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We experimentally investigated the influence of amplified spontaneous emission within the Brillouin gain bandwidth on the Brillouin scattering of a single-frequency signal. The experiments were performed for the case of artificial ASE injected in backward direction into a passive fiber, as well as in forward direction of a low-power fiber amplifier. A significant influence could be observed, when the ASE was counter-propagating to the signal. Injecting 160.6 nW of ASE within the Brillouin gain bandwidth led to a decrease of about 3 dB of the SBS-threshold of an approximately 335 m long passive fiber from about 80 mW to less than 40 mW. At a fixed signal power of 81 mW the backscattered power and the power in the Brillouin scattered Stokes maximum increased by a factor of 19.
© 2012 Optical Society of America
1. Introduction
Stimulated Brillouin scattering (SBS) is the main power limitation for the transmission and amplification of single-frequency signals in optical fibers. In order to understand and model this nonlinear effect, and to increase the onset of the stimulated process, several research groups have carried out a variety of calculations and measurements on the Brillouin scattering process in single-mode optical fibers. The experimental investigations included for example the measurement of the Brillouin gain spectra [1], threshold values [2], and gain factors [3]. Different impact factors on these parameters such as glass composition [4], external strain [5], and temperature gradients [6] have been identified and studied. The invention of large-mode-area (LMA) fibers led to significantly higher SBS thresholds, and the characterization of the Brillouin scattering process has also been extended to these fibers [7, 8]. Within the last few years, single-frequency signals in the 1 μm range have been amplified up to 500 W in different fiber geometries [9–11]. Recently, a 300 MHz linewidth signal was amplified in a gain-tailored SBS suppressing photonic crystal fiber up to 990 W [12]. The common concept used was the master-oscillator power amplifier (MOPA) scheme, in which the seed source usually delivers a maximum output power of a few Watts. Amplifying such a signal with gain factors around 20 dB can lead to a high sensitivity towards parasitic lasing processes and a significant amount of output power in amplified spontaneous emission (ASE). Therefore, it is common to use intermediate amplifier stages with output powers of several 10 Watts. Unfortunately, besides preamplifying the single-frequency signal, these amplifier stages also generate ASE photons, even if the overall ASE power can be kept comparably low. In particular, also ASE photons within the Brillouin gain bandwidth will be injected into the high power amplification stage, unless a very narrow bandpass filter is used in front of it. Rayleigh-backscattered ASE within the Brillouin gain bandwidth could then potentially seed the SBS process in the main amplifier. However, the effect of ASE on the Brillouin scattering threshold of a single-frequency signal has not been experimentally studied, yet. At least Pannel et al. [13] and Hildebrandt et al. [14] have included a term accounting for ASE in their calculations of Brillouin scattering in optical amplifiers, indicating that an effect is expected. In this paper, we demonstrate that the ASE in the Brillouin gain bandwidth can seed the Brillouin scattering process, using a passive fiber and counter-propagating ASE. We also investigated the possibility that Rayleigh-backscattered co-propagating ASE might be sufficient to seed the SBS process. Furthermore, we calculated numerically the SBS threshold of a single-frequency fiber amplifier. The case, when a term accounting for backward ASE was included in the differential equation for the Brillouin power, was compared to the case, when no such term was implemented.
2. Experiments with backward ASE injected into a passive fiber
2.1. Experimental setup
The experimental setup is depicted in Fig. 1. As signal source, a commercial non-planar ring oscillator (NPRO), delivering up to 400 mW at 1064 nm with a signal linewidth of approximately 1 kHz, was used. The NPRO was protected from backreflections by a Faraday isolator (nominal isolation ≥35 dB), which was followed by a variable attenuator, consisting of a half-waveplate and a polarizing beam splitter (PBS). To monitor the signal-to-fiber-coupling and to detect a sample of the backscattered light, a 90/10-tap-coupler (all tap-couplers were built in-house; the typical value for the return loss is ≥35 dB) was used. The fiber generating the Brillouin scattered Stokes signal was an approximately 335 m long piece of HI-1060-Flex from Corning, a commercially available passive fiber with a nominal core diameter of 3.4 μm. A 70/30-tap-coupler was spliced to the other end of the fiber to couple in and monitor the ASE as well as to extract a sample of the transmitted signal.
