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Abstract
We present the first experimental realization of a new mitigation strategy for TMI based on controlling the phase shift between the modal intensity pattern and the thermally induced refractive index grating. If specific modulation parameters are applied while pulsing the seed and/or pump radiation, the direction of energy transfer is forced from the higher-order modes into the fundamental mode. In this way, the fiber amplifier can operate at an average output power significantly higher than the TMI threshold with a diffraction-limited beam profile. A stable beam profile is observed at an average output power that is 83% higher than the TMI threshold of the free-running system, with an intra-burst average power that is 4.15 times higher than the TMI threshold.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The average power and pulse energy emitted by fiber laser systems with diffraction-limited beam quality have grown exponentially over the last decades [1]. This combination of high power/energy and high beam quality has paved the way for the use of this technology for applications in industry, medicine, and security [2,3]. Hereby the development of large-mode diameter fibers has been pivotal since it helps mitigate the onset of hampering nonlinear effects, which has resulted in the power scaling of both CW and pulsed systems with excellent beam profiles [4,5]. Furthermore, significant efforts have been made to eliminate the multimode operation that results from increasing the active core diameter. This has resulted in the development of very effective higher-order modes (HOMs) mitigation strategies for ultra-large mode area fibers, such as the concept of higher-order modes delocalization in large-pitch fibers or distributed mode-filtering rod-type fibers [6,7]. Despite these efforts, the onset of harmful thermo-optic effects currently limits power scalability [8,9]. This is because the heat load gives rise to a radially and longitudinal-dependent temperature profile that modifies the index profile of the fiber. A severe consequence of this thermally-induced index change is the effect of transverse mode instability (TMI), which suddenly occurs once a certain average output power is reached (i.e., the TMI threshold (PTMI)) [10]. TMI is characterized by beam fluctuations that render the laser radiation ineffective for applications.
TMI requires the propagation of a fundamental mode (FM) and (at least one) HOM in the fiber core. These modes interfere, giving rise to a quasi-periodic modal interference pattern (MIP) [11]. This MIP gets imprinted in the inversion profile and gives rise to a heat load that mimics it. Subsequently, the thermally-induced change of the refractive index profile leads to a quasi-periodic, thermally-induced refractive index grating (RIG) [12]. Previous studies have revealed that a shift between the MIP optical phase and RIG is required to induce energy transfer between the fundamental mode (FM) and the higher-order modes (HOMs) [13–16].
Numerous mitigation strategies for TMI have been proposed in the last few years, exploiting the knowledge gained about the physical origin of this effect [17]. Most of these strategies act upon the MIP and/or the RIG. In particular, one of these strategies required the modulation of the pump power to weaken the RIG [18]. What made this mitigation strategy particularly noteworthy is that it was reported that the magnitude and the sign of the phase shift (i.e., the sign that determines the relative position of the MIP/RIG maxima along the fiber) could be periodically controlled with the pump modulation [19]. In this way, periodic energy transfer regions are induced during the pump modulation cycle resulting in temporal intervals of dominant FM and other intervals with dominant HOMs. This observation paved the way for a completely new family of TMI mitigation strategies based on controlling the phase shift between the MIP and the RIG. Based upon this vital report, a subsequent theoretical study proposed a novel TMI mitigation scheme that controls the sign of the phase shift by modulating the heat load in a fiber laser system. This was achieved by operating in burst regime [20]. Recently, we have demonstrated the first experimental realization of this theoretical study [21,22].
In this work we significantly expand upon that first experimental report in Refs. [21,22] and systematically study different schemes to achieve TMI mitigation via heat-load modulation in a fiber laser system. Moreover, the physical and technical limitations of this technique as well as the optimum modulation parameters are systematically explored. This approach always allows operating with dominant FM at an average output power significantly higher than the TMI threshold. It is important to mention that all these schemes are, in one way or another, pulsed or, more accurately, quasi-continuous. From now on, we will refer to these long output signal pulses as bursts. It will be shown that the intra-burst peak power can be several times higher than the TMI threshold, which could be attractive for various quasi-continuous wave applications [23,24]. From the implementation viewpoint, this new technique can easily be incorporated into existing systems.
This paper is organized as follows: Section 2 explains the theoretical background of controlling the sign of the phase shift. In section 3, the experimental setup is described. In section 4, the different technical embodiments of heat-load modulation are explained. Additionally, the results of the heat-load modulation are introduced, which are mainly compared in four different operating regimes (i.e., free-running system, pulsed seed operating regime (PSOR), pulsed pump operating regime (PPOR), and pulsed seed and pump operating regime (PSPOR)). Finally, the results interpretation and potential impact will be discussed in section 5.
