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Abstract
In this work we present a novel way to manipulate the effect of transverse mode instability by inducing traveling waves in a high-power fiber system. What sets this technique apart is the fact that it allows controlling the direction of the modal energy flow, for the first time to the best of our knowledge. Thus, using the method proposed in this work it will be possible to transfer energy from the higher-order mode into the fundamental mode of the fiber, which mitigates the effect of transverse mode instability, but also to transfer energy from the fundamental mode into the higher-order mode. Our simulations indicate that this approach will work both below and above the threshold of transverse mode instability. In fact, our model reveals that it can be used to force a nearly pure fundamental mode output in the fiber laser system almost independently of the input coupling conditions. In this context, this technique represents the first attempt to exploit the physics behind the effect of transverse mode instability to increase the performance of fiber laser systems.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fiber laser systems have become essential tools in many applications in industry, medicine, or fundamental science, just to mention a few. This is because such systems are characterized by hands-off operation, low maintenance costs, high-power and diffraction-limited beam quality [1–3]. Specially the combination of the last two characteristics, high power and excellent beam quality, has contributed to the rapid growth in popularity of this technology. However, in 2010 the effect of transverse mode instability (TMI) was discovered, which still threatens the reputation of single-core fiber lasers and amplifiers as power-scalable systems [4,5]. The effect of TMI results in a formerly stable, nearly-diffraction-limited beam emitted by a fiber laser system to break up and fluctuate once that a certain average power threshold has been reached [6]. This renders the output of these systems ineffective for most applications.
In this context, it can be understood that the effect of TMI represents the biggest challenge for the further development of fiber laser technology. Given the importance of this topic, it is unsurprising that many researchers worldwide started studying the physical origin of TMI [7–13], which has led to a rapid understanding of this effect. Currently it is generally accepted by the scientific community that the effect of TMI is originated by the presence of a modal interference pattern (MIP) in the fiber core which, through the thermo-optical effect, induces a refractive index grating (RIG) that is able to couple energy between different transverse modes of the fiber [6]. In fact, it has been shown that the beam fluctuations characteristic of TMI are a manifestation of an unstable energy transfer between different transverse modes of the fiber [14]. However, the presence of a thermally induced refractive index grating alone is not enough to get energy transfer between the modes of a fiber. As originally pointed out in [8], an additional condition is required: a phase shift between the MIP and the RIG. Indeed this phase shift is a crucial ingredient for TMI and its sign, as it has been experimentally demonstrated recently [15,16], determines the direction of the energy flow: i.e. from the fundamental mode (FM) towards the higher-order modes (HOM) or the other way around. This knowledge has been recently used, for example, to experimentally determine that pump noise is the most likely driver of TMI in high power fiber laser systems [17].
Due to the wide-reaching impact of TMI on fiber laser technology, mitigation strategies for this effect have been continuously searched for. Over the years plenty of such strategies have been proposed and demonstrated (see e.g. [18–25]). What all these “classic” strategies have in common is that they try to weaken either the MIP or the RIG. However, recently a new family of mitigation strategies that acts upon the phase shift has been proposed [6,26]. These new techniques have the potential to transcend the limitations of classic TMI mitigation strategies by exploiting the physics behind TMI to enhance the performance of fiber laser systems.
In this work we theoretically propose a technique that belongs to the family of mitigation strategies acting upon the phase shift. This is achieved by injecting traveling waves in a fiber amplifier to generate a permanent positive or negative phase shift (as defined in [15]) between the MIP and the RIG. In this context, this technique is more than just a mitigation strategy for TMI since, as it will be shown, it will allow controlling the direction of the modal energy transfer. Thus, among other things, it should be possible to obtain a nearly perfect FM output beam almost independently of the excitation conditions of a few-mode fiber using this technique. In this respect, this method can be considered as the first proposal to exploit the physical principles behind TMI.
This paper is organized as follows: in section 2 the operating principle together with a possible experimental implementation will be described; in section 3 the results of the simulations for several operation conditions (different pump configurations above and below the threshold, different excitation conditions of the fiber, etc) will be presented and discussed. Finally, some conclusions will be drawn.
