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Abstract
This paper investigates the static fluctuating behavior of output parameters in 1018 nm fiber lasers using 20/400 µm and 25/400 µm ytterbium-doped fibers (YDFs). It is seen that by increasing the pump power, some static fluctuations is induced in the output characteristics of the lasers, such as output power, back-reflected power, and beam quality factor (M2). The growth of these parameters fluctuates versus the pump power, without any modulation frequency in the temporal behavior of the output beam profile. This effect, which to the best of our knowledge is reported for the first time, occurs at powers much lower than the threshold for dynamic transverse mode instability (TMI). It was found that the static mode-coupling occurs between two lowest-order modes and causes these fluctuations in the lasers’ output parameters. Conducting the experiment for 1080 nm fiber lasers with different lengths of YDF, in addition to confirm the descriptions about how the static fluctuations occurs, shows that this effect occurs in other wavelengths as well.
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1. Introduction
One of the most critical limitations on the power scaling of fiber lasers is the transverse mode instability (TMI), which introduced the strongest theoretical output power limitation of 28–38 kW for diode pumping and 35–52 kW for the tandem pumping method [1]. This effect was observed in 2011 by Eidam et al. when they were studying a fiber amplifier [2]. Such behavior has also been studied in fiber oscillators, which is more complex than amplifier systems [3–6]. Many theoretical and experimental investigations have been conducted on the origin of TMI. In general, the thermo-optic coupling between the fundamental mode (LP01) and the first higher-order mode (LP11) has been introduced as the main cause of this phenomenon [7–11]. The modal interference pattern (MIP) between the LP01 and LP11, thermo-optically causes periodic changes in heat load and consequently in refractive index in the YDF. In other words, interfering between the LP01 and LP11 leads to a self-written long-period refractive-index grating (LPIG) [7,8]. Moreover, the formed LPIG can transfer energy from the LP01 to both types of guided and leaky higher-order modes (HOMs) [8,9]. A kHz-level frequency shift between the LP01 and LP11 causes the LPIG to move in the YDF [9]. As a result, the output beam profile also oscillates on the same time scale. In other words, TMI in single-pass fiber amplifiers is inherently a dynamic phenomenon. However, the static mode instability of a two-mode fiber amplifier in a double-pass configuration has been investigated theoretically and experimentally by Laegsgaard et al. [11,12]. He found that “… the thermo-optic nonlinearity can couple light at the same frequency between LP01 and LP11 modes, leading to a static deformation of the output beam profile … This novel phenomenon is caused by the interaction of light propagating in either direction with thermo-optic index perturbations caused by light propagating in the opposite direction.” The static mode instability appears at a power level much lower than the dynamic TMI threshold. Laegsgaard et al. demonstrated that there is no frequency shift between the interfering modes in this case and the LPIG formed in each direction can only scatter light propagating in the opposite direction. In this work, static modal instability has been studied experimentally in 1018 nm fiber oscillators based on 25/400 µm and 20/400 µm YDFs. In the first setup, the active medium is 2.8 m of 25/400 µm YDF (four-mode fiber). The output characteristics of the lasers showed fluctuating behavior. For a better understanding of this behavior, another system with the same specifications except for the core diameter, 20/400 µm YDF, was used as the gain fiber. As was expected, the phenomenon was detected again. This behavior is related to the static coupling of the allowed propagating modes, and it will be discussed in detail in the text. To investigate the origin of the fluctuations of laser output parameters versus pump power, we studied two systems with different geometrical conditions, such as the core and coiling diameters of the YDF. However, comparing or optimizing these conditions to achieve better beam quality and higher output power in 1018 nm YDFLs is not the main goal of this work.