2. Theoretical background
2.1 Sign of the phase shift
In order to illustrate the meaning of the phase shift sign, Fig. 1 shows a schematic representation of the periodic profiles of the MIP and RIG along the fiber. If we now consider a situation when a sudden pump/temperature increase occurs in the fiber, a significant upstream movement of the MIP profile (i.e., more exactly a compression) will be observed. This movement is the result from the change in the temperature profile leading to a local compression of the beat length (more explanation on this effect, see section 2.2). Additionally, the maxima of the MIP towards the end of the fiber are strongly shifted due to the accumulated change of all beat lengths over the whole fiber length. Due to the slow thermal response, the thermal RIG always lags the optical MIP, thus leading to a positive phase shift. If now we consider a decrease of the pump/temperature in the fiber, the opposite will occur. The MIP will be stretched, leading to a negative phase shift with respect to the RIG.
Fig. 1. Schematic representation of the MIP periodic profile (red curve) compared to the RIG (green curve) for different relative phase shifts. The green arrows between the simulated transversal modes show the direction of the energy transfer. This figure is adapted from the Ref. [20].
If the MIP and RIG are in phase (Fig.1a), then there is no net energy transfer per grating period between the fiber modes. However, if their relative phase shift is lower than π radians (Fig.1b) (i.e., positive phase shift, meaning that the MIP is shifted upstream of the fiber with respect to the RIG), the HOM power is transferred to the FM, as schematically shown on the right-hand side of Fig. 1(b). In the case of a phase shift larger than π radians (Fig. 1(d)) (i.e., negative phase shift or, in other words, the MIP is shifted towards the fiber output with respect to the RIG), the FM power content is transferred to the HOMs. If the phase shift is exactly π radians, as represented in Fig. 1(c), then no net energy transfer per grating period is allowed. Therefore, the phase shift influences the amount of modal energy transfer in the fiber. It can be said that the TMI dynamics are shaped by the grating strength, the temporal evolution of the phase shift, and its magnitude along the fiber amplifier. In other words, the phase shift sign controls the direction of the modal energy transfer.
2.2 Operating principle
As previously, the pulsed seed operating regime (PSOR) was proposed to induce dominant FM operation via sustaining a positive phase shift between the MIP and the RIG [20]. The idea is that when the seed pulse (schematically represented by the red curve in Fig. 2(a)) with a few hundred microseconds pulse width is launched in a fiber amplifier with a CW pump (green curve), there is a sudden increase in the temperature. This increases the difference between the effective modal indices of the FM and the HOMs and, thus, reduces the modal beat length. Consequently, the MIP profile undergoes a compression that causes an upstream movement of the MIP profile with respect to the RIG (Fig. 1(b)) [15]. Due to the slow thermal response of the fiber (and, therefore, of the RIG), this movement will be transferred to the RIG profile with a delay, which gives rise to a positive phase shift between the MIP and the RIG. As explained in Fig.1b, in this situation, the energy will flow from the HOMs to the FM.
Fig. 2. Schematic representation of technical approaches for the heat-load Modulation. a) Pulsed seed operating regime (PSOR). b) Pulsed pump operating regime (PPOR). c) Pulsed seed and pump operating regime (PSPOR).
Following the temperature increase, the phase shift value will keep increasing until it reaches the π value (Fig. 1(c)) when the modal energy transfer stops. If the temperature keeps rising, the accumulated movement of the MIP profile along the amplifier will lead to the phase shift becoming larger than π, which reverses the direction of energy transfer and results in energy flowing from the FM to the HOMs (Fig. 1(d)). To prevent this reversal of the modal energy transfer from happening, the seed bursts should stop at a time point before the onset of negative phase shift. This can be done by choosing a suitable duty cycle and frequency for the burst signal. At this point, it should be stressed that it is key to let the fiber cool down (by reducing the heat load) for this approach to work. This happens in the off-time interval (i.e., the time between signal bursts), which allows the temperature to sink when there is no signal amplification. This way, the temperature can rise again when the next signal burst arrives, leading, again, to a positive phase shift.
As mentioned above, the pulsed seed operating regime (PSOR) was originally proposed in [20] as a technical approach to modulate the heat load. However, it is worth noting that heat-load modulation can also be obtained with a pulsed pump operating regime (PPOR) or with a pulsed seed and pump operating regime (PSPOR). Figure 2(b) shows a schematic representation of the PPOR where the input seed signal is CW (red curve), and the pump is modulated (green curve) with a specific duty cycle and modulation frequency. Similarly, Fig. 2(c) shows the PSPOR where the input seed and pump have a synchronized modulation. These different operating regimes give flexibility to the user to implement a suitable operating regime into an existing system.
