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We report on theoretical and experimental investigations on spontaneous and stimulated Brillouin scattering during operation of a high-power single-frequency polarization-maintaining ytterbium doped fiber amplifier. For different amplifier configurations with co- and counter-propagating seed and pump radiation the evolution of Brillouin scattering spectra was investigated with a heterodyne detection scheme. Spontaneous Brillouin gain spectra at low powers were additionally investigated using a pump-probe technique. The data obtained from these experiments have been compared with a theoretical model based on coupled intensity equations. A Brillouin scattering suppression has been investigated theoretically and experimentally with externally applied temperature gradients along the fiber resulting in up to 3.5 dB suppression and 115 W of amplifier output power.
©2008 Optical Society of America
1. Introduction
In narrow-linewidth fiber optical communication systems and novel high-power rare-earth doped fiber amplifiers stimulated Brillouin scattering (SBS) is the most limiting effect in terms of power handling capacity [1,2]. Brillouin scattering (BS) is a nonlinear process that arises from interactions of acoustic phonons with optical signal waves and results in backscattered light shifted from the original signal by the acoustic wave frequency [3]. The Stokes frequency shift and spectral shape of Brillouin scattered light depend on the excitation signal frequency and fiber characteristics such as core dimensions and glass composition [4]. At low signal intensities spontaneous Brillouin scattering originates from thermally excited phonon fluctuations. Signal and backscattered waves can beat together and induce density variations by means of electrostriction. Signal light waves that are scattered off the resulting refractive index variation constructively add to the spontaneously generated Stokes wave and thus initiate a growth of SBS. At a certain intensity threshold SBS starts to grow rapidly and limits the transmitted signal power. The transition from spontaneous to stimulated BS is accompanied by gain narrowing of the Brillouin spectrum [3]. For single-mode fibers BS spectra have been investigated using experimental approaches such as pump-probe and heterodyne detection methods [4,5]. Theoretical models have been developed to describe its initiation and growth [3,6]. Introducing non-uniformities along the fiber by temperature and strain gradients or different doping materials and concentrations has been found to influence the Brillouin spectrum and the intensity threshold for SBS [7–9].
These techniques have been adapted to investigate and prevent SBS in high-power single-frequency large mode-area fiber amplifier systems. Temperature gradients induced by intense pump light substantially shift the centre frequency of the BS gain spectrum and therefore lower the overall Brillouin gain along the fiber [10]. Special fiber doping distributions have been developed to reduce the transversal overlap of optical and acoustic modes in the active fiber core region [11]. With nearly diffraction limited beam quality both techniques enabled an amplifier output power of up to 500 W. Simulations based on coupled intensity equations predict output powers in excess of 1 kW [11,12]. These simulations show good agreement with the experimentally observed intensity evolution of signal, pump and Brillouin scattered radiation. The spectral evolution of BS in such high-power fiber amplifier systems has, to the best of our knowledge, not yet been investigated neither experimentally nor theoretically.
In this paper we present experimental and theoretical studies on BS generated during high-power operation of a single-frequency ytterbium doped fiber amplifier system. For two different amplifier configurations with co- and counter-propagating seed and pump radiation the evolution of BS spectra was investigated using heterodyne detection [5]. The results for spontaneous BS gain spectra at low intensities were verified with a pump-probe technique [4]. Spectral and power characteristics of the fiber amplifier were compared with theoretical simulations using coupled rate-equations. The presented simulations and heterodyne detection system have been applied to investigate means to increase the SBS threshold by introducing temperature gradients along the fiber.
