Next-generation gravitational wave detectors require single-frequency and high power lasers at a wavelength of 1.5 µm addressing a set of demanding requirements such as linearly-polarized TEM00 radiation with low noise to run for long periods. In this context, fiber amplifiers in MOPA configuration are promising candidates to fulfill these requirements. We present a single-frequency monolithic Er:Yb co-doped fiber amplifier (EYDFA) at 1.5 µm with a linearly-polarized TEM00 output power of 100 W. The EYDFA is pumped off-resonant at 940 nm to enhance the Yb-to-Er energy transfer efficiency and enable higher ASE threshold. We also performed numerical simulations to investigate the off-resonant pumping scheme and confirm the corresponding experimental results.
© 2017 Optical Society of America
High power lasers at 1.5 µm have been proposed as potential sources for next-generation gravitational wave detectors (GWDs) since silicon, which will be used as a material for optical substrates due to its excellent properties at cryogenic temperatures, is not transparent at 1064 nm . Fiber amplifiers are good candidates considering the great evolution of the fiber technology of the last years. However, there is a need to develop and characterize single-frequency high-power fiber amplifiers that address the demanding requirements for GWDs with respect to noise, stability and reliability, and linearly-polarized TEM00 mode content. In this context, co-doping erbium with ytterbium has often been used in the past to increase the absorption at 976 nm since at this wavelength the absorption of Yb is ten times higher than in Er. Additionally, Yb also behaves as a solvent for Er, increasing the achievable concentration of Er without the detrimental effects of clustering . Nevertheless, at high pump power levels, Er-Yb co-doped amplifiers are limited by Yb-band ASE produced due to bottlenecking effects of the Yb-to-Er energy transfer, leading to a reduction of the overall performance of the amplifier. To overcome this limitation, the amplifier can be co-seeded at 10xx nm . By co-seeding, the excess energy is removed from the Yb ions, resulting in a controlled auxiliary signal, which can be reabsorbed if the fiber is sufficiently long. Nonetheless, the inclusion of an auxiliary signal adds complexity to the system and a trade-off between the SBS threshold and the output power arises if full absorption of the auxiliary signal is desired, compromising a single-frequency high-power output signal at 1.5 µm. Another technique that has been widely investigated is the resonant pumping of erbium at 1480 nm  and at 1535 nm . However, high-power lasers at these wavelengths are not commercially available.
A different approach consists of an off-peak pumping scheme . The idea is to improve the Yb-to-Er energy transfer efficiency by pumping away from the maximum absorption wavelength, reducing the Yb inversion and therefore increasing the Yb-band ASE threshold at the expense of needing a slightly longer active fiber. A strong advantage of this scheme is that the pump absorption and consequently also the gain are distributed more homogeneously along the fiber, which makes the thermal management easier without adding complexity to the system. Even if the optimum pump wavelength remains unclear and needs to be object of study, the market availability of high-brightness fibered pump diodes restricts the choices for off-peak pumping scheme to 915 nm and 940 nm. In this work we numerically simulate and compare the behavior of an EYDFA at 1556 nm pumped at 915 nm, 940 nm and 976 nm, considering a maximum accepted Yb-band ASE level. Then, we empirically demonstrate an over-100 W laboratory prototype and investigate its properties aiming to its potential use in the third generation of GWD. The system characterization includes optical efficiency, TEM00 content and its evolution with output power, relative power noise, frequency noise and long-term power stability, keeping the system always free of SBS and Yb-band ASE.
2. Numerical simulations
The energy level diagram for Er:Yb co-doped fibers pumped at 9xx nm is depicted in Fig. 1. Pump photons are absorbed by Yb ions and populate the 2F5/2 energy level. From there, the energy is transferred to the Er ions via a dipole-dipole interaction. Thereby, the Er ions are excited to the 4I11/2 energy level. The excited 4I11/2 energy level rapidly relaxes via non-radiative multi-phonon transitions towards the metastable energy level 4I13/2 and then to ground level via radiative emission stimulated by the seed laser in the wavelength band of 1.5 µm. Up-conversion can take place involving two sufficiently close erbium ions, resulting in the relaxation of one of the ions to the ground level while the other is excited to the higher energy level 4I9/2, from which it relaxes to 4I11/2 again. At high pump power levels, the Er inversion reaches its maximum density, depleting the ground state of the Er ions and preventing Er to absorb further energy. In this situation, the rate at which the energy is transferred from Yb to Er is limited and the energy in the Yb energy level 4F5/2 relaxes to 4F7/2, producing optical emission in the Yb-ASE band (i.e between 1.0 and 1.1 µm). The whole process can be analytically described by means of the following rate equations 8]
To compare different pump wavelengths in the 9xx nm range we computed the output power and Yb-ASE power for a system seeded at 1556 nm and pumped at 915, 940 and 976 nm since these are typical wavelengths for commercially available high power pump diodes. The parameters used in the simulations are listed in Table 1. The background losses of the active fiber as well as the back-transferred energy (R35) and up-conversion (Cup) coefficients have been omitted due to their little impact on the results. The fiber length has been selected in order to achieve 95% absorption of pump light in each case.