Overall, the bottom line of all these techniques is that by pulsing the seed and/or the pump radiation with specific modulation parameters, a dominant FM operation is enforced above the TMI threshold by inducing a permanent positive phase shift between the MIP and the RIG. However, it is noteworthy that this approach differs from the pump modulation technique mentioned above [18,19]. The TMI threshold is increased via weakening the RIG in the pump modulation. In contrast, this approach achieves the TMI increase by controlling the phase shift between the MIP and the RIG. The main tangible difference between these two approaches is that, whereas in the pump modulation technique, there are always (brief) moments in which the output is dominated by the HOMs, in this technique, the output beam is always dominated by the FM. For example, we have used this technique in a system- with a 228W free-running TMI threshold, which can be forced to operate at an average output power of 416W with an intra-burst average power of 946 W in a dominant FM operation.
3. Experimental setup
In order to test the technique of heat-load modulation, a free-running fiber amplification process (i.e., CW seed and CW pump operation) is set up and compared to the pulsed operating regimes under the same operating conditions (i.e., similar input seed and output signal powers). In our setup, shown in Fig. 3, a ytterbium-doped large-pitch fiber (LPF) is employed as the main amplifier with a length of 1.1 meters, an active core diameter of ∼ 68 µm, and a hole-to-hole distance (i.e., pitch) of 37 µm [5,6]. Stretched femtosecond seed pulses (of wavelength 1030 nm, 7 nm spectral bandwidth at 3 dB, ∼1 ns pulse duration at 20 MHz repetition rate) are amplified along the LPF, which is pumped at 975 nm in the counter-propagating direction by a low brightness diode laser. Different average input seed powers are used during the experiments varying from 2W to 6.5W, which results in a change of the TMI threshold (in the free-running system) from 200 W to 228 W, respectively, due to the gain saturation [25].The 4QPD characterization method is used to measure the TMI threshold and the frequency of the TMI fluctuations [26]. The frequency for this fiber is measured at 300 Hz. Additionally, a low-speed camera (LSC) records the near-field image of the emitted beam profile at 40 frames per second, and a high-speed camera (HSC) with a 20 µm pixel size is also used to record intensity frames of the near-field image of the beam. These frames are 128 × 128 pixels and are measured with 105 frames per second (i.e., 10 µs temporal resolution). The HSC videos are presented in the following sections by slowing them down to 25 frames per second. A slow thermal power meter is employed to measure the average output power and to calibrate the signal photodiode (output signal PtD), which measures the instantaneous power.
Fig. 3. Setup used for the experiments. AOM: acousto-optic modulator. BS: beam splitter. DC: dichroic mirror. BD: beam dump. LD: laser diode. PtD: photodiode. HSC: high-speed camera. 4QPD: 4-quadrant photodiode. PM: power meter. LSC: low-speed camera. LPF: large-pitch fiber. AWG: arbitrary wave function generator.
An acoustic-optic modulator (AOM) is introduced in the seed optical path to generate the input seed bursts with flexible modulation parameters. It should be noted that such a seed modulation can also be achieved by modulating the pump of the pre-amplifier system. In all the experiments described in this work, a modulation depth of 100% is maintained to cool down the system in off-time intervals. Moreover, the modulation frequency and the duty cycle will be adjusted to the experimental requirements, as described in the results section. The AOM driver is controlled by a modulating signal produced by an arbitrary wave function generator. The modulated optical signals at the input and output of the fiber are measured with photodiodes (PtD) connected to a 12-bit oscilloscope with a sampling rate of 107 samples/s. Figure 3 also shows that our experimental setup offers the possibility of modulating the pump and even synchronizing this modulation to that of the seed. This can be achieved because both modulation signals (for the seed and pump) are generated by the same AWG.
The modal content of the output beam is characterized using the HSC. Every frame represents a coherent superposition of the fiber modes at a particular power level and time point. These frames, recorded with a temporal resolution of 10 µs, are fed to an intensity-based modal reconstruction algorithm to retrieve the temporal evolution of the instantaneous output modal power (and phase) of the decomposed FM and HOMs [27]. This modal reconstruction process is similar to the one presented in Ref. [19]. Please note that the reconstruction process is not carried out in the off-time intervals (i.e., the instantaneous power is less than 10% of the maximum instantaneous power) since there is an insufficient intensity to be analyzed as depicted in Visualization 1, which shows the modal content analysis of a PPOR example - more explanation in section 4.2- at an average output power of 416W.
