1. Introduction

With the rapid development of semiconductor lasers, fiber fabrication technology, and optical fiber devices, fiber lasers have experienced impressive progress in the last few decades [1–5]. Thanks to the MOPA structure, the output laser can integrate with an amplifier's high power and high energy output while preserving the seed laser's excellent output characteristic [6–8]. To achieve high-efficiency extraction in a MOPA structure, the amplifiers often operate in their gain saturation state, resulting in pulse shape distortion. Most of the population inversion is depleted by the leading edge, leaving less inversion available for the trailing edge, leading to different gains for the leading and trailing edges [9]. The pulse distortion process can influence the temporal and spectral characteristics of the output and consequently affect the efficient energy extraction within the system [10,11]. Additionally, pulse waveforms are crucial in nonlinear frequency conversion, affecting laser processing applications that demand specific waveform characteristics. For instance, uniformly intense rectangular pulse benefits in nonlinear frequency conversion applications [12–15], and pulses with a constant derivative of the laser intensity concerning time can suppress spectral broadening caused by self-phase modulation (SPM) [16,17]. Different waveforms yield different aluminum alloy welding effects [18], and editing the temporal morphology enhances the material removal efficiency in micro-milling and improves surface quality [19]. Hence, active temporal pulse shape method control to achieve specific waveforms is essential. The realization of arbitrary waveforms has been extensively studied by researchers in Ytterbium-doped and Erbium-doped fiber lasers through comprehensive analysis using numerical calculations and model analytical methods [10,11,20–22].

The analytical expressions reported so far are predominantly based on the Frantz-Nodvik equation, which reveals the relationship between the input and output waveforms [9]. D.N. Schimpf et al. [11] and A. Malinowski et al. [23] have presented analytical models for the relationship between the targeted pulse waveform and the seed pulse waveform. G. Sobon et al. improved the expression by considering the distinct gain functions of each amplification stage [24]. These methods ease the calculation of the optimal seed pulse waveform needed to obtain an arbitrary target pulse waveform [6,11,24,25]. In numerical methods, the targeted pulse is acquired by adjusting the injected waveform on the proposed algorithm after multiple calculation iterations. K.T. Vu et al. obtained the target pulse by an iterative approach based on the simulated annealing method [10]. M. Jiang et al. achieved the optimum input pulse using the stochastic parallel gradient descent algorithm [26]. H.X. Chang et al. demonstrated proportional control methods for active temporal pulse manipulation [22]. As the complexity of the target pulse shape increases, achieving the desired results using this method becomes progressively more challenging. Typically, the pulse shaping is conducted by regulating the current of the seed laser diode [27]. However, the method has limitations due to the low output power and transients of the laser diode. The utilization of fiber-coupled acousto-optic modulators (AOM), electro-optic modulators (EOM) [23,28,29], or Pockels cells [30]can partially address this issue. However, these solutions still require synchronization techniques and are constrained by the threshold characteristics of the fiber-coupled modulation devices. The pulse stacker can operate at higher power, but temporal instability of pulses may occur due to interference between adjacent pulses, and engineering complexity limits its application [31,32]. Partially coherent light stacking can address this issue but cause significant loss [33]. Therefore, a pulse shaping system with a high threshold that is stable and compatible with various seed sources is needed.

This paper employs a non-coherent stacking technique to generate a non-coherent nanosecond pulse, achieving optimized amplification for industrial lasers. The system is composed of fiber components eliminating the need for electronic devices. Additionally, it can achieve flexible waveform control through parameter adjustments. Combining different delayed waveforms, this pulse shaper forms a pre-shaped pulse favorable for the targeted waveform. We verified the effectiveness of the pulse shaper in a system using a general seed, achieving four types of pre-compensated pulses, including the broadened, the ‘M’-shaped, the triangular, and the pre-pulse-shaped waveforms. The targeted ‘M’-shape is chosen as an example to show the process of pulse pre-compensation by this pulse shaper to achieve the desired waveform, and we investigate the impact of the presence and absence of the shaper on the amplification. This pulse shaper is easy to construct and can integrate into nanosecond pulse systems. Due to its high-threshold characteristics, it can effectively shape pulses that undergo distortion after amplification, thereby reducing the number of amplification stages. This not only mitigates the complexity of the amplification system but also minimizes the accumulation of nonlinear effects during multiple-stage amplification. The design could benefit in various laser designs and applications related to laser processing.