The simulation results are shown in Fig. 2. Due to uncertainties of some fiber parameters (especially the parameters R61 is critical), the absolute values for output power cannot be accurately computed. Hence, Fig. 2 shows the output power normalized with respect to the highest output power, the ASE power is normalized with respect to the highest ASE power and the pump power is normalized versus the maximum pump power.
The results show almost the same performance of the amplifier for 915, 940 and 976 nm at low power levels, however the ASE between 1.0 and 1.1 µm significantly increases at low pump power levels when pumping at 976 nm with respect to 915 and 940 nm. As described before, this fact has usually been the limiting factor for power-scaling of Er:Yb fiber amplifiers, because at high pump power levels the slope suffers from a significant roll-off, as can be observed for the output power in Figue 2. On the other hand, because of the lower Yb inversion, the slope of the amplifier is linear for higher pump power levels for 915 and 940 nm. The ASE threshold is higher and the achievable output power before the ASE carries a significant power is higher. The trade-off for having lower pump absorption is a longer active fiber. The simulations show a slightly better behavior at 940 nm in comparison to 915 nm. In order to achieve 95% of absorbed pump light in our simulations, fiber lengths of 2.0, 2.9 and 0.7 m were required for pump wavelengths of 915, 940 and 976 nm, respectively.
3. Experimental setup
Following the results of the numerical simulations presented in Section 2, a single-frequency fiber amplifier at 1.5 µm pumped at 940 nm was developed. Figure 3 depicts the MOPA setup, which was set in counter-propagation pumping configuration using double-clad large mode area (DC LMA) fibers. The master oscillator was a fiber laser module (The Rock, NP Photonics, Inc.) delivering 2W at 1556 nm with kHz-linewidth. The output of this seed module is a single-mode passive fiber that can be directly spliced to the amplifier. However, in order to acquire sample signals of the seed laser for measuring and monitoring purposes, a free-space stage was installed in which an optical isolator was included. Although the setup was mostly built with LMA fibers, the beam is free-space coupled to a single-mode fiber for two main reasons. On the one hand, to mimic an all-fiber MOPA, since commercially available single-mode fiber seed sources use single-mode output fibers. On the other hand, coupling the beam to a single-mode fiber avoids the risk of exciting higher order modes (HOM). In return, this requires an adaption of the mode area from the single-mode fiber to the LMA fiber. For that, we designed and built an in-home-made mode field adapter (MFA) to fit the mode fields of SM to the LMA fiber. Because of the counter-propagation pumping scheme, an in-home-made cladding light stripper (CLS)  was used right after the MFA to remove any residual pump light from the fiber. After the CLS, 5.5 m of DC Er:Yb LMA fiber (LMA-EYDF-25P/300-HE, Nufern) was spliced. Using a LMA fiber is critical to increase the threshold of non-linear effects as SBS and SRS by reducing the light intensity [10, 11]. This choice brings to play a new trade-off, since LMA fibers are generally not purely single-mode but few-modes fibers. This issue can be solved by choosing the bending diameter of the fiber carefully [12, 13]. In our setup, the active LMA fiber was coiled with a diameter of 30 cm around a V-grooved aluminum spool to additionally achieve passive cooling. The seed power at the input of the co-doped fiber was 1.2 W due to the losses of the free-space isolation stage, signal sample pickup and coupling to the fiber. The amplifier was cladding-pumped by two fibered 140 W diodes at 940 nm (ST-Series, Lumentum) through a (2+1)×1 in-home-made pump combiner (PC)  made of a passive matching LMA fiber (LMA-GDF-25/300, Nufern) with a coupling ratio of 90% between the pump ports and the signal port. Both pump diodes were independently temperature stabilized in order to set the working wavelength and driven by independent current sources. The output port of the PC constitutes the output of the amplifier, from which approximately 15 cm of the low index polymer coating was removed and substituted by high index optical gel to remove any cladding light propagated in forward direction.
