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Abstract
The effect of transverse mode instability is a limitation for the power scaling of fiber laser systems, that can originate due to heat caused by stimulated Raman scattering. In this contribution, we experimentally investigate the threshold of transverse mode instability caused by stimulated Raman scattering in a passive fiber. Both, the Stokes seed power and the fiber length of a core-pumped Raman fiber amplifier are varied to systematically study this effect. Mode resolved measurements reveal that the threshold occurs at approximately the same Stokes output power for all tested configurations, independent of the total Raman conversion efficiency. These results increase the understanding of this type of mode instability and show which parameters are important for a further power scaling of high-power Raman fiber amplifiers.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High-power fiber lasers with excellent beam quality are essential for many applications in science, industry and defense. This has sparked intense research and led to a significant increase of their output power [1]. However, the wavelength of these laser systems is limited to the emission regions of the active dopants used, mainly the comparatively small bands around $1.05\,\mathrm{\mu}\mathrm{m}$ (Yb), $1.55\,\mathrm{\mu}\mathrm{m}$ (Er) and $1.8\,-2.2\,\mathrm{\mu}\mathrm{m}$ (Tm). One possibility to develop high-power fiber lasers outside these wavelength regions are Raman fiber amplifiers (RFA) [2]. RFA have two main advantages: Firstly, a wide wavelength range is accessible and secondly, they do not show photodarkening because they lack active dopants. Several kW-level RFAs with beam quality $M^2>2.5$ have been reported recently [3,4]. Hybrid Yb-Raman fiber amplifiers have also reached the kW-level and were shown to exhibit a better beam quality with broad-band [5] and narrow-band spectral width [6]. In systems with single-mode beam quality, an effect well-known to limit the performance of active fiber lasers, transverse mode instability (TMI), has recently been reported in RFAs as well [7]. TMI are caused by a thermo-optical modal coupling within the fiber, which leads to an energy transfer between different transverse modes and results in a fluctuating output beam profile [8]. There have been reports about SRS-induced mode distortion in active fiber laser systems [9–11] and theoretical work has even shown that TMI can also occur in passive fibers [12]. In this context, we presented the first experimental evidence of SRS-induced TMI in a passive fiber [7] last year. In the same year, SRS-induced TMI has also been observed in an Yb-RFA [13] and it could also be responsible for the temporal instability that limited the results obtained in [4]. Since TMI might be a limitation for single-mode, high-power RFA, it is of great importance to fully understand the process and gain knowledge about the main influential parameters.
Theoretical work presneted by Naderi et al. [12] predicted that only the total converted power is relevant (and not the conversion efficiency) for SRS-induced TMI in cladding-pumped RFA. This means, that the TMI threshold should be independent of the fiber length. For core-pumped RFA, the authors of the theoretical study [12] stated that a dependence of the threshold on the fiber length is possible due to a wavelength-dependent difference of the propagation constant of the fundamental (FM) and higher order modes (HOM). However, the influence of this effect was predicted to be small (some %, depending on the fiber parameters). In spite of this, no experimental investigation of this aspect has been performed to date. Our contribution experimentally tests these predictions and investigates the influence of fiber length and Stokes seed source power on the SRS-induced TMI threshold.
2. Experimental setup and methods
A core-pumped Raman fiber amplifier was used to investigate SRS-induced TMI. It comprised a Stokes seed source, a kW-level Yb-doped fiber amplifier and a passive fiber, as schematically depicted in 1. The Stokes seed source, depicted in red, operated at $1110\,\mathrm {nm}$ with a $3\,\mathrm {dB}$ linewidth of $108\,\mathrm {pm}$ and could provide between $4.1\,\mathrm {mW}$ and $21.3\,\mathrm {mW}$ output power. The seed source of the Raman pump laser had a central wavelength of $1060\,\mathrm {nm}$ ($3\,\mathrm {dB}$ linewidth of $204\,\mathrm {pm}$), with $3\,\mathrm {W}$ output power. Both of these light sources were coupled into polarization maintaining fibers and combined by a WDM (using non-PM fibers thereafter).