Fig. 1 The setup used in our experiments with a passive fiber. The ASE was counter-propagating to the single-frequency signal.
The artificially generated ASE was supposed to resemble ASE generated in a fiber amplifier. Therefore, the ASE source consisted of components typical for a single-frequency fiber amplifier. As active fiber, 10 m of the PLMA-YDF-10/125 by Nufern were used, which were cladding-pumped through an in-house built pump combiner by a commercial 25 W fiber-coupled diode at 976 nm. To protect the ASE source from the NPRO signal transmitted through the HI-1060-Flex, two Faraday isolators with a nominal isolation of ≥35 dB each were implemented. Behind the isolators, the maximum ASE power was 139 mW, limited by the onset of parasitic lasing processes. About 60 % of the ASE power could be coupled into the 70/30-tap-coupler, of which the 70 %-port was spliced to the HI-1060-Flex. At all fiber ends, angle-polished fiber connectors were used to protect the fibers from backreflections. Furthermore, all lenses used had AR-coatings at the relevant wavelengths.
2.2. Measurement method and results
To determine the SBS threshold of the used fiber without additional injected ASE, the signal power was increased via the variable attenuator, while the backscattered power and optical spectra were detected at the backwards directed 10 %-output-port of the first tap-coupler. Additionally, the transmitted power was measured at the 30 %-output-port of the second tap-coupler. This procedure was repeated for four different levels of ASE power in the Brillouin gain bandwidth.
As only ASE photons within the Brillouin gain bandwidth can potentially seed the SBS process, the ASE source was set up such that the ASE maximum was roughly at the Brillouin wavelength. Hence, the spectral shape can be considered as flat in the relevant spectral interval. To increase the overall ASE power in the fiber, the pump power was increased. From the measurement of the power and optical spectra at the 30 %-ASE-monitor-port of the tap-coupler, the ASE power in the Brillouin gain bandwidth (BGBW) was calculated. Assuming a Brillouin gain bandwidth of 50 MHz [15], the ASE power levels in the Brillouin gain bandwidth used in the experiments (PASE,BGBW) were between 3.8 nW and 160.6 nW. The corresponding optical spectra are shown in Fig. 2(a).
Fig. 2 (a): The optical spectra of the ASE injected into the fiber, measured at the 30 %port of the second tap-coupler, for four different power levels used in the experiments. (b): Backscattered power with respect to the signal power for different levels of ASE within the Brillouin gain bandwidth. ASE counter-propagating to the signal. The dashed line indicates where the backscattered power reaches 0.1 % of the signal power.