4. Measurements and results
4.1. Slope and spectrum
The measured amplifier output power versus the launched pump power and a corresponding linear fit are shown in Fig. 4(a).
A maximum output power of 111 W, corresponding to a gain of 19.7 dB, was achieved with an available pump power in the active fiber of 250 W. The fit of the data points indicates an optical efficiency of ∼46%, compared to the theoretical quantum limit of ~60% for seed and pump wavelengths of 1556 nm and 940 nm, respectively. This result is a higher output power with respect to single-frequency EYDFAs traditionally pumped at 976 nm, as well as improved conversion efficiency compared to Yb-band rejection schemes (~40% ) and EYDF lasers (∼43% ), while high TEM00 mode content is preserved as it will be shown later in Section 4.3.
Besides this, the system operated Yb-ASE free as can be seen in Fig. 4(b), which shows the spectrum from 1.0 µm to 1.1 µm as well as from 1.535 µm to 1.580 µm measured at the maximum power level of 111 W. In the Yb-ASE band the signal is clearly below the sensitivity of the spectrum analyzer, while in the Er-ASE band (i.e. between 1540 nm and 1580 nm) the amplified signal is more than 58 dB above the ASE level.
4.2. Long-term stability
Although laser sources in GWDs should include stabilization systems, the design of such systems depend on the free-running behavior of the laser. In Fig. 5 the power and PER over 1 h-time measurement at the highest output power is shown. The measurement was recorded after 1 hour warm-up time to minimize the impact of temperature gradients in the fiber and the used detectors were a F150A-SH-V1 (Ophir) for the output power and two 3A-FS (Ophir) for the PER. The observed output power fluctuations are mainly caused by analog-to-digital conversion noise in the detector. In any case, the range in which the output power fluctuates over 1 hour, including the mentioned noise sources, is less than ±0.2%. We observed that temperature gradients present in the fiber and spool lowered the PER, however it was possible to return to the initial higher values by retuning the half-wave plate of the measurement setup. It is worth to remind at this point that the LMA fiber used in this experiment was non-PM. We believe that a PM version of the LMA fiber will show a better polarization stability behavior. Notwithstanding this observation, the PER over 1 hour fluctuated between 12.5 and 13 dB during the first 35 minutes to later settle at 13 dB as shown in Fig. 5. The average PER during the whole measurement is ~12.8 dB. Resulting in an average power with linear polarization of ~105.4 W.
Regarding the long-term stability of the amplifier, the proposed system allows for several parameters of freedom to develop stabilization and control systems to tune not only the output power and polarization, but also the noise and modal content actuating on, for example, the seed signal, pump power of each diode, fiber and spool temperature and active polarization rotators.
4.3. Modal content analysis
Since GWDs require a pure fundamental transversal mode, a pre-mode cleaner (PMC) cavity is integrated before the interferometer to suppress any HOMs. This implies that all the optical power carried in HOMs will be discarded. Thus, a clear characterization of the power in the TEM00 mode is crucial to establish the suitability of the laser source for GWD. A typical parameter widely used to characterize the beam quality is M2. However, it has been demonstrated that a low value of M2 does not guarantee single mode operation , and how much power is carried by the TEM00 mode cannot be determined. Therefore, a different method to characterize the beam quality and the amount of power in the fundamental mode must be used.
The measurement setup for modal content evolution is shown in Fig. 6. To decompose the beam into the TEM modes, a 3-mirror cavity in a non-cofocal configuration was used . By scanning one of the mirrors the eigenmodes of the cavity changes, transmitting the different TEM modes existing in the beam depending on the mirror’s position. As this technique requires low power (<100 mW) and a linearly-polarized beam, two new free-space optics stages between the amplifier output and the cavity were included: A polarization filtering stage consisting of a quarter wave plate, a half wave plate and a polarization beam splitter, and a power tuning stage consisting of a half wave plate and a polarization beam splitter. Additionally, a pair of lenses was installed in front of the cavity for mode matching. The cavity had a free spectral range (FSR) of ∼714 MHz and a finesse of ∼250 for p polarization. A set of mode scans of the amplified seed signal was carried out at output power levels of 10.0 W, 24.0 W, 38.6 W, 55.2 W, 73.8 W, 84.6 W, 96.6 W and 111 W. This set of measurements allows to observe the evolution of the fundamental mode content with output power, which is shown in Fig. 7.