2. Operating principle
As it has been theoretically and experimentally shown [9,15–17], the sign of the phase shift between the modal interference pattern and the thermally-induced refractive index grating determines the direction of the energy transfer among the transverse modes of the fiber. This is schematically illustrated in Fig. 1, where the RIG is represented by the periodically spaced blue squares and the MIP is represented by the dashed red sinusoidal line. When these two elements are aligned, as in Fig. 1(a), then the phase shift is 0 and there is no energy transfer between the transverse modes of the fiber. On the contrary, if the MIP and the RIG are not aligned, there will be energy transfer between the FM and the HOM. In the case of a negative phase shift, i.e. in the case when the MIP is more shifted towards the fiber output end than the RIG, as illustrated in Fig. 1(b), the energy flows from the FM to the HOM. This is the process that causes beam degradation during TMI. On the other hand, if the phase shift is positive, i.e. if the MIP is more shifted towards the seed end of the fiber than the RIG, as illustrated in Fig. 1(c), the energy will flow from the HOM towards the FM. This will result in beam cleaning at the output of the fiber. All these processes, i.e. the beam degradation and the beam cleaning as a function of the phase shift, have been recently verified experimentally [15] both above and below the TMI threshold.
Fig. 1. Schematic illustration of the dependence of the direction of energy transfer between the FM and a HOM on the sign of the phase shift between the thermally-induced index grating (blue rectangles) and the interference intensity pattern (dashed red sinusoidal line). a) if the phase shift is zero, then there is no energy transfer between the modes; b) if the phase shift is negative (i.e. the modal intensity pattern is shifted downstream the fiber) the energy will flow from the FM to the HOM; c) if the phase shift is positive (i.e. the modal intensity pattern is shifted upstream the fiber) the energy will flow from the HOM towards the FM.
The schematic illustration in Fig. 1 also shows the basic idea behind the family of TMI mitigation strategies that operate upon the phase shift: to generate and sustain a positive phase shift (see Fig. 1(c)) between the MIP and the RIG to obtain a pure FM at the output of the fiber. Crucially, unlike in other families of mitigation techniques, the focus is not set in weakening the RIG or the MIP, but on exploiting their interplay to constantly transfer energy to the FM of the fiber. This way it should be possible to obtain diffraction-limited beam quality emission almost regardless of the excitation conditions of the fiber. At the same time, these methods, with the ability to clean the output beam by transferring energy from the HOM to the FM, can potentially contribute to relax the stringent limitations currently imposed on the numerical aperture of the core of large mode area fibers to obtain single-mode operation. As a consequence, these techniques should be able to help increasing the core size of fiber laser systems with diffraction-limited beam quality.
Interestingly, since the RIG is constantly evolving to adapt itself to the heat load created by the MIP [8,27], a phase shift means that the RIG will dynamically change while trying to catch the MIP, as recently shown in [16]. Below the TMI threshold, the RIG can catch the MIP, i.e. the phase shift is reduced to zero, and the modal energy transfer stops after a certain time. Therefore, the only way to sustain in time a phase shift is if the MIP is constantly moving in one direction, since the RIG will try to follow it but will lag behind due to the finite thermal response of the fiber [16]. This can be achieved either by burst operation [6,26] or by injecting a traveling wave in the amplifier, as we propose in this work. Such a traveling wave can be obtained if the FM and the HOM have slightly different central frequencies. This, which was originally introduced as one possible origin of TMI [8], is proposed here as a way to control the phase shift in fiber amplifiers.
The injection of two modes with slightly different frequencies in a fiber gives rise to a MIP that is moving at a constant speed, which depends on the frequency difference between the modes. Therefore, since the thermalization time, i.e. the speed of change of the thermal profile of a fiber, is roughly constant (for any given fiber), changing the frequency difference between the modes will lead to a different phase shift between the MIP and the RIG. Additionally, the direction of the movement of the MIP (i.e. upstream or downstream the fiber) will depend on whether the FM has a lower frequency (upstream movement) or a higher frequency (downstream movement) than the HOM. Note, however, that the optimum frequency difference between the FM and the HOM will depend on the fiber (and, most of all on its core size).
The key question is how to induce a traveling wave in a fiber laser system or, in other words, how to excite a FM and a HOM with slightly different central frequencies using a practical seed system. One conceptual approach is presented in Fig. 2. As can be seen, the light emitted by a single mode oscillator is split in two arms using a polarization beam splitter. Then, the beams in these two arms are frequency shifted using two synchronized acousto-optic modulators/frequency shifters (AOM). It is important to point out that the driving frequency of these two AOMs should be slightly different and, ideally, this frequency difference (Δf) should be tunable. This, as explained before, will allow controlling the speed of the traveling wave and, therefore, the magnitude of the phase shift in the fiber. Additionally, the sign of the frequency difference will determine the direction of movement of the MIP traveling wave and, therefore, whether the energy flows from the FM towards the HOM or the other way around.