4. Results
4.1 Operating regimes for heat-load modulation
Figure 4(a) shows the modulated signals in PSOR with a modulation frequency of 1.5 kHz, 100% modulation depth, and 48% duty cycle. The blue/red curves represent the modulated optical input/output signal. Hereby the rising edge of the input seed is shaped to avoid the high power spikes predicted in Ref. [20]. The red curve shows a noticeable reshaping of the output signal burst due to gain saturation. Under these modulation parameters, a stable beam is observed both with the LSC and the HSC (Visualization 2) at an average output power of ∼245 W and an average input seed power of 2 W. This is 23% higher than the TMI threshold (i.e., PTMI ∼ 200 W). Additionally, the intra-burst power of ∼520 W is ∼2.6 times higher than the free-running TMI threshold. Please note that the intra-burst power in all the analyses is defined as the mean value of the integrated instantaneous power when it exceeds 90% of the maximum peak power. The inset in Fig. 4(a) shows a beam profile extracted from the HSC video in the lower part of Visualization 2. This media file shows LSC and HSC videos comparing the free-running system at an average power level of 240W and PSOR at an average power level of 245W.
Fig. 4. Temporal traces of the modulated signals (bursts) in different operating regimes at a modulation frequency of 1.5 kHz and different duty cycles of the output modulated signal and different levels of the average output signal power. a) PSOR with a duty cycle of 48% and average output power of 245W. b) PPOR with a duty cycle of 42% and average output power of 330W. The Insets in a) and b) are taken from Visualization 2 and 3 respectively.
During these experiments, several challenges were found with the PSOR, which hindered the power scaling using this technique. One of the problems was parasitic lasing observed in the off-time intervals of the seed. Additionally, as could be expected, the slope efficiency in PSOR is significantly lower than that of the free-running system due to the off-time intervals of the input seed. For this reason, a reduction of around ∼ 45% in slope efficiency has been measured in this experiment. To alleviate these challenges, we switched to pulsed pump regimes (either PPOR or PSPOR).
Figure 4(b) shows an experimental example of PPOR at an average output signal power of 330 W. The black curve represents the modulated input pump whereas the red curve shows the modulated output signal with a duty cycle of 42% and a modulation frequency of 1.5 kHz. Please note that the minimum optical duty cycle of the input pump that can be obtained with our setup is 42%, limited by the maximum driving current of the pump driver (40 A). It is worth mentioning that the input seed is CW in the PPOR, which might not benefit some applications requiring a high signal contrast. For those applications reason, PSPOR should be the regime of choice.
The inset in Fig. 4(b) is taken from Visualization 3 to illustrate the impact PPOR in improving the beam quality, as it will be analyzed in the following. Please note that, for the sake of brevity, only the results of PPOR will be presented in the following since a very similar outcome was obtained using PSPOR as shown in Visualization 3 [22].
4.2 Pulsed pump operating regime (PPOR)
To study the impact of PPOR on the system performance, the temporal evolution of the output power and the reconstructed modal content should be analyzed above the free-running TMI threshold. Figure 5 shows the temporal evolution of the instantaneous output power (the upper plots) and the modal content of the output signal (the lower plots) at an average output power of 330 W in a free-running system (Fig. 5(a)) and with the PPOR (Fig. 5(b)). In this experiment, an input seed power of 2 W is used and the free-running TMI threshold is measured at an average power level of 200 W. In the free-running system measurement, the FM/HOMs (blue/red) modal content is not stable in time and evolves unpredictably. The insets in Fig. 5(a) are taken from the HSC video in the upper part of Visualization 3.
Fig. 5. Modal content analysis at an average output power of 330W.The insets are taken from the HSC videos in Visualization 3. a) Free-running system (FRS), b) PPOR with an intra-burst average power of ∼ 823 W. The modulation parameters are 1.5 kHz modulation frequency and 42% duty cycle. The green region represents a time window of ∼ 270 µs with dominant FM. The vertical arrow represents a 65% increase in the TMI threshold.
Similarly, when operating in the PPOR (Fig. 5(b)) at an average output power of 330 W, the input pump is modulated with a frequency of 1.5 kHz and a duty cycle of 42% (i.e., an on-time window of ∼270 µs). With these parameters, an intra-burst power of 823 W is measured. The lower plot of Fig. 5(b) shows that dominant FM operation is obtained over a time window of ∼270 µs (green region). Even though PPOR leads to a modulated output power, it makes the system operate at an intra-burst power of ∼ 4.1 times the free-running TMI threshold and average output power which is 65% higher than the TMI threshold of the free-running system. A stable, Gaussian beam at this power level can be seen as confirmed by the inset in Fig. 5(b), which is taken from the HSC video in the middle part of Visualization 3.