Fig. 1. Schematic of the experimental setup. LD: Laser diode. Y-/GDF: Ytterbium-/ Germanium doped fiber. CLS: Cladding light stripper. DM: Dichroic mirror. PD: Photodiode. PM: Power meter. OSA: Optical spectrum analyzer. WDM: Wavelength-division multiplexer.
The combined Raman pump and Stokes signal was fed into a $20/400\,\mathrm{\mu}\mathrm{m}$ Yb-doped double cladding fiber, coiled with a diameter of $12\,\mathrm {cm}$. Signal combiners ($6+1 \times 1$) were spliced to each end of the active fiber. The first one was used to couple the light of five laser diodes operating at $976\,\mathrm {nm}$ to further amplify the Raman pump in the YDF. The second signal combiner (oriented in counter-propagation direction) allowed monitoring the onset of TMI in the active fiber, as explained in [7]. This procedure is similar to monitoring TMI with a cladding light stripper, as described in [14]. After the second signal combiner, the Stokes signal was amplified to a power of several hundred Watts in a Germanium-doped passive $20/400\,\mathrm{\mu}\mathrm{m}$ fiber. The passive fiber was coiled with a bending diameter of $20\,\mathrm {cm}$. The length of this fiber was varied by cutting out segments of specified lengths . Both, the active and the passive fiber were water-cooled.
The fiber output signal was characterized by measuring the total output power, the power in the Raman pump and Stokes wavelength range as well as the Raman pump beam quality. The pump and Stokes beams were separated by the use of dichroic mirrors, which have a cross talk from Raman pump to signal below $0.1\,\%$. The ratio of signal power to Raman pump power (and thereby overall power) was measured by simultaneously measuring both ports of such a dichroic mirror with an individual power meter. Additionally a high-speed CCD camera was used to measure the near-field beam profiles of both, the Raman pump and Stokes radiation. A mode-decomposition algorithm was used to fit a combination of $\mathrm {LP}_{01}$ and even and odd $\mathrm {LP}_{11}$ to the measured beam profiles with the phases and mode amplitudes as fit parameters.
3. Results
3.1 Amplifier performance
For a given passive fiber length, the total Raman conversion efficiency depends on the Stokes seed power. This can be seen from numerical simulations as depicted in 2(a), where the Stokes power is shown along the passive fiber for different Stokes seed powers at a $976\,\mathrm {nm}$ power of $1.1\,\mathrm {kW}$. For these simulations the steady-state rate-equations and power propagation including the Raman term were solved [15]. The longer the passive fiber, the higher the Stokes power. This means that the total Raman conversion efficiency, defined as the ratio of Stokes power to total output power is also higher. Similar for the Stokes seed power: The higher the Stokes seed power, the higher the efficiency. 2(a) also depicts the corresponding local heat load along the fiber. It becomes clear that changing the Stokes seed power shifts the local heat load. However, the integrated heat load for a specific Stokes output power is the same, as the Raman process is the only heat source in the passive fiber. This means that for the same Stokes output power, the total heat load in the fiber will also be the same.
Fig. 2. (a): Numerical simulation of the evolution of the Stokes power along the fiber for different Stokes seed powers together with the corresponding local heat load. (b): Optical output spectra with maximum Stokes seed of $21\,\mathrm {mW}$ at a fiber length of $17.5\,\mathrm {m}$ and a total output power of $808\,\mathrm {W}$ (configuration 1, red line) as well as a fiber length of $14\,\mathrm {m}$ and a total output power of $1037\,\mathrm {W}$ (configuration 2, blue line).
We did a reference experiment without the Stokes seed, where the Raman pump beam had a beam quality of $\mathrm {M}^2=1.3$ at the output of the passive fiber and did not show any TMI up to an output power of $1.4\,\mathrm {kW}$. With the Stokes seed of $21.3\,\mathrm {mW}$, the spectrum shows clear, narrow-band Raman pump and Stokes peaks as shown in 2(b) for different configurations (see figure caption).
In the experiment with Stokes seed, TMI were observed, as explained in the following section. It should be noted that TMI modify the mode composition, which impacts the Raman conversion efficiency. This is not covered in the numerical simulations.