2. Experimental setup
2.1 Fiber amplifier and heterodyne detection system
A single-stage master-oscillator fiber amplifier system consisting of a non-planar ring oscillator (NPRO, Innolight Mephisto 2000NE) seed source and a polarization-maintaining large mode-area ytterbium doped fiber (Nufern, PLMA-YDF-20/400) provided the basis for the presented BS investigations. The seed laser emitted 2 W of continuous-wave output power at 1064 nm with a specified spectral linewidth of 1 kHz (measured over 100 ms). Approximately 60% of the seed power was coupled into the ytterbium doped core of the fiber, which had a specified diameter of 20.5 µm with a numerical aperture of 0.063. With a half-wave plate the linear polarized seed radiation was oriented to the birefringent axis of the fiber to obtain a polarized amplifier output. A Faraday isolator was installed to protect the NPRO against backward propagating light from the fiber amplifier. Pump light from a fiber coupled laser diode (Laserline, LDM 200-200, fiber ø300 µm, NA 0.22) was launched into the fiber cladding (ø400 µm, NA 0.46). The specified Yb2O3 doping concentration and absorption of this fiber were 0.8 wt.% and 1.7 dB/m at 975 nm resulting in ~95% of pump light absorption over a fiber length of 8 m. During amplifier operation an exponential temperature gradient is induced along the fiber proportional to the absorbed pump light. In order to prevent the fiber windings from heating one another, the whole fiber was coiled on a metal spool (16 cm diameter) with 10 mm distance between each winding. Both fiber ends have been polished with an angle of 8° to avoid laser oscillation through Fresnel reflections. Seed and pump radiation were separated with dichroic mirrors. The amplifier relative intensity noise (RIN) was monitored with a low noise photodiode in order to detect intensity noise induced by SBS. A schematic picture of the experimental fiber amplifier setup is shown in Fig. 1(a). Note that only one laser diode was used for either a co- or counter-propagating pump configuration.
Fig. 1. (a) Fiber amplifier setup for co- or counter-propagating seed and pump light. GS glass sheet, DC dichroic mirror. (b) Heterodyne detection system. GS glass sheet, DC dichroic mirror, IF interference filter.
A fraction of backward propagating light being reflected from a glass sheet was used for the detection of BS by monitoring the backward power and the heterodyne detection of RF spectra. The Brillouin frequency shift from the seed NPRO is approximately 16.2 GHz, determined by the seed wavelength 1064 nm, the optical refractive index of 1.45 and speed of sound in fused silica of 5.96 km/s [4]. With a fast photodiode (3 dB bandwidth 25 GHz) the beat signal between backscattered signal and a fraction of the NPRO seed beam could be detected. However, due to detector noise of this photodiode and the electronic spectrum analyzer at 16 GHz the BS spectra could only be detected close to the threshold of SBS. To improve the sensitivity of the heterodyne detection system and enable an investigation in the regime of spontaneous BS different measures have been taken (Fig. 1 (b)). Backward propagating light from the fiber amplifier was passed through an interference filter (IF, 10 nm transmission bandwidth at 1064 nm) to lower the ASE power on the photodiode. The filtered light was then amplified by a maximum of ~7 dB using a second fiber amplifier. At these low gain levels and signal intensities the amplifier did not show measurable effects on the spectral shape or width of the detected BS spectra. In front of the amplifier a Faraday isolator was placed in order not to couple light back into the main amplifier. With a second NPRO, frequency tuned close to the Brillouin frequency, a heterodyne detection with a low-noise photodiode (3 dB bandwidth 7 GHz) around 1.5 GHz was performed. The electronic spectrum analyzer was set to a resolution bandwidth of 200 kHz, sweep time of 50 ms and 100 times averaging. With a specified long term frequency stability of 1 MHz per minute the NPRO did not introduce measurable errors. Compared to the Brillouin spectral bandwidth in the MHz range the specified NPRO emission linewidth of 1 kHz is sufficiently narrow to neglect its influence on the detected heterodyne signals.
2.2 Pump-probe experimental setup
Important simulation parameters for the presented amplifier model are the shape, width and peak value of the spontaneous BS gain spectrum. In order to obtain accurate parameters a pump-probe measurement similar to the one presented in Ref. [4] was performed. The NPRO seed source was coupled into the active fiber as described above to generate Brillouin gain while no pump light was injected (Fig. 2). At these low signal intensities the heterodyne detection method was not sensitive enough to investigate the BS spectra. With a second NPRO coupled counter-directionally to the seed beam a frequency scan over the range of Brillouin gain was performed.
The transmitted probe intensity was monitored with a photodiode. Frequency tuning of the probe NPRO was done by slowly modulating its Nd:YAG crystal temperature. A frequency span of 0.8 GHz was scanned over 50 s with a resolution of approximately 1 MHz, mainly limited by the voltage modulation accuracy applied to the NPRO temperature driver. The linear polarization of both NPROs behind their respective isolators was oriented to the same birefringent fiber axis.