The current experiment aims at reaching the maximum average output power with a diffraction-limited beam profile using PPOR by carefully adjusting the modulation parameters in our setup. The maximum input average seed power of 6.5 W is used to allow for efficient amplification and to eliminate the reduction of the TMI threshold due to the low seed input power. Under these circumstances, the TMI threshold of the free-running system is increased to 228 W. The input pump is modulated with a frequency of 1.5 kHz, a duty cycle of 44% (i.e., an on-time window of 300 µs), and a modulation depth of 100%. As discussed in the impact of the duty cycle, a shorter duty cycle is vital to increase the TMI threshold with significantly higher intra-burst power.
Figure 6 shows the modal reconstruction analysis of the modulated output signal at an average output power of 416 W, which corresponds to an intra-burst power of 946 W. In the lower plot, it can be seen that the dominant FM operation is obtained over a time window of ∼250 µs (green region). After this temporal window, it can be seen that the HOMs content in the last ∼50 µs of the duty cycle increases significantly, as depicted by the red region. This HOMs increase is ascribed to the onset of a negative phase shift after 250 µs. Indeed, this significant increase in HOMs content can be potentially mitigated by shortening the duty cycle of the modulated signal. Unfortunately, current technical limitations in our setup limit the minimum duty cycle to 44% at this power level.
Fig. 6. Modal content analysis for PPOR at an average output power of 416 W with an intra-burst peak power of 946 W. The modulation parameters are 1.5 kHz modulation frequency and 44% duty cycle. The green and red regions represent the dominant FM and HOMs regions, respectively. The insets are taken from the HSC video in Visualization 4.
Even though the system operates at an average output power of 416 W (∼83% higher than the free-running TMI threshold), the beam profile is stabilized with a dominant FM operation. Despite a significant increase of the HOMs modal content in the trailing edge of each burst, a stable beam profile can still be seen in the LSC/HSC videos over the whole operation time, as shown in Visualization 4. Under these experimental conditions, a single-mode operation is obtained at a high intra-burst average power that is ∼ 4.15 times higher than the TMI threshold of the free-running system. Other authors have recently reported an increase in the TMI threshold when modulating the pump [28,29]. However, the physical reason for this increase has not been discussed, and the TMI threshold has not been increased above 36%.
The following parts of this section investigate the effect of tweaking the modulation parameters (i.e., duty cycle and modulation frequency).
4.2.1 Impact of modulation frequency
The TMI phenomenon is a thermal problem that depends on the properties of each specific amplifier system, such as the thermal diffusion time and the mode-field diameter [27,30,31]. For this reason, the optimum modulation frequency for efficient heat-load modulation is ultimately determined by the fiber design and the experimental conditions. For example, when the active core diameter increases, we expect a lower optimum modulation frequency due to the longer thermal diffusion time. To verify the effect of this parameter, a frequency scan is performed in PPOR while fixing other system parameters (such as a duty cycle of 47%, input seed power of 2 W, and average output power of 330 W). Please note that, due to the use of a lower average seed power of 2 W, a reduction of ∼ 12% in the free-running TMI threshold with respect to that reported in the previous experiment is observed (i.e., PTMI ∼ 200 W). Under these experimental conditions, the modulation frequency is scanned from 500 Hz to 2.5 kHz with a 100 Hz step. Then the corresponding instantaneous intra-burst power and reconstructed modal content are analyzed. Figure 7 shows the modal reconstruction analysis for three modulation frequencies: at 700 Hz (Fig. 7(a)), 1.5 kHz (Fig. 7(b)), and 2.5 kHz (Fig. 7(c)). In the modulation frequency of 700 Hz, the on-time interval is ∼ 670 µs. It can be seen that, in each burst, dominant FM operation can be obtained within a time window of ∼ 320 µs before the onset of the negative phase shift interval. Indeed, the long on-time window at 700 Hz induces a negative phase shift interval after about 320 µs, as clearly shown by the HOMs rise in the second half of the duty cycle in the lower plot of Fig. 7(a). Figure 7(b) shows a similar analysis with a modulation frequency of 1.5 kHz corresponding to an on-time window of ∼ 310 µs for the same duty cycle of 47%. In this situation, the induced on-time window is shorter than the negative phase shift time window, so the whole-time window consists of dominant FM operation. Finally, in the case of the 2.5 kHz modulation frequency (Fig. 7(c)), even though the on-time window is shorter than the required time window for dominant FM, the off-time interval is not long enough to allow the system to cool down properly. For this reason, a positive phase shift for each pulse cannot be guaranteed. In other words, there is thermal crosstalk between consecutive bursts in the case of 2.5 kHz modulation frequency, as can be clearly seen in Fig.7c.