2. Theory of pulse propagation and shaping and principle of pulse shaper

When the system operates in a saturated state, the rectangular pulse undergoes substantial gain reshaping, as shown in Fig. 1(a). The leading edge becomes steeper due to high gain, while the amplitude of the trailing edge drops rapidly due to less population inversion. L. M. Frantz and J. S. Nodvik have derived an analytical solution for the pulse transmission equation in the gain saturation state [9]. However, the pulse undergoes pulse distortion and is no longer conducive to the energy extraction of the system and to the applications that require specific waveform characteristics. Fortunately, the pre-compensation of the distortion effect can address these issues. A rectangular pulse can be obtained by designing the pre-pulse, as shown in Fig. 1(b). D. N. Schimpf et al. [11] derived the following analytical solution by solving the Frantz-Nodvik equation in reverse to figure out the best input pulse waveform needed to achieve an arbitrary target pulse shape.

 

Fig. 1. The process of pulse distortion and pulse pre-compensation.

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The currently available shaping methods primarily rely on pre-designed seed waveforms for electrically driven diode seed source, which limits their applicability to other seed sources [6]. AOM and EOM can operate at higher power levels [29] but require electronic components and are restricted by the damage threshold limits of the devices. We have designed a pulse shaper capable of shaping distorted waveforms without restricting the type of seed source used. The pulse shaper is placed between two systems, as illustrated in Fig. 2. The preceding system generates the waveform to be shaped, which is then shaped by the shaper before being injected into the amplification system. This system is composed of fiber components and operates without needing for electronic devices.

 

Fig. 2. The Schematic diagram of the system.

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The structure of the pulse shaper is illustrated in Fig. 3, including six optical couplers (OCs) and a 7 × 1 signal combiner. In theory, pulse shaping can be achieved with more than two channels; increasing the number of channels tends to result in smoother output pulses. However, the number of channels should match the combiner to minimize the degradation in beam quality. Here, we take 7 paths as an example in this research. When the distorted pulse is introduced into the pulse shaper, it is split into seven segments. After the OCs, different lengths of optical fiber are spliced, hence time delays occur between the seven small pulses. These fibers used for different delays can be passive or active. When choosing an active fiber, this channel can undergo amplification. This allows for flexible adjustment of output pulses in the system. Subsequently, all these pulses are combined into a new pulse using a signal combiner. Interference effects in the multiple beam splitter stackers [32] have not been considered here, as the pulses used for shaping are partially coherent and the phases are not locked, making interference effects not significant. Different from the shaping approach of fiber stacks [33], we greatly reduced loss by utilizing an optical fiber combiner that matches the next amplifier. The fibers used in OCs are 10/125µm, while the combiner has an input fiber size of 10/125µm and an output fiber size of 48/400µm. Loss comes from the intrinsic loss of each OC and the combiner, as well as fusion splicing loss. The intrinsic loss of each OC is approximately 0.1 dB, and the combiner introduces a loss of 0.18 dB. We can customize the output waveform with three degrees of freedom: adjusting the delay between pulses, scaling individual channel pulses, and varying the amplification ratio of individual channels.

 

Fig. 3. Schematic diagram of the pulse shaper.

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The output intensity ${I_{out}}(t)$ after the shaper can be represented as follows:

We designed a two-stage amplification system, as shown in Fig. 4, to generate a distorted output pulse. Pulse shaping is implemented using this pulse. The output waveform in the time domain is captured with an oscilloscope (Keysight-MSOX3014 T) equipped with a photodetector (Thorlabs-DET08CL/M, 5 GHz InGaAs).

 

Fig. 4. Schematic of a two-stage nanosecond pulsed fiber laser system.

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The collected waveform shows the pulse shape distortion, characterized by a steeper leading edge of 59.2 ns and a slower falling edge, as illustrated by the black curve in Fig. 5. Using this pulse, we can generate four waveforms, as shown in Fig. 5. These waveforms include the broadened waveform, the ‘M’-shaped waveform, the triangular waveform, and the pre-pulse waveform as shown in Fig. 5(a), 5(b), 5(c) and 5(d), respectively. The implementation of these four different waveforms serves as validation for the effectiveness of waveform shaping in the pulse shaper.

 

Fig. 5. (a) Shaping process of the distorted waveform (b) the ‘M’-shaped waveform (c) the triangular waveform (d) the pre-pulse waveform.

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Taking the broadened waveform as an example, we will now implement the details of the shaping process. In this case, the values are set as 0 m, 7 m, 13.2 m, 18.2 m, 24.8 m, 30.4 m, and 37.2 m, corresponding to respective values of 0 ns, 34 ns, 64 ns, 88 ns, 120 ns, 147 ns, and 180 ns. Additionally, we set the scaling factors for each channel as 0.35, 0.15, 0.125, 0.0625, 0.0625, 0.125, and 0.125. We obtained the seven small pulses with these settings as depicted in the lower part of Fig. 5(a). After passing through the combiner, we successfully achieved the desired broadened output pulse, as shown in Fig. 5(a). The reshaped pulse shows a gradual rise in the leading edge of 141.8 ns, which increased by 137%, and an increase in pulse width of 359.2 ns, which increased by 48%. The parameters used for the other three waveform shaping processes are detailed in Table 1.

