in Figure 3b. The memory time decay step is implemented using an exponential moving average (EMA) approach. This method continuously updates and maintains a historical record of fitness values associated with each specific angle setting, thereby quantifying the temporal stability of the laser’s operational state. VS points that correspond to stable mode-locking will consequently maintain a consistently high EMA value, reflecting their robustness over time. Let ${\theta }_c=({\theta }_{c1}, {\theta }_{c2}, {\theta }_{c3})$ represent an arbitrary point in the VS. The time decay function is defined as follows:

$$V_{new}\left({\theta }_c\right)=\alpha F_{merit}\left({\theta }_c\right)+\left(1-\alpha \right)V_{old}\left({\theta }_c\right)=∆V\left({\theta }_c\right)+V_{old}\left({\theta }_c\right),$$

(1)

$$∆V\left({\theta }_c\right)=\alpha \left(F_{merit}\left({\theta }_c\right)-V_{old}\left({\theta }_c\right)\right),$$

(2)

where $V_{new}\left({\theta }_c\right)$ represents the updated fitness value at the current parameter ${\theta }_c$ in the VS, while $V_{old}\left({\theta }_c\right)$ represents the previous fitness value at the same parameter. The weight α determines the sensitivity of the fitness to changes. $F_{merit}\left({\theta }_c\right)$ is the merit function computed from the current laser output, which can be constructed as needed, and $∆V\left({\theta }_c\right)$ represents the increment of the fitness. The temporal decay of memory mitigates the fitness discontinuity arising at the same parameter ${\theta }_c$ near the stable ML region, where mode-locking is achieved in one generation but lost in the subsequent generation. This helps to alleviate the oscillations of the GA in the presence of hysteresis and facilitates convergence toward the stable ML region.

The second step of fitness update in the VS is spatial diffusion, which signifies that a given point influences neighboring regions in the VS, thereby quantifying the stability of the parameter space. In regions where ML EPC angles cluster, enhanced stability is observed, accompanied by a collective increase in fitness values. We define the discrete parameter neighborhood of ${\theta }_c$ with a radius of $r$ as follows:

$$N\left({\theta }_c, r\right)=\left\{\theta =\left({\theta }_1, {\theta }_2, {\theta }_3\right)\in \mathbb{Z}||{\theta }_i-{\theta }_{ci}|\le r, i=1,2,3\right\},$$

(3)

where $\theta$ is an arbitrary point within the discrete parameter neighborhood $N\left({\theta }_c, r\right)$ and $\mathbb{Z}$ represents the set of integers. A three-dimensional hollow Gaussian kernel centered at ${\theta }_c$ is employed to perform incremental convolution over the neighborhood $N\left({\theta }_c, r\right)$ for spatial diffusion. The specific form is given by:

$$V_{new}\left(\theta \right)=V_{old}\left(\theta \right)+∆V\left({\theta }_c\right)·G_{\sigma ,hollow}\left(∆\right), \forall \theta \in N\left({\theta }_c, r\right),$$

(4)

$$G_{\sigma ,hollow}\left(∆\right)=\left\{\begin{array}{cc}{\displaystyle \frac{1}{C}}\exp \left(-{\displaystyle \frac{{‖∆‖}^2}{2{\sigma }^2}}\right),& ∆\ne (0, 0, 0)\\ \hfill 0,& ∆=(0, 0, 0)\end{array},\right.$$

(5)

$$C={\sum }_{∆\ne (0, 0, 0)}\exp \left(-{\displaystyle \frac{{‖∆‖}^2}{2{\sigma }^2}}\right),$$

(6)

$$∆={\theta -\theta }_c=\left({\theta }_1-{\theta }_{c1}, {{\theta }_2-\theta }_{c2}, {{\theta }_3-\theta }_{c3}\right), \forall \theta \in N\left({\theta }_c, r\right),$$

(7)

where $V_{new}\left(\theta \right)$ and $V_{old}\left(\theta \right)$ respectively represent the VS values within the neighborhood $N\left({\theta }_c, r\right)$ after and before spatial diffusion. $G_{\sigma ,hollow}\left(∆\right)$ is a normalized hollow Gaussian kernel with a standard deviation of $\sigma$, where $∆$ represents the offset of $\theta$ relative to ${\theta }_c$ within the neighborhood. ${‖∆‖}^2={\left({\theta }_1-{\theta }_{c1}\right)}^2+{\left({{\theta }_2-\theta }_{c2}\right)}^2+{\left({{\theta }_3-\theta }_{c3}\right)}^2$ is the distance of $\theta$ relative to ${\theta }_c$. $C$ is a normalization constant that ensures the sum of weights of the Gaussian kernel (excluding the central point) equals 1, thereby preventing unbounded growth of the fitness. Spatial diffusion takes into account the influence of neighboring parameter states, enhancing the algorithm’s focus on parameter regions where ML tends to cluster and enabling a faster identification of stable ML parameters.