3.2 Influence of seed power on the TMI threshold
In order to systematically study the impact of the Stokes seed power on the system, this parameter was varied between $4\,\mathrm {mW}$ and $21\,\mathrm {mW}$. For all tested seed powers, there was an output power threshold, below which the Raman pump beam profile remained stable. Above this threshold, a clearly fluctuating beam profile was observed. At the same time, the signal at the counter-coupler port monitoring the active fiber remained stable, so we can conclude that these fluctuations were the result of SRS-induced TMI in the passive fiber, as discussed in great detail in [7]. In fact, the beam emitted by the active fiber remained stable for all of the measurements presented in the following.
To quantify the TMI threshold behaviour, a mode analysis was performed on the video data gathered with a $20\,\mathrm {kHz}$ frame rate. Intensity profiles were simulated and fitted to the measured ones [16], whereby the simulated intensity profiles were calculated as a superposition of the FM $LP_{01}$ and first HOM, even and odd $LP_{11}$. Further HOM were neglected, since the propagation losses for these HOM are high. There are four fit parameters of the simulated intensity profiles: Two relative phases and two relative mode amplitudes. We assumed that the total mode content equals unity and set this as a boundary condition, which defines the third relative modal amplitude. This also neglects camera noise and potential cladding light. With beam profile fluctuations, the reconstructed modal decomposition fluctuates correspondingly, allowing for TMI analysis.
An exemplary result of such a mode decomposition is shown in 3. In the region below the TMI threshold, the mode content does not change over time and the FM content is dominant over the HOM content. However, the HOM content is larger than the $5\,\%$ that [12] used as criteria for the TMI threshold. This criteria is, therefore, too strict to be applied here. Above the TMI threshold the average HOM content increases and the mode content strongly fluctuates with time. As TMI manifest themselves in a strong mode content fluctuation, they lead to an increase of the standard deviation of the mode content. Consequently, this standard deviation can be used as a measure of the TMI threshold. This method is similar to the method of using a photodiode after a pinhole, as introduced in [17] but is more robust, as only mode fluctuations and no intensity fluctuations are considered and there is no sensitivity to the pinhole position relative to the beam. We performed a benchmark measurement of the two methods and the results were very similar: the extracted TMI threshold was the same and the pearson correlation coefficient between the standard deviations resulting from both methods was $r>0.8$. Note that for fibers and systems where the HOM content is completely erased before the fiber output, for example through very tight bending, the mode fluctuation is not visible on the camera and thus cannot be used for analysis.
Fig. 3. Exemplary results of the mode decomposition of the Raman pump beam profile at the fiber output. The calculated mode content is shown over time well below (a) and above the TMI threshold (b). The insets show the measured Raman pump beam profiles at the fiber output at two different time points. The corresponding FM standard deviation is given in the lower right corner.
The standard deviations of the mode content are shown in 4 for three different Stokes seed powers over the total output power (a) and the Stokes power (b) for a passive fiber length of $17.5\,\mathrm {m}$. The curves clearly show the onset of TMI as an increase of the standard deviation of the mode content. A clear trend can be observed in 4(a): The higher the Stokes seed (the higher the total Raman conversion efficiency), the lower the total output power at the TMI threshold. There is no clear trend observable for the Stokes output power at the TMI threshold, as the curve for the lowest seed power in 4(b) (green line) rises first but then crosses the curves for higher Stokes seed powers (red and blue lines).
Fig. 4. Standard deviation of the FM mode content over the total output power (a) and the Stokes output power (b) for three different Stokes seed powers at a fixed passive fiber length of $17.5\,\mathrm {m}$.
3.3 Influence of fiber length on the TMI threshold
The length of the passive fiber was also varied. An existing fiber splice after the counter-coupler was opened, a specified fiber length was cut off, and the fiber was re-spliced. Thus, no additional fiber splice had to be introduced.