3. Rate-equations
A theoretical model based on rate-equations was solved under steady-state approximation to simulate the signal amplification in the fiber amplifier system according to Ref. [12]. In the so called localized, non-fluctuating source model the initiation of BS is described by a Brillouin photon scattered off a thermally excited phonon at the rear of the fiber [6,12]. A comparison of various SBS initiation models showed that in the range of the SBS threshold and below this is a good approximation [3]. In practice, the onset of SBS is usually detected by monitoring the backward propagating light power. This light consists not only of BS, but mainly amplified spontaneous emission (ASE) and some Rayleigh scattered light. For this reason terms for backward and forward propagating ASE were included in the model according to Ref. [13]. The following set of differential equations was solved numerically using a Runge- Kutta algorithm and a shooting method with the secant method for root-finding to obtain the seed, pump, ASE and BS signal powers (Ps, Pp, Pase and Pbs) along the amplifier fiber. Signals propagating in the forward direction were calculated in positive and in backward direction in negative z-direction.
The excited ion density N 2 is described by stimulated emission and absorption rates of all contributing signals and the spontaneous decay rate with the inverse fluorescence lifetime of 1/τ. Under steady-state approximation the time derivative of the inversion density dN2/dt equals zero. Emission and absorption cross-sections of the ytterbium doped fiber are σe and σa. The doping concentration of the ytterbium ions N 0 is assumed to be equal to the sum of ion densities in the upper N 2 and lower N 1 energy levels. In order to account for the overlap of the guided LP01 mode with the doped step index core region and the double-clad fiber pumping configuration the filling factors Γs and Γp are introduced for the seed and pump radiation. Background losses induced by fiber imperfections and Rayleigh scattering are αs and αp. For simplicity the overlap factor and background loss as well as the effective mode field area Aeff for the seed signal are assumed to be equal for ASE and BS. The broadband emission of backward and forward propagating ASE is described by a discrete number j of spectral lines. Each line at its wavelength λase is initiated by a noise photon power P 0=2hc/λase ·Δνase within the calculated linewidth Δνase. A similar description was used for the backward propagating BS signal with a discrete number i of BS lines separated by a linewidth Δνbs. These lines were calculated in the frequency range of BS gain which was described by the following Lorentzian shaped profile with peak gain value gB o and bandwidth of ΩBS.
The Brillouin frequency shift from the seed signal λs is defined by νB=2nva/λs with the optical refractive index n and the acoustic velocity va [4]. Temperature gradients ΔT along the fiber induced by absorbed pump radiation or externally applied temperature cause a linear shift of the centre frequency cf of the Brillouin gain profile [4,7]. The fiber temperature distribution was approximated according to Ref. [14] and the resulting frequency dependence was included in Eq. (6). The growth of BS is described by the interplay of seed and Brillouin scattered radiation with Brillouin and amplifier gain. The process initiation is approximated with a noise photon PN=hνB·Δνbs within the calculated linewidth as the boundary condition at z=(L) [15]. Parameters used for the simulations can be found in Table 1.
Table 1. Simulation parameters for rate-equation model.
4. Results
4.1 Pump-probe experiment
At low seed intensities without amplification through the Yb-doped fiber a spontaneous Brillouin gain spectrum is generated with a Lorentzian line shape [3]. By scanning of the probe NPRO emission frequency over this range of Brillouin gain these spectra could be detected. At maximum coupled seed power of approximately 1.25 W the power transmitted through the active fiber was measured to be 750 mW. The observed losses are mainly attributed to absorption of the seed beam. A Lorentzian shaped BS spectrum with a bandwidth of ~50 MHz full width at half maximum (FWHM) was measured at this seed power (Fig. 3 a).
Fig. 3. (a) Pump-probe Brillouin scattering gain spectrum measured at 1.2 W coupled seed power. (b) Brillouin scattering spectral width (FWHM) as function of coupled seed power.
Decreasing the seed power resulted in a linear broadening of the detected spectra up to ~57 MHz around 200 mW of coupled seed power (Fig. 3 b). With a linear fit of the obtained data a spontaneous BS gain bandwidth ΩBS≈58 MHz at zero seed power was estimated. A broadening of the detected spectral width by a depletion of seed radiation, as was reported in Ref. [4], was not observed in the probe power range from 5 mW to 50 mW. Nevertheless, a relatively low probe power of 10 mW was used for the presented experiments. The high transmission losses of the signal beam through absorption of the ytterbium ions and the resulting effects on the transmitted probe power prevented a determination of the Brillouin gain value gBo.