We refer to this improved GA as the memory-diffusion genetic algorithm (MDGA). The essence of MDGA lies in incorporating temporal reproducibility and parameter space stability into the fitness evaluation. The parameters of the VS, including the discrete step size of 1°, the neighborhood radius $r=4$, the Gaussian kernel standard deviation $\sigma =2$, and the EMA weight $\alpha =0.5$, were empirically selected based on a series of preliminary optimization tests. A typical optimization trace under the chosen parameters is shown in Figure 4a, with convergence achieved by the 7th generation in about 18 min. The parameter selection was validated through comparative tests. Enlarging the radius to $r=40$ increased the per-update time to about 1 s and total optimization to ~62 min, while diluting the central weight (Figure 4b). Reducing $\alpha$ to 0.05 delayed convergence beyond 20 generations, taking over 38 min (Figure 4c). Using $r=1$ and $\alpha =0.5$, which mimics a conventional GA, halved the STML success rate. The value $\sigma =2$ ensures >93% of the weight lies within the $r=4$ radius, providing smooth interpolation without blurring. The adopted parameters thus optimally balance convergence speed, algorithmic stability, and the resolution needed to map the stable mode-locking region.

3. Experimental Results and Discussion

Guided by the MDGA, the all-fiber laser with large modal dispersion can automatically achieve stable STML at a pump power of 3.7 W. In the experiment, the GA population size and the maximum number of generations were both configured to 20. The merit function is given by:

$$F_{merit}=\left\{\begin{array}{cc}P∆t,& v_{pp} > threshold1 and P_{\mathrm{m}\mathrm{a}\mathrm{x}\_\mathrm{r}f}>threshold2\\ \hfill 0,& other\hfill \end{array}\right.,$$

(8)

where $P$ represents the output power measured by the power meter (accounting for 30% of the total output), and $∆t$ represents the average time interval between peaks in the pulse train, and $P∆t$ represents the single-pulse energy. $v_{pp}$ is the peak-to-peak value of the pulse train measured by the oscilloscope (unit: V). In the experiment, threshold1 is set to 0.6 V, which filters out the CW state. $P_{\mathrm{m}\mathrm{a}\mathrm{x}\_\mathrm{r}f}$ represents the power of the maximum RF component measured by the RF spectrum analyzer (unit: dBm). In the experiment, threshold2 is set to −40 dBm, which eliminates certain unstable pulse output states. The combined use of these two thresholds ensures the effectiveness of the merit function in identifying STML states.

Using Equation (8) as the merit function, the output optimized by the MDGA is shown in Figure 5. Figure 5a illustrates the fitness distribution in the VS after MDGA optimization. The final EPC parameters converge to (33, 120, 24), with the parameters during optimization clustering around this point, indicating successful algorithm convergence to the stable ML region (the red area in Figure 5a where the fitness approaches 1). As shown in Figure 5d, the fitness value gradually stabilizes after the 12th generation, confirming the convergence of the MDGA optimization process. The characteristics of the STML single-pulse output optimized by the MDGA are shown in Figure 5. The pulse interval is approximately 57.6 ns, corresponding to a repetition rate of 17.353 MHz, with a signal-to-noise ratio of 57 dB. The spectrum in Figure 5e is centered around 1045 nm and shows distinct double peaks, resulting from nonlinear effects during pulse propagation in the multimode fiber. The pulse width was measured to be 46.3 ps using an autocorrelator (FEMTOCHROME, FR-103XL, Berkeley, CA, USA) as shown in Figure 5f. The output power measured by the power meter was 44.6 mW (30% of total output), with a total output power of 148.7 mW and a single-pulse energy of approximately 8.6 nJ. Figure 6a,b shows the RF spectra and optical spectra obtained from different spatial sampling points. While the optical spectra exhibit slight variations, the RF spectra overlap, confirming the presence of spatiotemporal mode-locking [37,38].

A 24 h stability test was conducted on the single-pulse STML state optimized by the MDGA, with the results presented in Figure 6c,d. The average output power was 44.5 mW with a standard deviation of 0.67 mW, corresponding to a fluctuation of 1.5%. Over the 24 h period, the overall output power decreased by approximately 1 mW, accompanied by slight spectral variations, particularly at the long-wavelength peaks. These changes were attributed to parameter drift caused by thermal accumulation and mechanical deformation of the fiber. Despite parameter drift, the laser maintained a stable single-pulse STML output throughout the 24 h period, indicating that the parameter point identified by the MDGA within the stable ML region exhibits high tolerance to drift. This demonstrates that the MDGA enables robust and stable automatic STML operation. Increasing the pump power can lead to higher single-pulse energy, but this will increase output instability, with pulse splitting or loss of STML occurring within minutes. Such state transitions are accompanied by abrupt changes in output power and spectrum.