It is worth to say that these measurements are very sensitive to the mode-matching to the cavity, alignment and pointing noise. In order to take account of the short term fluctuations, each data point is an average of 100 full measurements. The system shows an excellent modal content behavior, with 94.8% of the power in the fundamental mode at 111 W. The details of the mode scan at the maximum output power are shown in Fig. 8, where the normalized intensity versus the normalized frequency is presented. The 100-times averaged samples are used to fit functions of fundamental and HOMs. The ratio between the integral of these two fits is the relative TEM00 mode content. Computing the fits increases the accuracy of the result compared to direct use of the discrete raw data points. It also allows for the identification of bad mode-match to the cavity, which produces recognizable frequency features not fittable as TEM modes. It also prevents ASE and residual s-polarization to alter the result, since neither of them are as TEM modes. It is fair to specify that this result does not mean 94.8% of 111 W is linearly-polarized pure fundamental mode, since the amplifier’s output is not purely linearly polarized. However, as it was shown in 4.2, the PER was around 13 dB, resulting in a true linearly-polarized TEM00 mode of ~100 W. This constitutes a scale of almost a factor of two compared to the highest previously achieved power reported for single-frequency, single-mode records at 1.5 µm [3, 19]. Furthermore, the works reported in  and  required specialty fibers and were not monolithic systems.
4.4. Relative power noise
Another important characteristic of laser sources for GWDs is the power noise. Fluctuations in the power with respect to its average value, the so called relative power noise (RPN), are directly coupling to the read-out signal of the photodetector in the dark port of the interferometer in GWDs. The setup deployed to measure the amplifier’s relative power noise is shown in Fig. 9. Similar to the setup used to measure the modal content, a polarization filtering and a power tuning stage was installed to obtain a sample of the high power beam. As the power measurement required to focus the beam on a fast photodiode, an additional set of optical density filters was used to further attenuate the beam. The utilized photodiode (PDA10CF, Thorlabs) was a InGaAs detector with 150 MHz bandwidth, and its signal was acquired by two signal analyzers: from 1 Hz to 100 kHz the RPN was recorded with a SR785 (Stanford Research Systems), while the range between 100 kHz and 6 MHz was recorded with an E4440A (Agilent). In order to compare the RPN, it is plotted for medium (55 W) and high (110 W) power together with the seed source RPN in Fig. 10.
To measure the RPN at 55 W the amplifier was pumped with only one pump diode, while both pump diodes were used for 110 W. The graph shows that the seed RPN is lowered by the amplifier at frequencies below 1 kHz, most probably due to the effective high pass filtering caused by the amplification process . At frequencies between 1 kHz and 100 kHz the RPN of the amplifier signal is slightly higher than the seed’s RPN. There is noticeable a bump around 10 kHz present at the highest output power. However, the fact that this feature only appears when the two pump diodes are in use suggests that it is likely generated in the pump diodes due to cross-coupling light between the pump ports of the pump combiner and hence coupled to the amplified signal via the gain process, although the actual origin was not experimentally investigated. Furthermore, as it was mentioned in Section 4.3, the pump diodes are not stabilized in power, so their own individual noise characteristic is coupled to the amplified seed signal during amplification via gain. At frequencies over 100 kHz the RPN of the amplified signal follows the seed RPN.
4.5. Frequency noise
A great challenge of the next-generation GWD lasers at 1.5 µm is to achieve single-frequency and low frequency-noise emission. This is critical because frequency noise induces phase noise when the beam is splitted in the Michelson interferometer, causing power fluctuations due to inequalities in the arms length. These power fluctuations couple to the DC read-out at the dark port, reducing the overall sensitivity of the detector . Since the detection of gravitational waves is achieved by measuring the small changes caused in the arms length, frequency noise can spoil the sensitivity even in a hypothetical detector with perfectly matched arms. In regard to this not only the frequency noise of the master oscillator, but also the excess noise of the power amplifier stage must be studied.