4.2 Fiber amplifier and heterodyne detection
The presented single-frequency master-oscillator fiber amplifier system generated a maximum output power of 92 W in counter-propagating and 35 W in co-propagating pump configuration with slope efficiencies of ~77% with respect to the launched pump power. Coiling the fiber on a 16 cm diameter spool sufficiently suppressed higher-order modes resulting in a measured beam propagation factor M2 of better than 1.15 [16]. At maximum output powers the amplified beam showed an ASE suppression of 44 dB in counter-propagating and 42 dB in co-propagating pump configuration, calculated by integrating over measured optical spectra. A polarization extinction ratio in the range of 20 dB was measured with a rotary polarizing beam splitter.
By monitoring the RIN of the amplified output beam during amplifier operation SBS can be detected (Fig. 4(a)). The origin of SBS induced broadband signal intensity noise has been attributed to Stokes and anti-Stokes Brillouin scattering [17]. With a low noise photodiode the RIN at 5 MHz was monitored over the whole amplifier power range with a photocurrent kept constant at 3 mA (Fig. 4 (b)). At low amplifier output powers a constant RIN around -156 dB/Hz was detected. In the regime of SBS the intensity noise started to increase exponentially with threshold levels around 50 W for counter- and 25 W for co-propagating pump light.
Fig. 4. (a) Relative intensity noise spectra of amplifier output beam at 30 W and 54 W in counter-pump configuration and NPRO. (b) Relative intensity noise at 5 MHz versus amplifier output power for co- and counter-pump configuration.
With the presented heterodyne detection system the BS spectra could be investigated nearly over the entire amplifier power range. Two typical heterodyne signals recorded at 5 W and 92 W are plotted in Fig. 5. As has been reported for passive fibers in Ref. [3] the BS spectra showed a transition from a Lorentzian shape in the low Brillouin gain regime to a Gaussian shape towards higher amplifier intensities through spectral gain narrowing. This effect resulted in narrowing of the measured spectral widths (FWHM) from 58 MHz down to approximately 15 MHz for counter- and 13.5 MHz for co-propagating pump light (Fig. 6). In this range a saturation of the spectral narrowing process was observed which is caused by seed signal depletion and represents a transition from spontaneous to pure stimulated BS, also indicated by the observed Gaussian spectral shape [5]. The spectral width was determined with a Voigt fitting function applied to the experimental data.
Fig. 5. Heterodyne detection of the Brillouin scattering spectra at 5 W and 92 W of fiber amplifier output power.
The detected backward propagating light power showed a linear increase up to amplifier output powers of approximately 80 W for counter- and 32 W for co-propagating pump light (Fig. 6). In this regime mainly backward ASE and Rayleigh scattered signal is detected. At higher output powers BS starts to rise over these contributions resulting in an exponential increase of backward propagating light power. A characteristic that is typically regarded as the threshold of SBS. Increasing the amplifier pump power even more resulted in damage of the cores at both fiber ends, most likely due to chaotic SBS. Either monitoring the backscattered light power or more sensitively the amplifier output RIN can be utilized to detect SBS. The observed lower SBS threshold for co- compared to counter-pumped amplifiers can be explained by the different gain, signal intensity and temperature distributions along the amplifier fiber. High amplifier gain at the seed input side of the fiber in co-pumped systems rapidly increases the signal intensity to a critical level to generate SBS, which itself experiences strong laser gain to build up. Additionally in co-pumped configuration the temperature gradient induced by absorbed pump light is less pronounced at the rear of the fiber where most of the SBS radiation is generated and consequently the temperature induced frequency shift of the BS gain spectrum is lower [10].
Fig. 6. Brillouin scattering spectral width (FWHM) and backward propagating light power as function of amplifier output powers for (a) counter- and (b) co-propagating pump configuration. Scattered plots for experimental and line plots for simulated data.
The simulated results for the signal and pump powers were in good agreement with the experimental results. In order to obtain a reasonable spectral resolution, one hundred spectral lines have been calculated for each back- and forward propagating ASE and the Brillouin scattered signal. With the peak Brillouin gain coefficient gBo set to 2.4·10-11 m/W the increase of simulated backward propagating ASE together with the BS power showed a very good agreement with experimental data for either the co- and counter-propagating pump configuration (Fig. 6). The initial parameter for the bandwidth ΩBS of the Lorentzian shaped spontaneous BS gain profile was set to 58 MHz as was previously determined with the pump-probe experiment. Results for the simulated evolution of the spectral width with respect to the amplifier output power showed a gain narrowing progression very similar to the one observed experimentally.