In Fig. 2(b), the backscattered power is plotted versus the signal power for different injected ASE power levels. Note that the power offset created by the transmitted ASE was subtracted in the graph for better comparison. The definition of the SBS threshold in the literature is quite ambiguous. Common definitions are the amount of signal power where the backscattered power departs from linear behavior, or reaches a certain reflectivity. In order to compare the SBS thresholds in our experiments, we chose the SBS threshold to be the amount of signal power where the backscattered power reaches a reflectivity of 0.1 %. With no counter-propagating ASE, the backscattered power started to rise very slowly compared to the cases when additional ASE was injected into the fiber. In fact, only at a signal power of 81 mW, the evolution of the backscattered power departed from linear behavior. A reflectivity of 0.1 % was not reached even at the maximum signal power. It can be clearly seen that the more ASE was added, the smaller was the signal power when the backscattered power started to rise exponentially. With power values within the Brillouin gain bandwidth of 3.8 nW and 53.8 nW, a reflectivity of 0.1 % was reached at a signal powers of 67 mW and 44 mW, respectively. With power values within the Brillouin gain bandwidth of 115.1 nW and 160.6 nW, a reflectivity of 0.1 % was reached at signal powers smaller than 40 mW. At a signal power of 81 mW, the backscattered power was 19 times as high when 160.6 nW of ASE were added, compared to the case when no additional ASE was used. To obtain more information about the power evolution of the Brillouin scattered signal, the optical spectra of the backscattered light were measured with an optical spectrum analyzer (OSA) with a resolution bandwidth (RBW) of 0.01 nm. In these spectra, the signal at the seed wavelength generated by Rayleigh scattering and spurious backreflections could clearly be separated from the Brillouin scattered signal. In Fig. 3(a) the optical spectra of the backscattered light for the case of no additional ASE in the backward direction are shown. At low power the Brillouin triplet, consisting of the elastic Rayleigh scattering peak, and the two inelastic Stokes and anti-Stokes peaks at the shifted wavelength of ∼60 pm corresponding to a frequency shift of ∼15.9 GHz, is evident. With increasing signal power, the Stokes component of the spectrum increases due to the onset of stimulated Brillouin scattering. Figure 3(b) shows the evolution of the backscattered optical spectra when 3.8 nW of ASE within the Brillouin gain bandwidth were added counter-propagating to the signal. Due to the transmitted ASE, which can be seen as the −47 dB offset in Fig. 3(b), the Stokes and anti-Stokes peaks cannot be seen at low signal powers. At higher signal powers, only the Stokes peak is evident besides the Rayleigh peak, indicating the onset of the stimulated Brillouin scattering process. Comparing the power in the Stokes peak to the ones in Fig. 3(a) indicates that the small amount of added ASE already seeds the stimulated Brillouin scattering process. In the case of no additional ASE, injecting a signal power of about 49 mW resulted in a power of −48 dB in the Stokes peak. When only 3.8 nW of ASE power in the Brillouin gain bandwidth were added counter-propagating to the signal, the power in the Stokes peak was already about −42.6 dB for only 43.5 mW of signal power. Injecting 81 mW of signal power yielded power in the Stokes peak of about −28 dB and −26 dB for no ASE and PASE,BGBW = 3.8 nW, respectively. For higher ASE power levels, the backscattered optical spectra looked alike, but the offset due to ASE was even higher.
Fig. 3 (a): Evolution of the backscattered optical spectra for the case of no additional ASE and (b): when 3.8 nW of ASE power within the Brillouin gain bandwidth were added counter-propagating to the signal with increasing signal power.
Figure 4 shows the Stokes-peak power with respect to the signal power for the ASE levels corresponding to Fig. 2(a). Again, it can be clearly seen that the more ASE power in the Brillouin gain bandwidth was injected into the fiber, the stronger was the exponential increase of the Brillouin scattered signal. Accordingly, the power in the Brillouin peak at a fixed value of signal power increases with increasing ASE power. At a signal power of 81 mW the power in the Brillouin peak was 19 times as high when 160.6 nW of ASE in the Brillouin gain bandwidth were injected, compared to the case when no artificial ASE was added. The exponential rise of the backscattered power is a characteristic typically considered as the threshold of SBS [14]. Therefore, it can be concluded from the data above that with increasing ASE power within the Brillouin gain bandwidth and co-propagating with the Brillouin scattered signal, the SBS threshold decreases. This effect could contribute to the fact that decreasing the seed power for a fiber amplifier increases its SBS threshold [13], as not only the overall amplification gain factor is reduced, but also the amount of generated backwards ASE. In master oscillator fiber amplifier systems, gain factors can be as high as several 10 dB, which can yield a significant amount of power in generated ASE in the backward direction. According to our experimental results, this can possibly seed the SBS process.
Fig. 4 Stokes peak power with respect to the signal power for different powers of ASE in the Brillouin gain bandwidth. ASE counter-propagating to the signal.
