1. Introduction

With their emission wavelength range (1780–2056 nm) [1] covering the water-absorbing band and atmospheric transmission window, ultrafast thulium (Tm) / holmium (Ho)-doped fiber lasers are widely used in the fields of laser surgery [2], LIDAR [3], and optical communications [4]. In comparison to the intrinsic disadvantages of easy damage, chemical disability, and high cost of the current artificial mode-lockers, such as SESAM [5], 2D materials (graphene [6], carbon nanotubes [7]), mode-lockers of nonlinear polarization rotation (NPR) have been regarded as the most promising methods for achieving high-quality ultrafast pulses in fiber lasers, ensuring high damage threshold and low cost. In particular, the NPR-based mode-locked thulium (Tm)-doped fiber laser (TDFL) is extensively used for producing 2 μm ultrafast fiber lasers owing to its advantages of simple structure, small size, and high photoelectric conversion efficiency [8].

However, fiber lasers based on NPR have rich and complex dynamics, both advantageous and disadvantageous for creating a stable ultrafast laser. By adjusting the PC, pump power, and laser structures, such as traditional soliton [8,9], dissipative soliton [10], dissipative soliton resonance (DSR) [11], unequal pulses [12], bound solitons [13], and noise-like pulses (NLPs) [14], various pulses can be generated. A manual control makes it challenging to achieve a specific type of stable ultrafast pulse output, and the modulated mode-locked fiber laser still faces the risk of the output pulse state mutation. This situation severely limits the use of ultrafast fiber lasers in extreme and unattended environments [8].

In contrast to conventional mode-locked erbium-doped fiber (EDF) lasers at 1.5 μm, which operate in the nearly zero dispersion regime, silica-based fibers typically exhibit large anomalous group velocity dispersion (GVD) in the 2 μm region [8]. Therefore, mode-locked TDFLs would usually operate in the 2 μm deep negative dispersion regime [8,9], resulting in conventional solitons requiring a precise balance of anomalous GVD and self-phase-modulation (SPM). Thus, obtaining a stable 2 μm mode-locked pulse (MLP) solely through intracavity dispersion and nonlinear management is more challenging. Meanwhile, there are almost no effective means and devices in the 2 μm band for controlling the dispersion and nonlinearity well in fiber lasers. For example, in conventional dispersion compensation fibers with small cores (such as UHNA4), the intensity of GVD and SPM cannot be controlled independently and precisely. In addition, it is well known that NPR-based fiber lasers are susceptible to environmental disturbances [15,16], which undoubtedly affect the stability of ultrafast pulses in the 2 μm band.

With the rapid development of artificial intelligence (AI) technology in recent years, the combination of AI technology and laser shows the potential for realizing “dream pulsed laser [17–19],” particularly in mode-locked fiber lasers (MLFL) based on NPR [16]. When subjected to thermal instability and mechanical vibration, polarization control in the NPR-based MLFL becomes increasingly tricky [20,21]. Thus, fast and programmable polarization-control-based automatic mode-locking is required. Genetic [22–25], evolutionary [26,27], human-like algorithms [28], and machine learning [21,29] have been successfully used in MLFL to achieve several types of target lasers. Automatic mode-locking (AML) techniques are a new research area in ultrafast lasers that combine lasers with machine speed, computing capability, and precision [18].

Because the AML technique has shown to have a significant effect [18–30], the majority of this study is focused on the 1 μm [22,29,30] and 1.5 μm bands [21,23–28]. Few studies have been conducted to design an automatic MLFL in the short-wave infrared region band (2–5 μm). In a recent publication, Sheida Mahmoodi [31] introduced an automatic characterization of a mode-locked TDFL in the soliton regime based on a versatile scheme of NPR mode-locking. They also provided maps of laser operation in various modes. However, the MLFL based on NPR is an environmentally sensitive device, and the mode-locked region is not invariable, which is affected by temperature, other environmental conditions [21], and pump power. Retrieving all mode-locked regions is not of significant value unless the environment variables are kept constant.

In this study, a GA with an adaptive mutation rate was used to automate the self-tuning of a TDFL to achieve a stable mode-locked NLP without manual operation. A stable ultrafast laser, such as noise-like MLP, with an output power of 57.7 mW was obtained at 6.5 W pump power, which is centered at 1973nm. The radiofrequency (RF) spectrum signal with a signal-to-noise ratio (SNR) of 52 dB was measured, and the coherence spike width of the noise-like pulses was 325 fs (Gaussian fitting). In the experiment, a closed-loop feedback system was set up. The feedback device was a photodetector, and the feedback signal was the time-domain signal intensity sequence measured by an oscilloscope. The control center was a laptop computer, and the executive device was an electric polarization controller. In addition, the report investigated evolutionary dynamics of the GA-controlled ultrafast TDFL with different mutation rates, which also proved the effectiveness of the proposed method. This is the first study on intelligent MLFL in the 2 μm band to the best of our knowledge.