2. Experiments
Figure 1 depicts the experimental setup, which consists of a co-pumped oscillator YDFL that is pumped by six 976 nm wavelength-stabilized laser diodes via a (6 + 1) x1 combiner, allowing a maximum pump power of 1020 W to be injected into the gain medium. The cavity consists of a pair of 1018 nm HR- and OC-FBGs with reflectivities of about 99% and 10%, respectively. The spectral bandwidths of the corresponding FBGs are 1.56 nm and 0.61 nm. In the following, the experimental data related to the studied lasers, in which the 25/400 µm and 20/400 µm YDF are used as the active medium, will be presented separately in detail. Before starting the experiments, we predict the approximate optimum length for YDF by performing some simulations with the “Liekki Application Designer version 3.3”. The emission cross-section of Yb3+ ions has a relative peak of around 1030 nm, which is much bigger than the emission cross-section at 1018 nm. So, severe gain competition between the amplified spontaneous emission (ASE) and the signal at 1018 nm wavelength would happen, which may suppress the oscillation of the signal at 1018 nm. The strength of the ASE peak depends on the YDF length, so tailoring the cavity parameters is essential for operation at 1018 nm [13,14]. Figure 2 shows the simulation results of the 1018 nm output signal power versus the YDF lengths for the 25/400 µm and 20/400 µm active fibers. As seen, assuming 40 dB of ASE suppression, the optimum lengths for the 25/400 and 20/400 µm YDFs are 302 and 283 cm, respectively. Since the investigation of the static mode coupling is the main purpose of this research, to avoid the effect of YDF length on the results, the YDF length was chosen to be 280 cm for both setups.
Fig. 1. The schematic diagram for the experimental setup of the co-pumped fiber lasers under the study.
Fig. 2. Simulation of the output 1018 nm signal power, versus the YDF length. As can be seen, ASE suppression (ASES) is higher than 40 dB for YDF lengths shorter than 283 cm in 20/400 µm (302 cm in 25/400 µm).
2.1 First setup: 25/400 µm active fiber
In the first experiment, the active medium of the cavity is a 2.8 m 25/400 µm YDF with the cladding pump absorption of 1.80 dB/m at 975 nm and a core/cladding numerical aperture (NA) of 0.06/0.46 (Nufern; LMA-YDF-25/400-VIII). The active fiber is coiled with a diameter of 12 cm on a water-cooled aluminium plate. Figure 3 represents the output spectrum of this fiber laser at the maximum injected pump power. This spectrum shows over 30 dB of ASES. Figures 4(a, b) show the output and back-reflected power, as well as the optical efficiency, versus the input pump power for three different coiling diameter values. As shown in these figures, output power and optical efficiency drop with some specified amount of input pump power for the case when the coiling diameter is 12 cm. This also happens inversely for the back-reflected power. The beam quality factor exhibited the same fluctuating behavior, as shown in Fig. 4(c).
Changing the coiling diameter of the YDF shows different results. Figures 4(a, b) show that increasing the coiling diameter to 20 cm results in the disappearance of output power and efficiency fluctuations (orange solid symbols). Given that this YDF can support the propagation of four modes, increasing the coiling diameter to 20 cm reduces the bending loss for higher-order modes, resulting in an increase in both power and the beam quality factor (M2). However, in this fiber laser with lower coiling diameters, bending loss leads to leaking the higher-order modes out of the core area. Figures 4(a, b) show that the output, back-reflected power, and efficiency have a normal behavior versus the pump power in the case of 9 cm coiling diameter.
To better understand this phenomenon, we measured the beam quality for different pump powers at three different coiling diameters of the active fiber (Ø≈9 cm, 12 cm and 20 cm). Figure 4(c) shows that the beam quality fluctuates when the pump power is increased for the case when 12 cm (dark brown solid square symbols), i.e., the beam quality improves for the amounts of pumping power for which the laser's back-reflected power drops (A, B, C, D, …). However, for coiling diameters of Ø≈9 and 20 cm, the beam quality factor shows a normal slow-growing behavior.
Fig. 3. Output spectrum of the 25/400 µm 1018 nm YDFL at the highest pump power of 1020 W. The inset shows the back-reflected spectrum (Yokogawa optical spectrum analyzer, the wavelength resolution is 0.05 nm).
Fig. 4. (a) Output (circles) and back-reflected (diamonds) powers, along with (b) corresponding efficiencies and (c) the beam quality factor (M2) of the laser outputs; versus the injected pump power (for 1018 nm YDFL with 25/400 µm gain fiber). Error bars refer to multiple data measurements at different times.
Because this effect depends on the modal behavior of the output beam, we recorded the temporal characteristics of the output laser beam for when this phenomenon appears (Ø≈12). The time trace on the millisecond scale and the corresponding kHz level Fourier transform of the output beam profile are depicted in Fig. 5. As can be seen, there is no modulation frequency in the temporal evolution of the output beam profile, which differentiates this behavior from TMI [15].