Fig. 7. Modal content analysis in PPOR at different modulation frequencies a) 700 Hz. b) 1.5 kHz. c) 2.5 kHz) for a fixed duty cycle of 47% and average output power of 330 W.
Based on the findings in Fig. 7, it can be concluded that there is a specific frequency range within which a dominant FM operation (i.e., a stable beam profile) can be obtained. For this reason, the reconstructed modal content is analyzed over the whole frequency scan range from 500 Hz to 2.5 kHz, as shown in Fig. 8. This analysis describes the evolution of the integrated average modal content (y-axis on the left hand) during the on-time intervals (in a 3 ms time window) for FM (blue curve) and HOMs (red curve) with increasing modulation frequency. Additionally, the y-axis on the right hand represents the intra-burst average power of the fundamental mode. Please note that the calculation of the intra-burst average power is performed only when the instantaneous power exceeds 50% of the maximum power. As can be seen, there is significant HOMs content (i.e., higher than 15% of the total power) in the frequency range below 1.3 kHz and above 2 kHz.
Fig. 8. Frequency scan in PPOR for a fixed duty cycle of 47% and for an average output power of 330 W.
Interestingly, an optimum modulation frequency window is found ranging from ∼ 1.3 kHz to ∼2 kHz within which a dominant FM is obtained. Strictly speaking, at this power level (i.e., Pout =330 W), there is a tolerance of around 700 Hz in the frequency range that can be applied to obtain single-mode operation. Indeed, the central frequency and width of this optimum region will depend on other system parameters (for example, on the output power and the duty cycle).
4.2.1 Impact of the duty cycle
The duty cycle is expected to be essential in sustaining the positive phase-shift condition at higher average output powers. In order to investigate this effect, measurements are carried out aimed at determining the integrated modal content as a function of the duty cycle. At the same time, all other operational parameters are fixed (i.e., modulation frequency 1.5 kHz, 2 W input seed, and 330 W output signal power). Figure 9 shows the modal content analysis at different duty cycles of 55% (Fig. 9(a)), 77% (Fig. 9(b)), and 80% (Fig. 9(a)). It is clear that with the duty cycle of 55%, the system exhibits dominant FM operation. On the contrary, at the duty cycle of 77% and 80%, the system undergoes a dynamic modal energy transfer in its on-time intervals. This energy transfer happens because the on-time window is long enough to induce a negative phase shift between the MIP and the RIG.
Fig. 9. Different duty cycles (a) 55%, b) 77%, and c) 80% at a modulation frequency of 1.5 kHz and average output power of 330 W.
A further duty-cycle scan is performed under these experimental conditions to investigate the tolerance of the mitigation strategy to the duty cycle. Figure 10 shows the integrated modal content as a function of the duty cycle. It can be observed that dominant FM operation is obtained at an average output power of 330 W as long as the duty cycle is below ∼75%. In other words, up to around 500 µs on-time window, dominant FM operation can be obtained at this power level.
Fig. 10. Duty cycle scan for PPOR at a fixed modulation frequency of 1.5 kHz and average output power of 330 W.
5. Discussion and conclusion
With these systematic experimental measurements, we have reported the mitigation of TMI via heat-load modulation at average output powers significantly higher than the free-running TMI threshold. This technique induces a permanent positive phase shift between the RIG and the MIP, forcing the energy to flow from the HOMs to the FM. This results in a stable, nearly pure FM emission (seen both with the LSC and the HSC). This is in contrast to the pump modulation technique reported elsewhere [18,19], where the TMI threshold is increased via weakening the RIG in the pump modulation. The main tangible difference between these two approaches is that, whereas in the pump modulation technique, there are always (brief) moments in which the output is dominated by the HOM, in this technique, the output beam is always dominated by the FM.
The control over the phase shift is experimentally realized by temporally modulating the heat load in the fiber amplifier with carefully chosen modulation parameters. Hereby it is possible to achieve this heat load modulation by pulsing the seed (PSOR), the pump (PPOR), or both simultaneously (PSPOR). Our experiments confirm the expectations raised by the previous theoretical study of this new mitigation strategy [20].