To increase the SBS-threshold by decreasing the gain factors, the utilization of an intermediate amplifier stage to pre-amplify a low power seed signal is a common approach. However, the ASE generated in the pre-amplifier is then usually also coupled into the high power main amplifier. The Rayleigh-backscattered part of the ASE within the Brillouin gain bandwidth could then potentially increase the strength of the Brillouin scattering process.
To compare the experimental results to theoretical predictions, we also modeled the SBS process in a passive fiber, using the analytic solutions in the undepleted pump limit [16]. Background losses as well as the Brillouin gain bandwidth were taken into account. The analytic model confirmed the general effect, but, as expected, the calculated values for the Stokes power were very sensitive to the choice of the peak Brillouin gain (gB). Nevertheless, with a low but still reasonable value of about gB=1.02·10−11m/W [17], they resembled the experimental data quite well.
3. Experiments with forward ASE injected into a fiber amplifier
The amount of power in the backward direction of an optical amplifier due to Rayleigh scattering and spurious reflections depends on various fiber parameters such as the used material composition and the homogeneity of the glass matrix, as well as the signal wavelength. A typical value for the Rayleigh scattering damping coefficient of a standard silica fiber for a signal wavelength of 1 μm is 1 dB/km [18]. However, in an active fiber due to the inhomogeneity of the fiber core induced by the implementation of the active ions, the overall backscattered power can be significantly higher and is difficult to estimate. Furthermore, the effect of optical amplification has to be considered, as the backward propagating light experiences the same gain as the forward propagating signal. Hence, in order to investigate the eventuality that the Rayleigh backscattered ASE within the Brillouin gain bandwidth could decrease the SBS threshold of an optical amplifier, experiments with artificially added ASE in forward direction of a low-power Ytterbium-doped fiber amplifier were performed.
3.1. Experimental setup
The setup is depicted in Fig. 5. A 90/10-tap-coupler was used to combine the signals from the NPRO and the ASE source, which was the same as described in section 2. Again, the ASE signal-to-fiber coupling was about 60 %. The port containing about 10 % of the NPRO power and 90 % of the ASE power was spliced to a second 90/10-tap-coupler, of which the backwards directed 10 %-port was used to monitor the backscattered signal. The seed monitor port contained 10 % of the power, while 90 % of the combined signal seeded the following fiber amplifier. Signal- and pump-beam were coupled into the active double-clad fiber, with nominal signal- and pump-core diameters of 5 μm and 125 μm, via a pump combiner. A fiber-coupled multi-mode diode provided a maximum pump power of 9 W at 976 nm.
3.2. Measurement method and results
The characterization of the amplifier was performed as follows. While the single-frequency signal from the NPRO remained at the same power level of 50 mW throughout the measurements, different amounts of ASE were artificially added. Hence, the ratio of the single-frequency signal and the ASE at the signal wavelength in the optical spectra, measured with a resolution bandwidth of 0.5 nm, was decreased down to 16.6 dB (see Fig. 6). Again, the ASE power within the Brillouin gain bandwidth was calculated from the measurement of the power and optical spectra at the 10 %-seed-monitor-port. Assuming a Brillouin gain bandwidth of 50 MHz, it varied between 14.5 nW and 365 nW and was limited by parasitic lasing processes. In Fig. 6 the optical spectra of the amplifier seed are plotted for no and three different power levels of ASE. The corresponding power values within the Brillouin gain bandwidth are given in Table 1. For each level of ASE power injected, the forward as well as the backward power and optical spectra were measured. In order to evaluate the evolution of the backscattered power and of the power of the Stokes-maximum, the power within the amplified narrow-linewidth signal was calculated from the measurement of the overall output power and the optical spectra. Figure 7(a) shows the evolution of the backscattered power with respect to the signal power for four different levels of artificially added ASE. The amplified signal power was limited in each case by parasitic lasing processes. Note that the threshold of parasitic lasing increased with increasing ASE power. No significant difference in the exponential rise of the backscattered power could be observed. Furthermore, the evolution of the Stokes-maximum was compared for the same power levels of injected ASE. It is shown on a logarithmic scale in Fig. 7(b) with respect to the signal power. Again, no significant difference in the rise of the Brillouin scattered power could be observed. The limitations of the experimental setup were, as mentioned above, the available ASE power and parasitic lasing of the fiber amplifier. However, the following conclusions can be drawn from the results. Comparing the evolution of the backscattered power and the power in the Stokes-peak for the three cases of different amounts of added ASE power yields no hint that the SBS-threshold was reached at different amplified signal power levels. For the sake of completeness it should be mentioned that when no additional ASE was injected, the amplifier was already limited at an output power of about 1.5 W. At this power level, the amount of Brillouin scattered power was still significantly lower than at an output power of 2.5 W, which could be extracted when more ASE was injected. However, the evolution of the overall backscattered power and the power in the Stokes peak was – according to Fig. 7 – identical for all levels of added ASE. Therefore, also for the case when no additional ASE was injected we do not expect a higher SBS-threshold.