2. Experimental setup and principle

The experimental setup of the proposed mode-locked TDFL is shown in Fig. 1(a). The gain spectrum centered at the 2 μm band was provided by a 2 m long Tm-doped double-cladding single-mode fiber (Nufern Inc., 10/130 μm and 0.15 NA) pumped by a 793 nm laser diode through a 793/2000 nm fiber combiner. The NPR was performed by combining a manual polarization controller, a motorized paddle fiber polarization controller (MPC320, Thorlabs) with a single-mode fiber (SM1950), and a polarizer. An optical isolator was used to enforce the unidirectional operation of the laser. The cumulative length of the undoped single-mode fiber (SMF-28e, Corning Inc.) was 18.6 m, which was used as a passive fiber to connect various components. A 90:10 fiber coupler was employed to extract 10% power from the laser cavity. The GVD of the passive fiber and gain fiber are β_SMF=-68 ps²⁄km and β_Tm=-91 ps²⁄km, respectively, in the 2 μm band. The junction between the output tail fiber and thulium-doped fiber is coated with a low refractive index adhesive to avoid leakage of the pump light, whereas the fusion of the Tm-doped fiber and SMF28e fiber is coated with a high refractive index adhesive to filter the pump light. The total cavity length is 22 m, and the total dispersion value in the cavity is -1.54 ps².

 

Fig. 1. Experimental setup. (a) intelligent thulium doped mode-locked fiber laser; (b) schematic; (c) algorithm flow chart of adaptive genetic algorithm.

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However, it should be noted that the diameter of the fiber winding disc of the MPC is 18 mm; therefore, if SMF28e fiber winding is used on the MPC, excessive bending loss will lead to abnormal loss of power in the cavity. To avoid this problem, a jacketed fiber (900 µm in diameter, SM1950) was used. In order to ensure the MPC320 can traverse the polarization space, the number of optical fiber turns wound on the three blades of mpc320 is 4:3:4 respectively. Polarization control is achieved by setting the angle of the three-wave plates through electric control. In the experiment, the minimum step is 1 °, which can realize a free adjustment between 0 ° and 170 °. As shown in Fig. 1(b), the output laser is converted into the corresponding electrical signal by a photodiode (EOT Inc., ET-5000, band width of 12.5 GHz), and the oscilloscope can obtain the time-intensity signal sequence of the output laser based on the electrical signal. The oscilloscope sends the signal to the computer for status identification, and then the computer sends new control parameters generated by the GA to the MPC. The flowchart of the adaptive genetic algorithm is shown in Fig. 1(c), which includes fitness calculation, selection, cross, population evaluation, variation rate adjustment, and mutation, the details are shown in Fig. 2.

 

Fig. 2. Schematic of adaptive genetic algorithm. (a) Schematic diagram of population initialization; (b) Schematic diagram of Fitness calculating; (c) Schematic diagram of Selection; (d) Schematic diagram of Cross; (e) Schematic diagram of Variation rate adjustment; (f) Schematic diagram of Mutation.

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The computer sends the control parameters to the MPC during each control cycle, and after MPC completes the corresponding operation, the oscilloscope sends the collected time-domain signal to the computer. The time-domain signal has a duration of 5 μs, following which, the state based on the received signal must be determined. To select an MLP regime, a merit function that discriminates between pulsed and continuous wave (CW) operations must be designed. It is well known that a uniform time-domain pulse signal is the time-domain characteristic of a stable mode-locked pulse. In this study, the three formulas in the program that determine the status of the laser are expressed as follows:

Through the above fitness function, CW, pulse (Q-switched, Q-switched mode-locking), and MLP can be effectively distinguished, as can be observed in the following results. In contrast to using the SHG value and the intensity of the cavity free spectral range (FSR) frequency spectral component as the fitness function [25], the above fitness function has a large value when calculating the time-domain signal of continuous light, and a small value when calculating the time domain signal of the mode-locked pulse. Therefore, during the execution of the GA, a smaller fitness function is followed to find the mode-locking state.

The most significant links in the GA are crossover and mutation. Crossover determines whether a high-quality individual can be inherited effectively, whereas mutation determines whether an individual can jump out of the local optimum. The mutation rate is the ratio of the number of genes changing parameters to the total number of genes. We can adjust the local random searchability of the GA by adjusting the mutation rate and simultaneously maintaining the diversity of the population [32,33]. We used floating-point coding for the genes of the genetic algorithm, that is, the blade angle of the MPC. When a mutation occurs, parameters are often added to a random value within the range, as shown in Eq. (4).