Achieving heat-load modulation via PSOR is easy, but it has some drawbacks (i.e., efficiency drop and possible parasitic lasing) that limit its performance. Furthermore, the existence of pump radiation in the off-time intervals might lead to photodarkening [32,33]. It becomes patent that this situation can be improved considerably by pulsing the pump (i.e., PPOR) and/or by synchronizing the pump duty cycle with the seed duty cycle (i.e., PSPOR).
This study proved that the modulation parameters play a central role in determining the sign of the phase shift and, hence, the stability of the output beam profile. The tolerance to these parameters depends on the system's thermal properties, the input seed power, the peak power of the burst, and the output signal average power. This work explores this tolerance to these parameters and shows that the tolerance range decreases with higher output average powers. For example, in the current amplifier system, it has been shown that an on-time window shorter than ∼310 µs and an off-time interval longer than 350 µs are required to operate the system at an average output power higher than 330 W with dominant FM operation. Meanwhile, this on-time window should be shorter than 250 µs when operating at a power level higher than 416 W.
In summary, this work presents the experimental realization and systematic investigation of a new mitigation strategy for TMI dynamics. This strategy controls the phase shift between the RIG and the MIP. Hereby, heat load modulation under specific parameters is exploited to achieve a positive phase shift between the RIG and the MIP. The technique is easy to implement in an already existing setup. Using this technique, it was possible to obtain a system operating with dominant FM at an average power of 416 W and intra-burst power very close to 1 kW, which represents an increase of ∼83% with respect to the free-running TMI threshold of 228 W.
Funding
Deutsche Forschungsgemeinschaft (416342637, 416342891); Fraunhofer-Gesellschaft.
Disclosures
We confirm that this manuscript has not been previously published and is not currently being considered by another journal, and we have no conflicts of interest to disclose. We have published a closely related conference paper entitled “Mitigation of transverse mode instability by heat load modulation in high-power fiber laser amplifiers” in the photonics west conference proceedings in 2022, paper number: 1198 10Z. Moreover, we have presented a poster entitled “The impact of heat-load modulation on transverse mode instability in high-power, quasi-continuous wave fiber amplifiers” in the Europhoton conference in 2022.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013). [CrossRef]
2. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives [Invited],” J. Opt. Soc. Am. B 27(11), B63 (2010). [CrossRef]
3. M. N. Zervas and C. A. Codemard, “High power fiber lasers: A review,” IEEE J. Sel. Top. Quantum Electron. 20(5), 219–241 (2014). [CrossRef]
4. Y. Jeong, J. K. Sahu, D. N. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1 kW continuous-wave output power,” Opt. Express 40(8), 470 (2004). [CrossRef]
5. F. Stutzki, F. Jansen, H.-J. Otto, C. Jauregui, J. Limpert, and A. Tünnermann, “Designing advanced very-large-mode-area fibers for power scaling of fiber-laser systems,” Optica 1(4), 233 (2014). [CrossRef]
6. J. Limpert, F. Stutzki, F. Jansen, H. J. Otto, T. Eidam, C. Jauregui, and A. Tünnermann, “Yb-doped large-pitch fibres: Effective single-mode operation based on higher-order mode delocalisation,” Light: Sci. Appl. 1(4), e8 (2012). [CrossRef]
7. A. Benoît, R. Dauliat, R. Jamier, G. Humbert, S. Grimm, K. Schuster, F. Salin, and P. Roy, “Highly efficient higher-order modes filtering into aperiodic very large mode area fibers for single-mode propagation,” Opt. Lett. 39(15), 4561 (2014). [CrossRef]
8. M. K. Davis, M. J. F. Digonnet, and R. H. Pantell, “Thermal effects in doped fibers,” J. Lightwave Technol. 16(6), 1013–1023 (1998). [CrossRef]
9. D. C. Brown and H. J. Hoffman, “Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers,” IEEE J. Quantum Electron. 37(2), 207–217 (2001). [CrossRef]
10. T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express 19(14), 13218 (2011). [CrossRef]