Fig. 6 The optical spectra of the amplifier seed for four different power levels of artificially added ASE. The single-frequency signal power was kept constant throughout the measurements. Resolution bandwidth: 0.5 nm.
Fig. 7 (a): Backscattered power and (b): SBS-peak power with respect to the signal power for different ratios of single-frequency signal and artificially added forward ASE in the Brillouin gain bandwidth.
Table 1. The ratio of the single-frequency signal and the artificially added ASE in forward direction and corresponding power within the Brillouin gain bandwidth. The resolution bandwidth of the optical spectrum analyzer was set to 0.5 nm.
Secondly, setting up a different, more powerful ASE source will eventually yield power levels within the Brillouin gain bandwidth high enough to decrease the SBS-threshold. However, seeding a high power fiber amplifier with a signal from an intermediate amplifier that contains an ASE suppression lower than about 15 dB (OSA RBW: 0.5 nm) is a very unlikely, if not even pathological configuration, and the general effect has been demonstrated in section 2.
4. Numerical simulations
To verify the significance of the observed effect for future designing and modeling of single-frequency fiber amplifiers, we have carried out calculations using the numerical model presented in Reference [14]. There the evolution of the signal power (Ps), the pump power (Pp), the forward and backward ASE power ( ), and the Brillouin scattered signal power (PBS) were calculated along the fiber by solving a set of differential equations. A Runge-Kutta algorithm and a shooting method were used. For the description of the Brillouin scattered radiation a discrete number of spectral lines within the Brillouin gain frequency range (ΩBS) was implemented. These spectral lines were separated by a bandwidth ΔνBS. For the noise initiation of the SBS-process a distributed, non-fluctuating source model with spontaneously generated Brillouin noise power at different positions along the amplifier fiber was used. The noise photon power at the frequency νi of the i-th Brillouin line was given by
Here, h is Planck’s constant, νB the Brillouin shift frequency, ΔνB the Brillouin gain bandwidth, k Boltzmann’s constant, and T is the temperature in the fiber. In the differential equation for the power in the i-th SBS line, Γs accounts for the overlap of the guided LP01-mode and the doped step-index core region, N2 and N1 are the ion densities in the upper and lower energy levels, respectively, and are the emission and absorption cross-sections of the ytterbium doped fiber, α is introduced to account for background losses through fiber imperfections and Rayleigh scattering, and Aeff is the effective modefield area of the fiber. The last term in Eq. (2) accounts for the backward propagating ASE power at the Brillouin wavelength ( ), seeding the SBS process. Similarly to the Brillouin scattered radiation, the broadband ASE was described. A discrete number of spectral lines at wavelength λASEj, separated by a bandwidth ΔνASE was initiated by a noise photon power , with Planck’s constant h and c being the speed of light in vacuum. To account for the two possible polarization states, the factor of 2 was introduced.In Reference [14] it had already been shown that this numerical model is suitable to adequately simulate a single-frequency fiber amplifier, once the right fiber and amplifier parameters are implemented. Our aim was to show that there is a significant difference in the SBS power evolution whether a term accounting for backward ASE at the Brillouin wavelength is included in the calculation or not. Hence, our calculations do not resemble a particular fiber amplifier system, but they demonstrate the effect in general. The parameters used in our calculations are mostly taken from Reference [14] and can be found in Table 2. Representative results are shown in Fig. 8. The seed power in this case was 1 W and the pump light was counter-propagating to the signal. It can be clearly seen that the SBS threshold (defined as the signal power level where the Brillouin light reaches 0.01 % reflectivity) is increased by 14 % from 108 W to 123 W, when the last term in Eq. (2) was not included in the calculation. The power of the Brillouin scattered light decreased from 27.3 mW to 8 mW at a signal power of 117 W. This corresponds to a decrease by 71 %.