4.3 Temperature gradients
The simulations presented in the previous sections comprised an estimated temperature distribution along the amplifier fiber proportional to the absorbed pump light [14]. With a maximum launched pump power of ~125 W the SBS suppression caused by temperature gradients along the 8 m long fiber was calculated to be in range of 0.5 dB with ~20°C temperature difference between both fiber ends. Therefore only a little effect on the shape and evolution of the BS spectra and power was observed. However, by externally applying temperature gradients the SBS can be significantly suppressed [18]. To investigate this effect a 2 m long section approximately 40 cm from the rear of the amplifier fiber was coiled on a metal spool and heated on a hot plate. These investigations were carried out for the amplifier in counter-propagating pump configuration only. At a fixed amplifier output power of 70 W the hot plate temperature was slowly increased and the BS spectra were detected by heterodyne detection. At hot plate temperatures below 30°C only one peak was observed around 1.29 GHz. Towards higher temperatures a second peak evolved reaching a peak-to-peak separation of ~113 MHz at a hot plate temperature of 85°C (Fig. 7 a). The temperature dependent Brillouin frequency shift cf was estimated to be ~2.25 MHz/K by fitting the spectral peak separation with respect to the measured fiber spool temperature (Fig. 7 b). Using this value the BS spectra were simulated and showed a good agreement with the experimentally observed spectra, with a theoretically applied temperature at the heated fiber section set to 69°C (Fig. 7(a)). This temperature difference can be attributed to the thermal contact and resistance between the heated metal spool and the amplifier fiber. The simulated temperature distribution along the fiber together with a temperature profile with no heat applied is plotted in Fig. 8(a).
Fig. 7. (a) Measured and simulated Brillouin scattering spectra at 70 W of amplifier output power at 85°C hot plate temperature. (b) Frequency separation between Brillouin scattering spectral peaks with respect to temperature of heated fiber section.
At a hot plate temperature of 85°C the pump power was increased to investigate the resulting suppression of SBS (Fig. 8(b)). The backward propagating light power increased linearly up to amplifier output powers of 115 W and then started to increase exponentially indicating again the onset of SBS. Compared to the previously determined SBS threshold around 85 W with no temperature gradients applied, the output power could be increased by approximately 1.3 dB. Interestingly, the RIN of the amplifier output detected at 5 MHz showed an exponential increase in the same power range around 115 W. With no temperature applied this increase has been detected already at 50 W of amplifier output power, corresponding to a SBS noise threshold suppression of 3.5 dB.
Fig. 8. (a) Simulated temperature distribution along the amplifier fiber at 70 W of output power and hot plate switched off and at 85°C. (b) Backward propagating light power and amplifier RIN at 5 MHz as function of amplifier output power with hot plate at 85°C and switched off.
4. Conclusion
We have presented theoretical and experimental investigations on the spectral and power evolution of BS in a high-power single-frequency ytterbium-doped polarization-maintaining fiber amplifier system in counter- and co-propagating pump light configuration. The fiber spontaneous Brillouin gain profile was determined using a pump-probe technique and showed a Lorentzian shape with a bandwidth of 58 MHz. With a heterodyne detection system the BS spectra were detected over the entire amplifier power range. A transition from Lorentzian to Gaussian shaped profiles was observed with increasing output powers together with a gain narrowing from 58 MHz down to approximately 13–15 MHz bandwidth depending on the pump configuration. Monitoring the backward propagating light power an exponential increase was detected at amplifier output powers higher than 80 W for counter- and 32 W for co-pumping indicating the onset of SBS. An influence of SBS on the relative intensity noise in the MHz frequency range was observed at 50 W and 25 W. By applying a temperature profile along the amplifier fiber the BS spectra could be significantly distorted enabling SBS free operation with 115 W of output power. All experimentally determined spectral and power characteristics of the fiber amplifier have been compared with simulations based on a rate-equation model and showed very good agreement. With the presented theoretical and experimental methods the evolution of BS in high-power fiber amplifiers can be well characterized and reliable predictions for SBS thresholds in comparable amplifier systems can be made.
Acknowledgments
The authors thank the German Research Foundation for funding the Cluster of Excellence Centre for Quantum Engineering and Space-Time Research QUEST.
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