The beam quality at low output powers was measured to be identical in all configurations. Fiber lengths of $17.5\,\mathrm {m}$, $15.5\,\mathrm {m}$ and $14\,\mathrm {m}$ were investigated. A shorter fiber length would require higher Raman pump powers for the same Stokes power, which was not possible here due to thermal limitations of the cladding light stripper. For each tested fiber length the standard deviations of the mode amplitudes as a function of the total and the Stokes output power were measured. The results can be seen in 5, for a Stokes seed power of $21\,\mathrm {mW}$. Again, the curves clearly show the onset of TMI as an increase of the standard deviation of the fundamental mode content. The longer the fiber length, the lower the total output power (which comprises both the Raman pump and Stokes power) at the TMI threshold. If an increase of the initial standard deviation by a factor of 5 is chosen as threshold definition, the total output powers at the TMI threshold with increasing fiber length are $992\,\mathrm {W}$, $893\,\mathrm {W}$ and $800\,\mathrm {W}$. Again, there is no such trend observable with regard to the Stokes output power at the TMI threshold in 5(b): With the same threshold definition, the Stokes powers at the threshold fall within a range of $283\,\pm \,6\,\mathrm {W}$ Stokes power for all fiber lengths. However, the measurement uncertainty of the power determination is approximately $3\%$. That means that the TMI threshold is given by a specific Stokes output power independent of fiber length (within the measurement uncertainty).
Fig. 5. Standard deviation of the FM mode content over the total output power (a) and the Stokes output power (b) for three different fiber lengths at a fixed seed power of $21\,\mathrm {mW}$.
4. Discussion
The effect of TMI is known to be caused by the formation of a thermally induced, dynamic refractive index grating within the fiber [18]. However, since the beam emitted by the active fiber remained stable in the presented experiments, the refractive index grating causing TMI must stem from the passive fiber. On top of that, the observed TMI was SRS-induced and did not occur without Stokes seed (due to the lower Stokes power). Therefore, it can be concluded that the refractive index grating is most likely caused by the heat load of the Raman conversion from Raman pump to Stokes wavelength.
The theoretical work by Naderi et al. [12] predicted only a weak dependency of the SRS-induced TMI threshold on the fiber length. Specifically they numerically calculated a reduction of the Stokes power at the TMI threshold of $7\,\%$ when reducing the fiber length from $50\,\mathrm {m}$ to $10\,\mathrm {m}$. In our experiment the fiber length variation was much shorter (from $17.5\,\mathrm {m}$ to $14\,\mathrm {m}$) and no dependence of the threshold on the fiber length was observed within the measurement uncertainty. While this does not completely rule out an eventual influence of fiber length on the TMI threshold, it proofs that such an influence is small, thereby validating the theoretical work of [12] within the tested fiber length variations.
The fiber length variation showed that the Stokes power at the TMI threshold is nearly independent of the total Raman conversion efficiency of the RFA, and likewise the variation of the Stokes seed power showed a similar result: while the total TMI threshold power showed a clear trend, the Stokes power at the TMI threshold did not. The results of both experiments, the fiber length variation and the Stokes seed power variation, therefore, imply that the total heat load along the fiber is important for SRS-induced TMI, and not the maximum heat load at any point along the fiber.
5. Conclusion and outlook
In this contribution we have experimentally analyzed the SRS-induced TMI threshold in a core-pumped RFA. The Stokes seed power and passive fiber length of the RFA have been varied. Without Stokes seed, no TMI have been observed. With Stokes seed, TMI have been observed, but the beam emitted by the active fiber remained stable, which is evidence of the TMI originating in the passive fiber. Increasing the Stokes seed power led to a lower TMI threshold in terms of total output power. However, increasing the Stokes seed power also increased the Raman conversion efficiency, thus the TMI threshold was observed at approximately the same Stokes output power. The fiber length variation showed similar results: The longer the fiber, the lower the TMI threshold in terms of total output power (considering both the pump and the Stokes signal together). However, the threshold occurred at the same Stokes output power.
These observations show that SRS-induced TMI is a severe limitation of high-power RFA, which cannot easily be avoided by changing the Raman conversion efficiency. Thus, to further scale the output power of single-mode RFA it is necessary to focus on other TMI mitigation strategies like single-mode guidance and active TMI suppression [19]. Alternatively, hybrid Yb-Raman fiber amplifiers, that recently reached the kW-level [6], might be useful in the long wavelength region of the Yb gain, but their temporal stability behavior should be further investigated. For pure passive fiber RFA, the influence of fiber bending and core size should be looked at in a future work.
Funding
Deutsche Forschungsgemeinschaft (416342637).
Acknowledgement
We would like to thank Prof. Dr. Jens Limpert for his support and guidance. C.J. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation); 416342637.
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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