Fig. 5. Time trace and Fourier transform of the 25/400 µm YDFL output laser beam at full pump power with a coiling diameter of = 12 cm. There is no modulation frequency in the time trace of the output power. This means that the operation of the laser is not in the dynamic TMI regime. (A Si-detector with less than 10 ns rise time with a pinhole have been used to record this data)
2.2 Second setup: 20/400 µm active fiber
For a more detailed study of the subject, another 1018 nm fiber laser using 2.8 m of 20/400 µm YDF (Nufern LMA-YDF-20/400-9 M) with a corresponding NA of 0.065/0.46 and 1.6 dB/m cladding absorption at 975.3 nm (two-mode fiber) is set up. This fiber laser is similar to that examined in the previous section, but the only difference is the YDF core/cladding diameter ratios. Figures 6(a,b) depicts the output and back-reflected power by the corresponding efficiencies versus input pump power for this case. In the first stage, the YDF coiling diameter is set to 12 cm (orange solid symbols), leading the laser to operate in the single-mode regime [16]. As can be seen, output and back-reflected power grow normally in relation to input pump power. However, when the coiling diameter of YDF increases to 20 cm, the output power stops growing for some specified amount of input pump power (dark brown solid symbols). As the pump power increases again, the slope of the output power versus pump power gradually increases until the output power reaches the next stop point. This is similar to the behavior of the fiber laser, in which the 25/400 µm YDF coiled around 12 cm rings.
Fig. 6. (a) Output (circles) and back-reflected (diamonds) powers, (b) the corresponding efficiencies, and (c) the M2 factor, versus the input pump power (for 1018 nm YDFL with 20/400 µm active fiber).
For further investigation, the M2 factor for the fiber laser system with 20/400 µm YDF was measured at different points with a coiling diameter of 12 cm and 20 cm (Fig. 6(c)). As shown in this figure, the beam quality has a normal incremental behavior by increasing input pump power when the laser system operates in a single-mode regime (a coiling diameter of 12 cm). However, when the coiling diameter increases to 20 cm, at the points where the output power growth is relatively stopped (and the back-reflected power is rather increased), the M2 factor also experiences a relative increase. In general, it increases versus scaling up the pump power. The time trace and Fourier transform of the output beam were recorded, which demonstrates no modulation frequency, i.e., this laser does not operate in the TMI regime (Fig. 7). The strange behavior of the beam quality in both fiber laser systems implies a mode coupling origin for this phenomenon.
Fig. 7. The temporal characteristics of the output laser beam at full pump power for the 20/400 µm YDFL with the YDF’s coiling diameter of Φ = 20 cm.
3. Discussion
Since this phenomenon likely shows mode instability behavior, we expect it to be strongly related to the mode content inside the fiber. The core and coiling diameter of the active fiber have a prominent impact on the output beam's mode content. So, in this work, by changing these parameters, the relationship between this phenomenon and the mode content inside the YDF has been investigated. In other words, determining the related geometrical conditions of the fiber laser cavity can help mitigate the limitations resulting from this phenomenon. Based on the above experimental results, the 1018 nm fiber laser using 25/400 µm YDF which coiled around a ring with a diameter of 12 cm, behaved similarly to when it was fabricated using 20/400 µm YDF with the coiling diameter of ∼ 20 cm, i.e., in these two situations these fluctuations occur. Therefore, there is a common reason for this same behavior. Although a 25/400 µm fiber typically allows the lowest four transverse modes to propagate, with a very good approximation, it can be ensured that only the first two modes (LP01 and LP11) can propagate in this fiber when it is coiled with diameters lower than 15 cm [8].
On the other hand, when a 20/400 µm fiber is coiled with large diameters (for example, a 20 cm coiling diameter), only LP01 and LP11 modes can propagate. Therefore, only the two lowest-order modes can propagate in 20/400 µm and 25/400 µm YDFs with coiling diameters of 20 cm and 12 cm, respectively. It seems that the origin of the observed phenomenon is related to the excitation and propagation of two modes in the YDF. But, when the fiber laser operates single-mode or multi-mode, the output characteristics of the fiber laser show normal behavior. Table 1 shows these three operating regimes separately.
Table 1. The conditions in which the phenomenon occurs in 1018 nm fiber lasers with 25/400 µm and 20/400 µm YDF and different coiling diameters of the gain fiber (YDF length ∼ 2.8 m).
Besides, interference between LP01 and LP11 modes thermally induces an LPIG via the thermo-optic effect [17]. This is due to the strong depletion of the inversion in the same interference pattern of these two modes. Therefore, the presence of population inversion is necessary to create a thermal grating and, consequently, to create an LPIG.