Table 1. Parameters used in pulse shaping

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3. ‘M’-shape realization and impact on amplification

A schematic of the amplification setup is depicted in Fig. 6(a). Building upon the two-stage pre-amplifiers illustrated in Fig. 2, we fused 4 m-48/400 µm gain fiber (Yb48/400, Coherent/Nufern) as the third pre-amplifier. Subsequently, a 1.2 m Yb-doped fiber with a triple cladding of 100/140/400 µm was employed as the main amplifier. A cladding-pumped stripper (CPS) was connected to eliminate the residual pump light. An end cap was connected to mitigate reflective light and reduce the facet damage. All gain fibers were pumped by 976 nm Wavelength-locked Laser diodes. With our technology, we can tailor the shape of our output pulses, for example, by adjusting the delays of the pulses we can produce various complicated waveforms, such as an ‘M’-shape waveform output as shown in Fig. 6(b). Such a pulse shape might be useful in Material micromachining. The green curve in Fig. 6(b) is the pre-compensated optical pulse from the shaper. We measured the pulse evolution at the output average power of 21.4 W, 95.4 W, and 196.5 W at 30 kHz.

 

Fig. 6. (a)Schematic of a three-stage nanosecond pulsed fiber laser system, (b)’M’-shape waveform output.

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After integrating the pulse shaper, the changes in the output of the four-stage amplification are as follows: The intrinsic losses of OCs resulted in a 2.25 dB attenuation of the signal light injected into the third stage. However, the extraction of pump light is minimally affected. As the pump power increased, the output power showed linear growth with a slope efficiency of approximately 72%. As for the temporal pulse width, the pulse width variation is negligible, but the waveform variation is significant as shown in Fig. 6(b). The pulse evolution still followed the pulse amplification principle described in part 2. Due to the gain saturation, the peak in front of the pulse increased gradually. Although the introduction of the pulse shaper led to extra spectral structures due to the added fiber length, the spectrum is still clean and free of stimulated Raman scattering (SRS) signals and amplified spontaneous emission noise. The presence of the pulse shaper has more pronounced effects on the spectrum after the amplifiers. Figure 7(a) and Fig. 7(b) illustrate the output spectra after the third stage and the main amplification. The black curve is the output spectrum without the pulse shaper, the red curve shows the output spectrum after the pulse shaper is inserted, and the blue curve is the spectra at a higher pump power.

 

Fig. 7. (a) Output spectra at the pump power of 47 W after the third stage, (b) spectra after the main amplifier: the black curve is the spectrum with a peak power of 128 kW without the pulse shaper, while the blue one and red curve represent spectra with the pulse shaper at peak powers of 128 kW and 148 kW, respectively.

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Without the pulse shaper, we see a significant spectral degradation after the third stage, as depicted in Fig. 7(a). It is clear that spectral broadening is caused by non-linear effects. It is about -30 dB at the Raman wavelength compared to the center wavelength. Further increases in pump power may lead to amplification of SRS and a reduction in signal-to-noise ratio. The spectrum with a pulse shaper shows less broadening with no sign of Raman signal and 95% power within 10 nm of the spectral peak. In contrast, this value is only 82.3% without a pulse shaper. After the main amplification, the ‘shoulder’ on the right of the central peak in Fig. 7(b) shows a severe nonlinear effect in the absence of the shaper. However, the ‘shoulder’ was significantly reduced with the pulse shaper, even at higher peak power. This reduction occurs because pulse shaping decreases the peak power of the input light, resulting in a weaker nonlinear effect. At the same or even higher peak power when using a pulse shaper, a broader injected waveform effectively diminishes the spectral components injected into the main amplifier, as shown in Fig. 7(a). Finally, the average power with and without a shaper at the peak power of 128 kW is 162 W and 118 W, respectively. The peak power is 148 kW with an average power of 195.5 W. This is a significant increase in the pulse energy of the main amplifier.

4. Conclusion

We have developed a design for shaping the distorted output pulses in an amplifier operating in a gain-saturated state. This design enables the pre-compensation of nanosecond pulses, allowing the desired waveform to be achieved after amplification. We presented a fiber system consisting of six optical couplers and a fiber combiner to adjust the output waveform in terms of scaling factors, amplification ratios, and time delays. By implementing four different waveforms, we proved the effectiveness of such a pulse shaper. Additionally, we generated an ‘M’-shaped waveform through pre-compensation of the injected pulse in an amplification system. A comparison of the amplified output results with and without the pulse shaper shows effective suppression of spectral broadening caused by nonlinear effects. Furthermore, at the same peak power, the output energy was increased by about 36%. We believe that this pulse-shaping design has the potential to enhance the performance and flexibility of the nanosecond pulsed fiber amplifier systems, particularly when combined with multimode and wide-spectrum lasers. It provides optimized pulse waveforms for various applications, enabling more efficient optical signal processing.