In the mutation process, a sub-parameter in the selected genome was chosen randomly and transformed using Eq. (4). There are two types of variation: up variation (larger than the initial parameter) and down variation (smaller than the initial parameter). In the up variation, the parameters after mutation are still within the adjustable parameter space for control, 0 to 170. The difference between ${\mathop{\rm var}} \_\max$ and the parameter x is the maximum tunable quantity. To ensure randomness in the mutation process, the variable ${\mathop{\rm var}} \_\max - x$ is multiplied by a random number between zero and one, $\textrm{random}(0,1)$. In addition, a mutation step $\beta$ was used to control the variation accuracy, which was set to 0.3. In the following variation, a similar operation is performed on the parameters, as observed in Eq. (4).

3. Results and discussion

This study began with the general objective of obtaining an MLP. The pumping power was fixed at 6.5 W, and various laser dynamics could be obtained when the MPC is adjusted. The degrees of plates on the MPC define the genes for the following GA. As shown in Fig. 2, the algorithm begins with a population of 20 individuals composed of randomly generated genes. At each new generation, the four best individuals were cloned, and the remaining genes were retained if their corresponding fitness function values met the requirements, 10 being the maximum number of genes allowed to be retained. The remaining genes were produced from random crossover (interchange of the genes of two “parents”) to maintain a population of constant size. Next, we need to evaluate the optimal fitness of the current population and adjust the variation rate according to the evaluation results. The variation rate multiplied by the number of populations is the number of genes that mutate. One of the sub genes of the mutant gene would add a random value. It should be noted that the mutated gene still needs to be between 0 and 170. Thus, the new generation produced is subsequently tested, and the adaptive procedure is repeated until the algorithm converges toward an optimum for the control objective.

To the best of our knowledge, a higher mutation rate benefits the searchability of the algorithm, whereas a lower mutation rate aids the overall stability of the population [32,33]. In practice, it is expected that the target state can appear as soon as possible; at the same time, when the ideal state appears, the population gradually begins to converge to the target state. A fixed mutation rate could not satisfy the requirements; therefore, an adaptive mutation rate [34] was designed in GA. The adaptive variation rate varied with the fitness value of the optimal individual in the population ranging from 0.2–0.5. The fitness value of the optimal individual was high; that is, when the target pulse did not appear in the population, there was a high variation rate. With the evolution of GA, when individuals with low fitness (target pulse) gradually appeared in the population, the variation gradually declined, and the excellent individuals were retained as far as possible. In this case, variation still exists to find a better individual and maintain the algorithm's search capability.

The evolution curves of the adaptive mutation rate are shown in Fig. 3. The black curve corresponds to the average fitness for each generation, and the green curve indicates the fitness function value corresponding to the best gene in each generation. The pink curve represents the top ten optimal fitness functions of each generation, and the red dots indicate the proportion of the MLP to the population in each generation. In the optimization process, the pulse state corresponding to the parameter population of the first and second generation is CW, as shown in Fig. 3(a), and the corresponding fitness function value was high, which is the first stage. In the second stage, that is the Q-switched mode locking state, as shown in Fig. 3(b), from generation 3 to 8, the pulse state appeared in the parameter population, and the fitness function value was significantly lower than that in the first stage. In the third stage, that is the NLP state, as shown in Fig. 3(c), from generation 9 to 20, the mode-locking state began to appear, and with the increase in algebra, the proportion of the number of MLPs in the total population also gradually increased and finally tended to be stable. The fitness curves of the top 10 in each generation showed a better matching trend with the fitness curves of the optimal individual. All the fitness function curves clearly show a convergence trend from high to low, which is consistent with the GA. After the 14th generation, the effective proportion of MLP samples in each generation of individuals exceeds 50%, indicating that the proposed algorithm is effective.

 

Fig. 3. Convergence of the GA with the best (green points), average (black points) and the sum of the top ten (pink points) fitness and the proportion of the mode-locking pulse to the population in each generation (red points). (a) Time-domain signal of CW, (b) Time-domain signal of a pulsed laser, (c) Time-domain signal of MLP.