As seen in Fig. 8, based on numerical calculations for the 1018 nm fiber laser with a 2.8 m 25/400 µm YDF and 1020 W pump power, the amount of population inversion changes from 13.4% at the beginning (on the HR side) to 11.9% at the end (on the OC side) of the YDF. In fact, population inversion has changed a little from the beginning to the end. The presence of a large amount of unabsorbed pump power (445 W) at the end of the YDF is also an effective factor for the high amount of population inversion and the generation of the laser signal. Therefore, the laser signal can be generated and propagated at both ends of the YDF. Hence, the LPIG can be formed in both directions at the ends of short YDFs by propagating modes in the same direction. It is worth mentioning that the Right-LPIG is weaker than the Left-LPIG (Fig. 8) because of the lower reflectivity of the OC-FBG. According to Laegsgaard's theoretical and experimental results [11,12], the LPIG in each direction can couple propagating modes in the opposite direction. The experimental conditions in the present work (including the short YDF length, 2.8 m, short operational wavelength, 1018 nm, and no sign of temporal fluctuations in the output beam profile) are very consistent with those in Ref. [11] (short amplifier length, 1030 nm operational wavelength, and the static changes in the profile of the beam). Furthermore, as Laegsgaard discovered in static mode coupling, the power threshold in our work for the phenomenon is significantly lower than what is typically found for dynamic TMI. Since LPIG is formed on both ends of the short-length YDF, in a double-path fiber amplifier as well as in a fiber oscillator, the results of Ref. [11] can be used to explain the phenomenon studied in our work. As seen in Fig. 8, the modes propagating towards OC-FBG write the Left-LPIG and the modes propagating towards HR-FBG write the Right-LPIG. The Left-LPIG couples the propagated modes from the OC (which includes the back-reflected light), and the Right-LPIG couples the modes of the output beam. Thus, energy transfers periodically between the FM (LP01) and HOMs along the effective length of the LPIG (Leff) in the active fiber [18]. The effective length of the LPIG is defined as the distance at which the LPIG can strongly couple the modes. By injecting more pump power into the gain fiber and consequently increasing the power of the modes, the following results occur: A) the strength of the LPIG increases [9]. According to the mode-coupling theory, increasing the LPIG strength increases the rate of the mode coupling between LP01 and HOMs inside the LPIG [19]; B) the core temperature increases and consequently the pitch size of the LPIG decreases [15], and C) Leff increases. Thus, the way of the mode coupling changes. Thereby, the modal content at the end of the YDF changes, which affects the beam quality and the output power.
Fig. 8. Simulated results for the population inversion and pump absorption in the YDF’s core relating to a 1018 nm ytterbium-doped fiber laser (upper diagram). Because of the short length of the YDF in the cavity, there can be observed to be about half kilowatt of unabsorbed pump power at the end of the cavity. The lower schematic diagram depicts how the LPIG can be formed at the ends of the cavity. The formation of the LPIG on the OC side of the YDF is due to the presence of a large amount of population inversion.
It was discovered that fluctuations in power and beam quality with respect to pump power occur when only the two lowest-order modes in active fiber allow for propagation. In this situation, higher-order modes leak out as soon as they gain energy. Besides, in this case, the energy mostly transfers from LP01 to LP11, and other HOMs gain a small portion of the energy transfer. Thus, in the following, we will only study the behavior of LP01 and LP11 to describe the subject. The power loss of the LP11 throughout the bends is more than the LP01. Thus, after the Leff, the ratio of LP01 power (P01) to LP11 power (P11) at the end of the YDF affects the beam quality and output power. When the P01/P11 ratio is maximized, the beam quality improves (M2 decreases), and the output power of the laser increases. The A, B, C, … in Figs. 4 and 6 represent such conditions . At these points, the back-reflected power decreases, because the HR-FBG is very sensitive to the mode content, and its effective reflectivity is maximum when the FM portion in the cavity is maximized. Thus, when the ratio of P01/P11 is maximized, the back-reflected power is reduced in some way.
By injecting more pump power, which changes the LPIG characteristics, the beam’s modal content at the end of the Leff changes, leading to degradation of the beam quality until minimizing the value of the P01/P11 (M2 increases). Since the LP11 experiences more bending loss than the LP01, the output power growth declines (a, b, c, … points in Fig. 4 and Fig. 6). Moreover, the back-reflected power in this situation increases because the effective reflectivity of the HR-FBG is reduced by increasing the LP11 power (or by decreasing the P01/P11). Figures 5 and 7 show that there was no modulation frequency in the temporal behavior of the output beam profile. So, it can be concluded that in both fiber laser systems, the fluctuating effect of output characteristics is different from dynamic energy transfer in TMI.