Fig. 2. Proposed experimental setup to generate traveling waves in a fiber amplifier. AOM- acousto-optic modulator; Mode MUX- mode multiplexer; HWP- half-wave plate; PBS- polarization beam splitter; M-mirror; Amp. chain- amplifier chain.
The heart of the seed system proposed in Fig. 2 is a fiber-coupled mode multiplexer [28–30]. These devices are widely used for spatial division multiplexing in telecommunications [31,32] where different communication channels are transmitted through a single fiber multiplexed in its transverse modes. Thus, this multiplexing scheme requires a device that can selectively excite the different modes of a multimode fiber: the mode multiplexer. Usually the input of these devices is an array of single-mode fibers, each one addressing a single transverse mode of the output multimode fiber. Therefore, by controlling the power and phase of the signals injected in the input single mode fibers it will be possible to create any desired superposition of modes in the multimode output fiber. Thus, for the application proposed herein, the LP01 and the LP11 inputs will be used, each one connected to one of the beams that have been frequency shifted by the AOMs. This way, a traveling wave with fully controllable parameters will be generated in the multimode fiber at the output of the mode multiplexer. Later on, this traveling wave can be injected in a (multimode) fiber amplifier (or amplifier chain) to control TMI as it will be shown with the simulation results presented in the next section.
3. Simulation results
In this section the proposed technique will be theoretically analyzed using the model described in [24], which is a full temporally resolved 3D model of a fiber amplifier that considers thermally induced modal deformations as well as mode coupling. The fiber used in the simulations is a 1 m long rod-type fiber, with 80 µm core diameter and 228 µm pump cladding diameter. The fiber has an Yb-doping concentration of 3.25·1025 ions/m3 and it is pumped at 976 nm (small-signal pump absorption ∼44 dB/m) while being seeded with 30 W at 1030 nm. The seed power is distributed between two modes: the LP01 (from here on FM) and the LP11 (from here on HOM). To test the proposed mitigation strategy, it will be assumed that both modes have slightly different central frequencies, which will lead to the generation of a travelling wave in the amplifier. In most simulations, the FM carries 80% of the energy and the HOM has 20% of the initial energy. At this point it is important to point out that such high amount of HOM content has been chosen to clearly illustrate the strong ability of this technique not only to mitigate TMI but also to transfer energy to the FM. If we had used a more realistic value of HOM content (just a few percent) the simulation results would not have been clear enough (i.e. the changes in the modal content in our plots would not have been apparent enough). In this respect, the simulated system can be regarded as one with a very poor excitation, which will reflect in a low TMI threshold, as it will be shown in the following. The fiber will be operated both above and below the TMI threshold and with different pump configurations.
3.1. Counter-propagating pump configuration
The first set of simulations analyzes this technique in a counter-propagating pump configuration. Thus, Fig. 3 shows the simulation of the TMI threshold for the reference system described above when the FM and the HOM have the same central frequency at the fiber input, i.e. for the free-running system. As can be seen in Fig. 3(a), the system at ∼120 W is still stable (i.e. the FM power content represented by the blue line and the HOM power content represented by the red line do not fluctuate with time), but increasing the total output power (given by the black line) to ∼140 W (Fig. 3(b)) results in some isolated modal power fluctuations. The situation only gets worse when increasing the power to ∼170 W (Fig. 3(c)), where the system clearly operates above the TMI threshold and there are strong, periodic modal power fluctuations. Note that the peaks observed in the total signal power of Fig. 3(c) (black line) are a result of transverse hole burning as the beam temporally sees a higher gain when it changes its shape. To reduce the computational cost determining the TMI threshold, we will define it as the first power at which significant modal fluctuations are observed. This definition will be used throughout this work. Thus, in the case presented in Fig. 3 the TMI threshold is ∼140 W.
Fig. 3. Simulation of the TMI threshold of the free-running system, i.e. when the FM and the HOM have the same frequency and, therefore, there is no traveling wave injected in the system. The plots show the temporal evolution of the total signal power (black line), the modal content of the FM (blue line) and the modal content of the HOM (red line) at different output powers: a) ∼120 W, b) ∼140 W and c) ∼170 W.