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The final measurement results of the noise-like pulses are shown in Fig. 4. As shown in Fig. 4(a), the optical spectrum of the pulse is broad and smooth. It has a 3-dB bandwidth of about 20 nm and a center wavelength of around 1973nm. The output spectrum was monitored using an optical spectrum analyzer (Q6375,0.05 nm resolution, Yokogawa Meters and Instruments Corporation). Figure 4(b) shows an oscilloscope trace of a pulse train. The time interval between the pulses was 106 ns, matching the cavity roundtrip time and cavity length. This indicates that the fiber laser operates in a single-pulse-envelope mode-locking state. Figure 4(c) shows the corresponding autocorrelation traces measured under different scan ranges of the autocorrelator. The full width at half maximum (FWHM) of the shoulder was 458 fs. Assuming Gauss pulse profiles, the width was approximately 325 fs using a commercial autocorrelator (Pulse Check 50, APE). Figure 4(d) shows the corresponding radio frequency (RF) spectrum of the NLP fiber laser with a 2 kHz span and 10 Hz resolution bandwidth (N9320B, Agilent Technologies Inc.). The pulse repetition rate of the laser was 9.4045 MHz, exactly matching the cavity round-trip time of 106 ns and the cavity length of 22 m. The SNR was 52 dB.

 

Fig. 4. Experimentally observed NLP emission. (a) Optical spectrum, (b) pulse train, (c) autocorrelation trace measured under a narrow range of 1.5 ps, subgraph is autocorrelation trace measured under a wide range of 50 ps and (d) RF spectrum of the fundamental cavity repetition rate measured with a 2-kHz span and 10-Hz resolution bandwidth.

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Due to the peak-power-clamp effect, soliton pulses are easy to cause pulse splitting, so the pulse energy (usually less than 0.1nJ) and the average output power (several milliwatts) are too low. The laser worked under a high-power pump. Due to excessive nonlinearity, the noise-like mode-locked pulses are obtained in a mode-locked fiber laser based on nonlinear polarization rotation, with much higher average output power and pulse energy. As shown in the subgraph of Fig. 4(c), The autocorrelation curve shows a typical high peak and a strong pedestal, which is typical of noise-like pulses in fiber lasers. This is because, at a larger time scale, there exist a bunch of short pulses whose width and power are randomly varying [35]. Our autocorrelation measurement window is not long enough, and we could not see an entire pedestal, which caused a base of the autocorrelation trace higher than zero.

In addition, the evolutionary dynamics of different parameter structures of the GA-controlled ultrafast TDFL with varying mutation rates were further investigated, as shown in Fig. 5. When the mutation rate was initially set at 10%, after 20 generations of effective optimization, with a decline in fitness, the state of the optimal pulse in each generation gradually transited from CW to pulsed light. However, the optimal individual was only a laser with a large pulse envelope, not the expected MLP. In the case of a 30% variation rate, the MLP appeared in the 18th generation population and was effectively inherited by the 19th and 20th generations. In the case of a 50% variation rate, even if the target pulse appears quickly, the overall fitness of the population does not converge. This is the disadvantage caused by high variation rate. Subsequently, the GA with a 70% mutation rate was used, and the pulse signal appeared in the first generation, and the MLP evolved in the second generation. This is an excellent example of the initial population dependence of the GA [32,33].

 

Fig. 5. Evolution chart of fitness corresponding to different variation rates (The blue dots represent the average of the total fitness corresponding to the population, the red dots represent the best in each generation, and the green dots represent mutation probability in adaptive genetic algorithm).

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The MLP can be implemented more effectively with a high variation rate by comparing the fitness evolution curves under different mutation rates. The evolution trends of average fitness and best fitness can’t match well because of the excessive randomness of the population under a high mutation rate (50%,70%). On the contrary, in the case of a low variation rate (10%), the evolution trends of average fitness and best fitness show good consistency. However, the low mutation rate also leads to the low evolution speed of GA. In the GA-based intelligent mode-locked laser, effective results can be obtained by adjusting the mutation rate of GA according to different situations and needs.

4. Conclusion

In conclusion, an intelligent thulium-doped mode-locked fiber laser based on an adaptive genetic algorithm was demonstrated. In a thulium-doped fiber laser based on NPR, a GA with the adaptive mutation was used to control the internal dynamic processes to produce ultrafast pulses. An NLP with an output power of 57.7 mW was obtained at 6.5 W pump power, centered at 1973nm. The spectrum signal with an SNR of 52 dB was measured using the spectrum analyzer, and the coherence spike width of the noise-like pulses was 325 fs (Gaussian fitting). In addition, the evolutionary dynamics of the different parameter structures of the GA-controlled ultrafast TDFL with different mutation rates were further investigated. At present, intelligent MLFLs are mainly focused on the 1550 μm band [20,22–27]. This study is the first to report on an intelligent mode-locked fiber laser working in a 2 μm band to the best of our knowledge. The precise intelligent control on 2 μm mode-locked fiber laser, such as traditional soliton, dissipative soliton, dissipative soliton resonance (DSR), and bound solitons is our upcoming work. This study will pave the way for generating robust ultrafast lasers in the short-wave infrared region. It is also believed that the combination of computers, optimization algorithms, and lasers is a mainstream trend. With the deep combination of intelligent algorithms and fiber lasers, many optical puzzles may have other manifestations.