As discussed above and tabulated in Table 1, the fluctuating behavior originated from the existence of two lowest-order propagating transverse modes and consequently the formation of the static LPIG at both ends of the YDF. However, when the cavity operates in the single-mode regime (20/400 µm YDF with a coiling diameter of 12 cm and 25/400 µm YDF with a coiling diameter of 9 cm), mostly one mode propagates inside the core, so the LPIGs cannot be formed effectively, and hence, the mode coupling does not happen. Besides, when the fiber laser operates in a multi-mode regime (25/400 µm YDF with coiling diameters of 20 cm) the created modal interference pattern does not lead to the formation of a regular and strong LPIG. So, the static mode coupling does not occur. Thus, as can be seen in Figs. 4 and 6, the laser operates normally, and the mentioned phenomenon does not occur in these situations.
So, it can be concluded that the Right-LPIG (on the OC-FBG side) is responsible for the output beam fluctuations, and the Left-LPIG (on the HR-FBG side) induces back-reflected power fluctuations. To confirm these descriptions, one can change the YDFL cavity parameters in such a way that one of the LPIGs (Right or Left) does not form, and consequently, the output power or back-reflected power will not fluctuate. Since the Left-LPIG is always formed at the beginning of the YDF due to the presence of high pump power and high population inversion, by choosing a long YDF (for example 18 m), the conditions for creating the Right-LPIG (at the end of the YDF) can be very limited. In other words, it can be said that due to the absence of significant pump power and population inversion at the end of the long YDF, the Right-LPIG is not formed on the OC-FBG side. If these conditions can be created, it can be expected that due to the absence of the Right-LPIG at the end of the YDF, the output power of the YDFL will behave normally without any fluctuations. On the other hand, according to the simulation results shown in Fig. 2 and the experiments reported in the literature (listed in Ref. [20]), due to the presence of the destructive ASE phenomenon, YDF longer than about 4 m cannot be used in the 1018 nm YDFLs. Therefore, to provide these conditions, we examine a 1080 nm fiber laser system with an YDF length of 18 m.
The results of the simulations performed in Fig. 9(a) show that for a 1080 nm fiber laser with 18 m of YDF, only 11 W of pump power remains at the end of the active fiber (from the 1020 W injected pump power), and the population inversion drops from 3.6% at the beginning to 0.8% (approximately 1/5 of the initial value) at the end of YDF. Therefore, we expect the Right-LPIG to be negligible. Figure 9(a) shows these descriptions schematically, and as can be seen, it is expected that the output beam will behave normally without any fluctuation due to the non-formation of the Right-LPIG. It is also expected that the back-reflected power will fluctuate due to the presence of the Left-LPIG. Therefore, a 1080 nm fiber laser system with 18 m YDF and 1020 W injected pump power was examined. The coiling diameter of the YDF in this experiment was set to be 20 cm (the conditions where the output power fluctuates for the 1018 nm YDFL with a 20/400 µm YDF, shown in Fig. 6).
Fig. 9. (a) Numerical analyzes for the population inversion and pump absorption in the YDF’s core relating to the 1080 nm YDFL. Because of the long (18 m) length of the YDF in the cavity, unabsorbed pump power at the end of the cavity is negligible, and besides, the population inversion, which has the main responsibility for the creation of the LPIGs, is very weak at the end of the cavity. Consequently, as shown in the schematic diagram, the Right-LPIG on the OC side does not form. Also due to a large amount of pump power and population inversion, the Left-LPIG can be formed at the beginning of the YDF, which (with the help of the HR-FBG reflectivities) is responsible for the back-reflection fluctuations. (b) Output and back-reflected power of the 1080 nm YDFL with the length of 18 m gain fiber. As seen in this figure, the output power has a normal growing behavior without any fluctuation. However, the back-reflected power fluctuates versus the pump power because of the presence of a strong LPIG at the HR-FBG side of the cavity.
Figure 9(b) shows the experimental results of output and back-reflected power versus the pump power. As can be seen, the output power has a normal behavior without any fluctuation, which confirms that the Right-LPIG is not formed at the end of the YDF. Also, back-reflected power fluctuations show that the Left-LPIG is formed at the beginning of the YDF. The experimental results confirm that the main cause of the output power fluctuations is the formation of the Right-LPIG at the end of the YDF. As it is expected, the Beam quality parameter is smoothly grown by increasing the pump power with no sign of fluctuations. The M2 parameter was measured to be 1.62 at the full pumping power.