11. C. Jauregui, J. Eidam, J. Limpert, and A. Tünnermann, “Impact of modal interference on the output beam properties of large-core cladding-pumped fiber amplifiers,” Opt. Express 19(4), 3258–3271 (2011). [CrossRef]
12. C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Temperature-induced index gratings and their impact on mode instabilities in high-power fiber laser systems,” Opt. Express 20(1), 440 (2012). [CrossRef]
13. A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifier,” Opt. Express 19(12), 11318 (2011). [CrossRef]
14. B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express 20(10), 11407 (2012). [CrossRef]
15. C. Stihler, C. Jauregui, A. Tünnermann, and J. Limpert, “Phase-shift evolution of the thermally-induced refractive index grating in high-power fiber laser systems induced by pump-power variations,” Opt. Express 26(15), 19489 (2018). [CrossRef]
16. C. Stihler, C. Jauregui, S. E. Kholaif, and J. Limpert, “Intensity noise as a driver for transverse mode instability in fiber amplifiers,” PhotoniX 1(1), 8–17 (2020). [CrossRef]
17. C. Jauregui, C. Stihler, and J. Limpert, “Transverse mode instability,” Adv. Opt. Photonics 12(2), 429 (2020). [CrossRef]
18. C. Jauregui, C. Stihler, A. Tünnermann, and J. Limpert, “Pump-modulation-induced beam stabilization in high-power fiber laser systems above the mode instability threshold,” Opt. Express 26(8), 10691 (2018). [CrossRef]
19. C. Stihler, C. Jauregui, A. Tünnermann, and J. Limpert, “Modal energy transfer by thermally induced refractive index gratings in Yb-doped fibers,” Light: Sci. Appl. 7(1), 59 (2018). [CrossRef]
20. C. Jauregui-Misas, C. Stihler, J. Limpert, and A. Tünnermann, “Transverse mode instabilities in burst operation of high-power fiber laser systems,” Proc. SPIE, Fiber Lasers XV 10512, 6–32 (2018). [CrossRef]
21. S. E. Kholaif, C. Jáuregui-Misas, Y. Tu, and J. Limpert, “Mitigation of transverse mode instability by heat load modulation in high-power fiber laser amplifiers,” Proc. SPIE 11981, Fiber Lasers XIX Technol. Syst. 119810Z, 57 (2022).
22. S. Kholaif, C. Jauregui, Y. Tu, and J. Limpert, “The impact of heat-load modulation on transverse mode instability in high-power, quasi-continuous wave fibre amplifiers,” EPJ Web Conf. 267, 01027 (2022). [CrossRef]
23. N. P. Long, H. Daido, T. Yamada, A. Nishimura, N. Hasegawa, and T. Kawachi, “Experimental characterization of concrete removal by high-power quasicontinuous wave fiber laser irradiation,” J. Laser Appl. 29(4), 041501 (2017). [CrossRef]
24. Marco Mendes, “Fiber laser micromachining in high-volume manufacturing,” Ind. Laser Solut. l, (2015).
25. R. Tao, X. Wang, P. Zhou, and Z. Liu, “Seed power dependence of mode instabilities in high-power fiber amplifiers,” J. Opt. 19(6), 065202 (2017). [CrossRef]
26. S. Kholaif, C. Jauregui, Y. Tu, and J. Limpert, “Characterization of Transverse Mode Instability with a 4-Quadrant Photodiode,” Opt. Express 31(6), 10633–10644 (2023). [CrossRef]
27. F. Stutzki, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36(23), 4572 (2011). [CrossRef]
28. Z. Hong, Y. Wan, X. Xi, H. Zhang, X. Wang, and X. Xu, “High-peak-power pump-modulated quasi-CW fiber laser,” Appl. Opt. 61(7), 1826–1833 (2022). [CrossRef]
29. J. Chai, W. Liu, X. Wang, Q. Zhou, J. Zhang, H. Zhang, P. Liu, Y. Lu, D. Zhang, Z. Jiang, and G. Zhao, “Influence of Pump Current Waveform on The Mitigation of Transverse Mode Instability in Fiber Laser Oscillator,” (2023). [CrossRef]
30. H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnermann, “Temporal dynamics of mode instabilities in high-power fiber lasers and amplifiers,” Opt. Express 20(14), 15710 (2012). [CrossRef]
31. N. Haarlammert, O. de Vries, A. Liem, A. Kliner, T. Peschel, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Build up and decay of mode instability in a high power fiber amplifier,” Opt. Express 20(12), 13274 (2012). [CrossRef]
32. A. D. Guzman Chávez, A. V. Kir’yanov, Y. O. Barmenkov, and N. N. Il’ichev, “Reversible photo-darkening and resonant photobleaching of Ytterbium- doped silica fiber at in-core 977-nm and 543-nm irradiation,” Laser Phys. Lett. 4(10), 734–739 (2007). [CrossRef]
33. S. Jetschke, S. Unger, U. Röpke, and J. Kirchhof, “Photodarkening in Yb doped fibers: experimental evidence of equilibrium states depending on the pump power,” Opt. Express 15(22), 14838 (2007). [CrossRef]