We adopted Equation (8) as the merit function and performed 10 sets of optimization experiments using MDGA and the unmodified GA, respectively. To avoid unnecessary time waste, we used the same early stopping mechanism for both algorithms: when the maximum fitness is not 0 and the standard deviation of the maximum fitness over the last 3 generations is less than 1% of the mean, the experiment terminates and the EPC parameters corresponding to the maximum fitness of the last generation are adopted. Additionally, to ensure fairness in optimization time, we set the maximum generations and population size to 20 and 20 for MDGA, and 20 and 60 for the unmodified GA, respectively. Other parameters shared by MDGA and GA were kept consistent. Each test started from a random EPC state, and a test was considered successful only if the single-pulse energy after optimization was greater than 8 nJ. The experimental results are shown in Figure 7. Figure 7c shows that the success rate of the unmodified GA in maintaining STML output for more than 60 min is less than 50%, while that of MDGA reaches 90%—this indicates that MDGA can effectively improve the algorithm stability and achieve stable automatic STML when facing hysteresis. In this experiment, the unmodified GA had a minimum single optimization time of 21.4 min and an average of 24.9 min, while MDGA had a minimum of 16.4 min and an average of 24.5 min.

Additionally, the typical fitness evolution curves of GA and MDGA in the experiments are presented in Figure 7b,d corresponding to the 3rd and 7th test groups, respectively, and marked with arrows in Figure 7a. Although both GA and MDGA achieved stable STML lasting over 60 min in these two optimization tests, their fitness curves differ significantly. The GA curve exhibits strong fluctuations because hysteresis causes the best individuals of one generation to disappear in the next, a situation GA cannot effectively handle, leading to pronounced oscillations in the maximum fitness trace. Compared with the strongly fluctuating optimization curve of GA, the MDGA curve is smoother and converges more rapidly. This improvement arises because the temporal decay operation in the VS filters out parameter points with poor reproducibility caused by hysteresis, while the spatial diffusion operation increases the overall fitness of clustered regions more likely to support stable mode locking, thereby enhancing algorithmic focus on these regions. Combined with the acceptance mechanism, these enhancements accelerate the construction of parameter clusters favorable for mode locking. Together, these improvements significantly strengthen MDGA’s ability to identify stable STML parameters, ultimately enabling robust automatic STML even in the presence of hysteresis. MDGA not only improves the stability of automatic STML, but also the presence of the value space enhances the algorithm’s perception of the output-state distribution across the parameter space, thereby enabling more effective control of the STML fiber laser.

As summarized in

Table 1. The comparison of the output power and pulse energy of 1-μm STML laser.

ML Mechanism	Gain Fiber (μm)	Average Output (mW)	Single-Pulse Energy (nJ)	Ref.
MMI	YDF (10/125)	12	0.5	[39]
NALM	YDF (10/125)	1.304	0.195	[40]
NPR	YDF (20/125)	232.2	8	[23]
QD	YDF (10/125)	70.4	4.4	[41]
NPR	YDF (10/125)	43.1	2.15	[42]
NOLM	YDF (5/130)	4.4	4.1	[43]
NPR	YDF (20/130)	148.7	8.6	This work

, previous demonstrations of 1-µm STML fiber lasers relied on conventional manual optimization of various mechanisms—including multimode interference (MMI), nonlinear optical loop mirror (NOLM), nonlinear amplifying loop mirror (NALM), and quantum dot (QD) saturable absorbers—which often suffer from poor repeatability and limited operational robustness. In contrast, the present work achieves, to the best of our knowledge, the first intelligent STML operation under large modal dispersion, enabled by the proposed MDGA that effectively suppresses hysteresis effects. Importantly, the intelligent laser not only maintains stable operation but also achieves competitive performance, delivering a single-pulse energy of 8.6 nJ and an average output power of 148.7 mW. These results highlight that automation can achieve both stability and high energy, opening a new direction toward intelligent and robust STML fiber lasers.

4. Conclusions

To address the challenges of hysteresis-affected reproducibility in STML and the limited tolerance to environmental perturbations in NPR-based parameter tuning, we developed the MDGA. This algorithm successfully achieves stable, self-starting STML in an all-fiber laser operating under large modal dispersion. To the best of our knowledge, this is the first work to achieve automatic mode-locking in an all-fiber STML laser with large modal dispersion. The high-energy single-pulse mode-locked output of this all-fiber laser is of potential application value in fields such as laser machining and precision measurement, where high pulse energy is in demand. This work offers an approach for enhancing the stability of such lasers, which is crucial for practical applications.