The setup used to measure the frequency noise was the same described in Section 4.3 for the modal content analysis and is shown in Fig. 6 (see  for further details). The scanning cavity was locked to the fundamental mode and the signal required for the piezo to compensate the frequency fluctuations was recorded for 300 seconds. This time series is later used to compute the frequency noise. This measurement was performed for the seed source as well as for the amplified signal at 55 W and 110 W, which are show in Fig. 11(a). The noise measured for both amplifier output power levels follows the shape and level of the seed noise, which demonstrates that the amplifier stage does not influence the frequency stability and, thus, it is mainly determined by the seed source. The seed source linewidth was specified by the manufacturer to be <10 kHz based on a self-heterodine measurement with 120 µs delay time. In order to extend this characterization, the frequency bandwidth was calculated from the measured frequency noise asFig. 11(b). It confirms that the linewidth is ∼8 kHz at 8.3 kHz (i.e. for 120 µs) for the seed laser. The amplified signal linewidth remained practically unaltered, being ∼11 kHz and ∼8.4 kHz for 55 W and 110 W, respectively.
4.6. Stimulated Brillouin scattering
Brillouin scattering arises when an incident photon interacts with an acoustic phonon. The process becomes stimulated when a certain threshold is reached, at which the so called stimulated Brillouin scattering (SBS) starts. Due to the slightly lower energy of the stimulated wave, it appears in the optical spectrum shifted from the wavelength of the signal that induced it, to the detriment of the narrow band signal in single-frequency systems. Exploiting the fact that SBS causes broadband power noise in forward direction , its threshold can be reliably measured by observing the noise increase in a fiber amplifier at different output power levels .
Similar to Section 4.4, the RPN was recorded with the spectrum analyzer E4440A (Agilent). The data is shown in Fig. 12, it displays the RPN spectrum at frequencies above the relaxation oscillation peak, which was around 700 kHz in our experiment. Since the noise floor is the factor limiting the minimum SBS-induced power noise that can be observed, shot noise was calculated and dark noise was recorded and plotted in Fig. 12. As can be seen, all the measured noise curves overlap. Therefore, there are no signs of power-dependent noise present in the spectrum up to an output power of 111 W, as expected when SBS is initiated, demonstrating that the system operates SBS-free up to its maximum output power.
A high-power Er:Yb co-doped fiber amplifier candidate in the band of 1.5 µm for next-generation gravitational wave detectors has been demonstrated in this paper. The amplifier was off-resonant pumped at 940 nm in order to increase Yb-band ASE threshold following the results of the performed numerical simulations. The corresponding laboratory prototype achieved an optical efficiency of 46.2 % and an ASE-free output power of 111 W, evidencing an increased Yb-to-Er energy transfer efficiency with respect to similar systems pumped at 976 nm. The amplifier system was built imitating an all-fiber setup and characterized for the amplification of a single-frequency seed source at 1556 nm. A TEM00 mode content of 94.8% was measured at an output power of 111 W and a PER of 13 dB. Hence, the linearly-polarized pure TEM00 mode output power was ∼100 W with no signs of Yb-band ASE. The frequency noise was also measured at mid- and high power levels and compared with the seed frequency noise. No dependences on the amplifying process were found and the seed source frequency behavior was preserved in the amplified signal. On the other hand, the relative power noise of the amplified signal shows a filtering effect with respect to the seed’s noise at frequencies below 1 kHz, lowering the noise at this frequency range. The system showed no presence of SBS. Concerning this, we are confident that higher power levels are feasible by increasing the pump power without compromising the single-frequency operation nor the noise performance. Additionally, a relatively good stability of the free-running amplifier’s linear-polarization output was shown considering that no active stabilization was used.
This work demonstrates the high potential of fiber amplifiers as laser sources for the next generation of GWDs in general, and the off-resonant pumping scheme on Er:Yb LMA fibers in particular.
FP7 People: Marie-Curie Actions (606176).
The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/(PEOPLE-2013-ITN) under REA grant agreement n° . It reflects only the author’s view and the Union is not liable for any use that may be made of the information contained therein.