Once that the system is seeded with a FM and a HOM that have slightly different central frequencies (in this case the FM is 500 Hz downshifted with respect to the HOM), the behavior is very different as can be seen in Fig. 4 and Fig. 5. In particular Fig. 4 shows a frame from Visualization 1, in which the evolution of the MIP (upper subplot), the inversion pattern (middle subplot) and the RIG (lower subplot) can be seen at an output power of ∼250 W (i.e. ∼1.8 times above the TMI threshold). At the beginning of Visualization 1 there is an initial phase of instabilities, which is induced by the numerical adaptation from steady state to dynamic operation. Afterwards, it can clearly be observed how the system settles to a new dynamic steady state in which the MIP constantly shifts upstream the fiber (i.e. towards the seed side, which is located to the left of the plots), signifying that it is a traveling wave. Additionally, it can be seen that the inversion pattern is able to adapt itself almost immediately and replicate the movement of the MIP, but the RIG can only follow with a certain delay. This delay leads to a positive phase shift that is sustained in time and results in a permanent energy flow from the HOM to the FM. This, in turn, is translated in the progressive beam cleaning that can be observed in the MIP towards the end of the fiber in Fig. 4 and in Fig. 5(b) (where nearly all the energy is contained in the FM after a few ms). This beam cleaning can be clearly observed by comparing the temporal evolution of the output beam in Visualization 2 (free-running system) and in Visualization 3 (system with the traveling wave). Inducing a traveling wave in the system also leads to a smoother temporal evolution of the output power (black lines in Fig. 5). In fact, when operating above the TMI threshold, the free running system exhibits some short spikes in the output power (see black line in Fig. 5(b)). They usually happen when the HOM becomes dominant since it has access to regions of undepleted inversion in the core (usually those close to the core-cladding interface). Thus, these output power fluctuations are a direct consequence of the dynamic changes of the beam profile. Therefore, when TMI is mitigated (as in Fig. 5(b)), the output power fluctuations disappear as well.
Fig. 4. Frame extracted from Visualization 1. Here the temporal evolution of the MIP (upper subplot), the inversion pattern (middle subplot), and the radially anti-symmetric part of the RIG (lower subplot) can be seen for an output power of ∼250 W (with counterpropagating pump) when the FM has a frequency difference of -500 Hz with respect to the HOM.
Fig. 5. Frames of a) Visualization 2 and b) Visualization 3. These plots show the temporal evolution of the total output power (black line) the power of the FM (blue line) and the power of the HOM (red line) at an output power of ∼250 W (with a counter-propagating pump configuration): a) when the frequency difference between the FM and the HOM is 0 Hz (free-running system) and b) when the frequency difference between the FM and the HOM is -500 Hz (traveling wave). The insets show the output beam of the system at around 9.5 ms. When inducing a traveling wave a significant suppression of the TMI-related beam fluctuations can be achieved.
It is worth mentioning that the frequency difference between the FM and the HOM does not seem to require a very specific value. Our simulations with different frequencies show that the system still works e.g. with a frequency difference of -700 Hz. This is illustrated in Fig. 6 where the temporal evolution of the modal power content (FM in blue and HOM in red) is shown for an output power (black line) of ∼120W. Thus, this figure illustrates not only that there is a certain tolerance of some 100 Hz in the frequency difference between the FM and the HOM, but also that the proposed technique works below the TMI threshold (see Fig. 3(a)). In fact, as can be seen in Fig. 6, even though the system is seeded with 20% HOM, the output is clearly dominated by the FM with more than 98% of the energy concentrated in this mode. This is a key aspect of this technique since it makes it applicable to fiber laser systems to improve their beam quality even if they operate below the TMI threshold. In other words, the proposed technique is more than just a TMI mitigation strategy since it can also be used, e.g. for beam cleaning.
Fig. 6. Temporal evolution of the power content in the FM (blue line), in the HOM (red line) and of the total output power (black line). The system operates at an output power of ∼120 W using a counter-propagating pump configuration and the frequency difference between the FM and the HOM is -700 Hz. The fiber is seeded with 20% HOM content from which just 2% remain, in average, at the fiber output.