Then, the same 1080 nm fiber laser system was set up with a short YDF length of 2.8 m (as for the 1018 nm YDFL) and different YDF coiling diameters of 12, 20 and 40 cm. As depicted in Fig. 10 (and in comparison to Fig. 6), the 1080 nm YDFL with a short length of 2.8 m behaves similarly to the 1018 nm YDFL, i.e., the output and back-reflected power fluctuate versus the pump power when the coiling diameter is 20 cm. In the case of the 12 cm coiling diameter (almost single mode regime), the output and back-reflected power behave normally due to the absence of LPIGs. Regarding the coiling diameter of 40 cm, although the laser works in the two-mode regime, due to the large coiling diameter, the LP11 mode does not experience significant bending loss, and consequently, the output power fluctuations are very minor. But the back-reflected power fluctuates, which as mentioned before, is due to the different effective reflectivities of HR-FBG for different modes.
Fig. 10. (a) Output power (circles) alongside the back-reflected power (diamonds) versus the pump power for three different values of the coiling diameter in the 1080 nm YDFL with a short length (2.8 m) YDF. As illustrated, there is no fluctuation for the case when the coiling diameter is 12 cm (blue symbols). When the coiling diameter is 20 cm (purple symbols), fluctuations occur in both the output and back-reflected power. Finally, for a 40 cm coiling diameter, the back-reflection power suffers considerable fluctuations, whereas the output power grows almost normally. (b) The M2 factor related to different YDF coiling diameters versus the pump power.
On the other hand, this effect can be explained by considering the concept of mode beating. In general, this has been attributed to modal beating and, in particular, to the fact that the period of the beating becomes shorter for higher powers/fiber temperatures. The fluctuation of M2 may be caused by the inter-mode phase variation during power scaling.
Thus the output of the fiber is a periodic movement of the center of gravity of the beam from one side of the core to the other, as the power increases (assuming beating between the two lowest order modes, the LP01 and the LP11) [21]. This also affects the output power, since the beam overlap changes along the beating period. Thus, if there is a lower overlap of the beam with the doped region towards the end of the fiber, the output power will become lower or will stagnate with an increasing pump power. By the way, the overlap with the core, i.e., the shape of the beam at the gratings will also affect the effective reflectivity of the FBGs and, therefore, also produce the oscillations in the back-reflected power. And finally if the fiber is single-mode or multi-mode, this phenomenon cannot be seen because there is either no modal beating or its period is way too short.
4. Conclusions
In this work, the static mode coupling in 1018 nm fiber lasers was investigated experimentally based on 25/400 µm and 20/400 µm YDFs. When the geometrical conditions of the fiber lasers (different core sizes and coiling diameters of the YDFs) are adjusted so that only the two lowest-order modes are propagated in the lasers, the lasers’ output characteristics fluctuate versus pump power. By monitoring the temporal behavior of the output beam profiles, no modulation frequency was observed, even at the pump power of 1020 W. It can be concluded that this fluctuating effect on output characteristics is different from dynamic energy transfer in TMI. Therefore, it seems this phenomenon is a static mode instability of the output beam that occurred due to the propagation of LP01 and LP11 modes without any frequency shift. This results in energy transfer with no frequency modulation. To confirm these descriptions, 1080 nm YDFLs with long (18 m) and short (2.8 m) lengths of YDF were examined with different coiling diameters. The experimental results confirmed that the presence of the Right-LPIG (at the OC-FBG side) is mostly responsible for the output power fluctuations. Furthermore, the last experiments justified that this fluctuations can occur in other fiber lasers with different wavelengths utilizing short YDF lengths. Thus, suppressing this phenomenon is necessary to ensure the safe operation of these types of YDFLs, such as 1018 nm fiber lasers. Because these YDFLs cannot be made with long YDFs due to the appearance of destructive ASE phenomenon, the fluctuations can be suppressed by management of the coiling diameter of the YDFs so that the system works either in single-mode or in more than two-mode regimes. Finally, we hope that considering these fluctuations help to a better understanding of the fiber laser’s performance in different TMI regimes.
Acknowledgments
We would like to thank Dr. Mohammad Karimi and Dr. Reza Eyni Chenar for their useful comments and valuable cooperation in extracting experimental data.
Disclosures
The authors declare no conflicts of interest.
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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