Fig. 8 Calculated Brillouin power with respect to the amplified signal power when the term accounting for backward ASE was included in the numerical simulation (black squares) and excluded (red circles). The dashed blue line corresponds to a reflectivity of 0.01 %.
Table 2. Simulation parameters for the numerical model. gB0 is the Brillouin gain peak value and cf the coefficient for the temperature induced Brillouin frequency shift [14].
5. Conclusion
In conclusion, we have demonstrated in a passive fiber that ASE within the Brillouin gain bandwidth can increase the strength of the Brillouin scattering process and therefore decrease the SBS-threshold, when it propagates in the same direction as the Brillouin scattered light. This statement is supported by an obvious increase in the strength of the exponential rise of the backscattered power as well as the power in the Brillouin peak. The fiber used in the experiments was about 335 m long, had a nominal core diameter of 4 μm, and was seeded with a single-frequency signal, provided by an NPRO. Different power levels of ASE within the Brillouin gain bandwidth were added in the backward direction of the fiber. Injecting 160.6 nW of ASE power within the Brillouin gain bandwidth decreased the signal power level at which the backscattered power reached a reflectivity of 0.1 % from more than 81 mW with no additional ASE by about 3 dB to less than 40 mW. The backscattered power and the power in the Stokes-peak at a signal power were both about 19 times as high, compared to the case, when no ASE was added. In a fiber MOPA system with gain factors of several 10 dB, the generated ASE in the backward direction can be quite high and therefore possibly seed the SBS process. The effect demonstrated in our experiments could contribute to the fact that increasing the seed power for a fiber amplifier increases its SBS threshold. Previously, this has been attributed only to the reduction of the gain factor. Moreover, we have investigated the eventuality that Rayleigh-backscattered ASE from a fiber-based pre-amplification stage could seed the SBS process of a fiber amplifier. These experiments were performed with a single-frequency signal and artificially added ASE in the forward direction, seeding a typical low-power fiber amplifier. No effect was observed decreasing the ratio of the single-frequency power signal to the ASE at signal wavelength in the optical spectrum to 16.6 dB (OSA RBW: 0.5 nm). As the effect depends on the strength of the Rayleigh scattered light and spurious reflections in the backward direction, and therefore on fiber composition and length, the obtained results are not representative for any arbitrary fiber amplifier. Nevertheless, a fiber amplification stage employing a comparable standard fiber should not show a performance degradation in terms of a lower SBS-threshold, if the seed contains ASE from a pre-amplifier; at least as long as the ASE suppression is higher than 15 dB (OSA RBW: 0.5 nm). The experimental results presented in this paper contribute to better understanding and modeling of the SBS-process in fiber amplifiers. Using a rate-equation model that had been previously proven to be able to adequately simulate single-frequency fiber amplifers, we verified the significance of the observed effect by modeling of a high-power single-frequency fiber amplifier. In the example shown, an increase of the SBS threshold by 14 % was found when no term accounting for ASE was implemented in the differential equation for the Brillouin power, compared to the calculation including this term.
Acknowledgments
This work was conducted in the framework of the Cluster of Excellence “Centre for Quantum-Engineering and Space-Time Research” (QUEST), funded by the German Research Foundation (DFG). We would like to thank H. Tünnermann for useful discussions.
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