To test the limits of this technique, we have increased the pump power of the system (leaving all other parameters constant). Thus, the simulation in Fig. 7 shows the evolution of the modal powers (same colour coding as before) at ∼325 W, i.e. more than two times above the TMI threshold. As can be seen, even though there is an evident degradation of the results with respect to those shown in Fig. 5, the technique is still able to transfer most of the energy to the FM (with an average of ∼92% of the power). Nevertheless, it seems that the technique is reaching its limit. Even though this is still subject of current investigations, at this point we believe that this is a consequence of a strong longitudinal thermal gradient in the fiber with the counter-propagating pump configuration. In this situation it might happen that different sections of the fiber may require a different frequency detuning between the FM and the HOM and this disparity increases with a higher output power/longitudinal thermal gradient. Again, this point is still under investigation and, therefore, it is only a hypothesis. However, in order to test whether there is some truth behind this hypothesis or not, we have changed the pump configuration to a bi-directional one, which is known to significantly reduce the longitudinal thermal gradient in the fiber (both in lasers and amplifiers) [33,34].
Fig. 7. Temporal evolution of the power content in the FM (blue line), in the HOM (red line) and of the total output power (black line). The system operates at an output power of ∼325 W using a counter-propagating pump configuration and the frequency difference between the FM and the HOM is -500 Hz. The traveling wave still leads to a significant beam cleaning even at an average power more than 2 times above the TMI threshold.
3.2. Bidirectional pump configuration
In order to test whether the bi-directional pump configuration is able to improve on the performance of the counter-directional pump, we have repeated the high-power numerical experiment shown in Fig. 7. Thus, the system was driven at an output power of ∼325 W while pumping it bi-directionally (with the pump power being equally split between both directions). The results can be seen in Fig. 8 where, in spite of the change of pump power configuration, the free-running system is still operating clearly above the TMI threshold, as indicated by the strong fluctuations in the modal content seen in Fig. 8. However, in spite of the high power, when using a frequency detuning between the FM and the HOM of -700 Hz (Fig. 8(b)), the power flows to the FM (after a short numerically-induced unstable phase) and a near perfect diffraction-limited beam is obtained at the output of the fiber as shown in the inset. This indicates that this technique seems to operate better at high power when using a bi-directional pump configuration, at least in short rod-type fibers.
Fig. 8. Temporal evolution of the total output power (black line) the power of the FM (blue line) and the power of the HOM (red line) using a bi-directional pump configuration at an output power of ∼325 W when: a) the frequency difference between the FM and the HOM is 0 Hz (free-running system) and b) when the frequency difference between the FM and the HOM is -700 Hz (traveling wave). The inset in b) shows the output beam of the system after 16 ms.
As explained in section 2, changing the sign of the frequency difference between the FM and the HOM should lead to a change in the propagation direction of the traveling wave and, therefore, to a change in the direction of the energy flow. Therefore, if the frequency difference between the FM and the HOM is changed to 700 Hz (i.e. the FM has a higher central frequency) in the numerical experiment above (Fig. 8), it should be expected that the energy would flow to the HOM. The result of this simulation can be seen in Fig. 9. As expected, when changing the sign of the frequency difference, the energy flows to the HOM and, after a few ms a beam with, in average, more than 98% of the energy contained in the HOM is obtained at the output of the fiber. The inset in Fig. 9 shows the beam profile at the fiber output at the end of the simulation window. Therefore, this technique can also be employed to change the appearance of the output beam of a high-power fiber laser system.
Fig. 9. Temporal evolution of the power content in the FM (blue line), in the HOM (red line) and of the total output power (black line). The system operates at an output power of ∼325 W using a bi-directional pump configuration and the frequency difference between the FM and the HOM is 700 Hz. The inset shows the output beam of the system after ∼15 ms. As can be seen, in this case most of the energy is transferred to the HOM due to the sustained generation of a negative phase shift.
In order to further illustrate the strong ability of this technique to clean the output beam of fiber laser systems, we have carried out a simulation in which the seed beam of the bi-directionally pumped amplifier has 80% of the energy in the HOM. In order to transfer the energy to the FM, as already mentioned before, the frequency difference between the FM and the HOM is set to -700 Hz. As can be seen in Fig. 10, in spite of the system operating at ∼325 W, i.e. significantly above the TMI threshold of the free-running system, the proposed technique is able to successfully transfer the energy into the FM after a few ms. Thus, once the system has reached the new dynamic steady-state, the output beam has ∼98% of the energy in the FM. The insets show the output beam before (i.e. at 0 ms, on the left) and after switching the traveling wave on (i.e. at 16 ms, on the right).