References and links
1. ET Science Team, Einstein gravitational wave Telescope Conceptual Design Study, 2011.
2. J. L. Wagener, P. F. Wysocki, M. J. F. Digonnet, H. J. Shaw, and D. J. DiGiovanni, “Effects of concentration and clusters in erbium-doped fiber lasers,” Opt. Lett. 18(23), 2014–2016 (1993). [CrossRef] [PubMed]
3. M. Steinke, A. Croteau, C. Paré, H. Zheng, P. Lampere, A. Proulx, J. Neumann, D. Kracht, and P. Wessels, “Co-seeded Er3+:Yb3+ single frequency fiber amplifier with 60 W output power and over 90 % TEM00 content,” Opt. Express 22(14), 16722–16730 (2014). [CrossRef] [PubMed]
4. V. R. Supradeepa, J. W. Nicholson, and K. Feder, “Continuous wave Erbium-doped fiber laser with output power of >100 W at 1550 nm in-band core-pumped by a 1480nm Raman fiber laser,” in Conference on Lasers and Electro-Optics 2012, OSA Technical Digest (Optical Society of America, 2012), paper CM2N.8.
6. D. Creeden, H. Pretorius, J. Limongelli, and S. D. Setzler, “Single frequency 1560nm Er:Yb fiber amplifier with 207W output power and 50.5% slope efficiency,” Proc. SPIE 9728, 97282L (2016). [CrossRef]
7. M. Karásek, “Optimum Design of Er3+–Yb3+ Codoped Fibers for Large-Signal High-Pump-Power Applications,” IEEE J. Quantum Electron. 33(10), 1699–1705 (1997). [CrossRef]
8. Q. Han, J. Ning, and Z. Sheng, “Numerical Investigations and Power Scaling of Cladding-Pumped Er-Yb Codoped Fiber Amplifiers,” IEEE J. Quantum Electron. 46(11), 1535–1541 (2010). [CrossRef]
9. M. Wysmolek, Laser Zentrum Hannover e. V., Hollerithallee 8, Hannover 30167 is preparing a manuscript to be called “Micro-structured fiber cladding light stripper for kW-class laser systems.”
10. M. E. Fermann, “Single-mode excitation of multimode fibers with ultrashort pulses,” Opt. Lett. 23(1), 52–54 (1998). [CrossRef]
11. A. Galvanauskas, “Mode-scalable fiber-based chirped pulse amplification systems,” IEEE J. Quantum Electron. 7(4), 504–517 (2011). [CrossRef]
12. J. W. Nicholson, J. M. Fini, A. D. Yablon, P. S. Westbrook, K. Feder, and C. Headlay, “Demonstration of bend-induced nonlinearities in large-mode-area fibers,” Opt. Lett. 32(17), 2562–2564 (2007). [CrossRef] [PubMed]
14. T. Theeg, H. Sayinc, J. Neumann, L. Overmeyer, and D. Kracht, “Pump and signal combiner for bi-directional pumping of all-fiber lasers and amplifiers,” Opt. Express 20(27), 28125–28141 (2012). [CrossRef] [PubMed]
15. Q. Han, Y. Yao, Y. Chen, F. Liu, T. Liu, and H. Xiao, “Highly efficient Er/Yb-codoped fiber amplifier with an Yb-band fiber Bragg grating,” Opt. Lett. 40(11), 2634–2636 (2015). [CrossRef] [PubMed]
16. D. Y. Shen, J. K. Sahu, and W. A. Clarkson, “Highly efficient Er, Yb-doped fiber laser with 188W free-running and > 100W tunable output power,” Opt. Express 13(13), 4916–4921 (2005). [CrossRef] [PubMed]
21. J. B. Camp, H. Yamamoto, and S. E. Whitcomb, “Analysis of light noise sources in a recycled Michelson interferometer with Fabry–Perot arms,” J. Opt. Soc. Am. A 17(1), 120–128 (2000). [CrossRef]
22. M. Horowitz, A. R. Chraplyvy, R. W. Tkach, and J. L. Zyskind, “Broad-Band Transmitted Intensity Noise Induced by Stokes and Anti-Stokes Brillouin in Single-Mode Fibers,” IEEE Phot. Technol. Lett. 9(1), 124–126 (1997). [CrossRef]
23. M. Hildebrandt, S. Büsche, P. Weßels, M. Frede, and D. Kracht, “Brillouin scattering spectra in high-power single-frequency ytterbium doped fiber amplifiers,” Opt. Express 16(20), 15970–15979 (2008). [CrossRef] [PubMed]