Fig. 10. Temporal evolution of the power content in the FM (blue line), in the HOM (red line) and of the total output power (black line). The system operates at an output power of ∼325 W using a bi-directional pump configuration and the frequency difference between the FM and the HOM is -700 Hz. The input signal has 80% HOM content. The insets above the plot show the output beam before (left) and after switching the traveling wave on (right). Despite the poor excitation the technique is able to clean the output beam and transfer the energy to the FM.
3.3. Sensitivity to excitation conditions
Up to now we have assumed a perfect excitation of the fiber, meaning that the FM and the HOM have different central frequencies. However, in reality, it might happen that, due to misalignment for example, this condition is not met and there is some modal crosstalk due to imperfect excitation conditions. In this case there might be a certain amount of HOM at the central frequency of the FM and/or vice-versa. To illustrate the impact of this we have simulated the bi-directionally pumped system at ∼385 W when the frequency difference between the FM and the HOM is -700 Hz. In this simulation, as in most of the others, the total HOM content at the fiber input is 20%. The difference with the simulations presented in the previous subsection is that now the seed beam has a leakage of 2% HOM at the frequency of the FM (i.e. from the 20% HOM content, 2% have the same frequency as the FM and 18% a different frequency). In this case, it can be seen in Fig. 11 that the energy still flows to the FM resulting in an output beam with an average of ∼97% FM content (blue line). The main difference is that now periodic power fluctuations appear (black line) with a modulation period of 700 Hz and a peak-to-peak amplitude of ∼6%. These power fluctuations are most likely the result of the travelling wave sweeping through the quasi-static MIP (and, therefore, inversion grating) generated by the FM and the HOM at the same frequency. It is important to stress that, even though the output power oscillates periodically, the emitted beam is still nearly diffraction-limited. Besides, these power fluctuations can be, in principle, minimized by optimizing the input coupling or by modulating the pump power to compensate for them.
Fig. 11. Temporal evolution of the power content in the FM (blue line), in the HOM (red line) and of the total output power (black line) in the bi-directionally pumped system at an average output power of ∼385 W. The fiber is seeded with 80% FM and 10% HOM, whereby the frequency difference between them is -700 Hz. In order to simulate an imperfect excitation the input signal has 2% HOM content at the central frequency of the FM.
4. Conclusions
In this work we have proposed and theoretically analyzed a technique not only to mitigate TMI but to exploit the physics behind this phenomenon to improve the performance of high-power fiber amplifiers. The method proposed herein allows controlling and stabilizing the modal content of high power, few-mode fiber amplifiers both above and below the TMI threshold. This approach belongs to the family of strategies that capitalize on controlling the phase shift between the MIP and the RIG. The technique proposed in this work is based on inducing traveling waves in a few-mode fiber amplifier by injecting a FM and a HOM with slightly detuned central frequencies. Our simulations have shown that when the FM has a slightly lower frequency (several hundred Hz) with respect to the HOM, the energy is transferred from the HOM to the FM, thus resulting in a significant beam cleaning at the fiber output (even under very adverse excitation conditions). As mentioned above, it has been shown that this approach works both above and below the TMI threshold, thus opening the door to use it to improve the beam quality of high-power fiber amplifiers even if they do not reach the TMI-threshold.
Our simulations indicate that this technique still delivers the expected results up to an average output power roughly two times above the TMI threshold. Beyond that we observe a progressive degradation of the output beam quality and stability. Furthermore, it has been shown that this method seems to work better with a bi-directional pump configuration, at least for rod-type fibers. The most likely reason for this is the weaker thermal gradient along the fiber. Besides, it has been shown that reversing the sign of the frequency difference between the FM and the HOM leads to the energy being transferred from the FM into the HOM. This offers the possibility of using this technique to dynamically change the shape of the output beam of high-power fiber amplifiers.
The main practical challenge of this method is that, if there is a leakage of the FM or of the HOM to each other’s central frequency (due, for example, to an imperfect excitation) the output power will be modulated. These modulations, however, can be minimized by improving the excitation and compensated for by modulating the pump power.
Finally, we have described a potential setup for a seed system that would be able to generate the required seed beam to exploit this technique.
To the best of our knowledge this is the first attempt to exploit the physics behind TMI to enhance the performance of a fiber laser system.
Funding
Deutsche Forschungsgemeinschaft (416342637, 416342891); Deutsche Forschungsgemeinschaft - GRK 2101 (259607349); Fraunhofer-Gesellschaft (Cluster of Excellence “Advanced Photon Sources”.).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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.
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