Open Access
Add to BibSonomyAbstract
We demonstrate a technique for SBS reduction in a nanosecond Yb-fiber amplifier by imposing 1.19 GHz/ns frequency chirp on the seed pulses with a pulse-driven phase modulator. A nearly 9-fold increase in the SBS threshold was observed for 8.4 ns pulses. SBS threshold data and transient SBS gain for various degrees of chirp are reported and compared with theoretical calculations. We further demonstrate the recovery of the input narrowband spectrum by applying an opposite chirp with a second phase modulator after the amplification.
© 2016 Optical Society of America
1. Introduction
Fiber laser/amplifier systems are very attractive for remote sensing, especially from mobile platforms due to their ruggedness, efficiency, versatility and single mode operation. Typical pulsed lidars applications, require nanosecond pulse durations and millijoule level energies which result in megawatt peak powers. At this power level non-linear processes present a considerable challenge for fiber amplifiers. Stimulated Brillouin scattering (SBS) is typically the lowest threshold nonlinear interaction for nanosecond pulses [1], which limits power-scaling of these systems. The most common approaches for mitigating SBS involve increasing the effective mode area and spectrally broadening the SBS gain resonance. Both techniques are often used together for maximum effectiveness.
In the case of steady state SBS, it has been demonstrated that the gain is inversely proportional to the bandwidth [1,2]. While the transient SBS case is more complex to treat quantitatively, the qualitative behavior is essentially the same: gain decreases with increasing bandwidth. Various techniques have been demonstrated for CW amplifiers. The SBS gain peak can be broadened by varying the SBS shift distribution along the fiber by varying the dopant concentration [3], strain [4], or temperature [5]. Changing the acoustic guiding properties of the fiber has also been suggested [6]. All of these approaches have been primarily demonstrated with CW systems and have not been shown to reach bandwidths in the multiple GHz range required for effective suppression of SBS in nanosecond fiber amplifiers.
Spectral broadening of the master oscillator has proven to be a most effective approach for SBS mitigation in nanosecond fiber amplifiers. Techniques for spectral broadening reported so far impart a random [7] or pseudo-random phase [8,9] on the seed pulse (for pseudo-random modulation in CW case also see [10]). In CW case, such modulation results in discrete spectrum [9,11], with the number of lines related to the number of bits in the pattern. In the pulsed, the spectrum becomes a convolution of the time envelope spectrum and the modulation spectrum leading to broadening of the discrete lines. Overall the power remains distributed unevenly over the laser bandwidth with spectral peaks having more energy than would be expected from the average spectral envelope. Such oscillatory spectral features increase the likelihood of four-wave mixing in the power fiber amplifier.
In this work we propose an alternative modulation scheme that achieves an approximately linear frequency chirp. This approach produces a non-oscillatory spectrum, which intuitively, should be beneficial for avoiding four-wave mixing. Another benefit is that the driving signal is easier to scale in amplitude for driving a bulk phase modulator. As we show in our proof-of-principle experiment, this allows applying an inverse of the original phase modulation after amplification to recover the original master oscillator narrowband spectrum. Such narrow spectra are necessary for a number of lidar applications that require resolution of a few 100s MHz or better, such as Doppler lidar, HSRL (high spectral resolution lidar) and some DIAL (differential absorption lidar) applications [12].
SBS suppression using a linear frequency chirp generated by sweeping frequency of a single-mode semiconductor laser with drive current modulation has been reported previously [13–15]. Chirp rate of up to 70 GHz/µs was reported for this system [14]. However, to the best of our knowledge the technique has not been demonstrated with nanosecond pulsed amplifiers, where chirp rates on the order of GHz/ns are required. Reference [15] describes a pulsed system with approximately 1 µs pulse duration and a maximum chirp of 5 GHz/µs. While the pulsed operation is significant for the amplifier dynamics, the SBS in this amplifier can be understood as quasi-steady state, considering the pulse duration of 1 µs is considerably longer than phonon lifetimes (2-10 ns) as well as fiber transit time of 87 ns. On the other hand with a pulse duration of only a few nanoseconds, SBS can no longer be treated as steady state.
2. Experimental setup
For this experiment a two-amplifier-stage MOPA (master oscillator power amplifier) fiber laser was constructed, as shown in Fig. 1. The master oscillator (MO) consists of a DFB (distributed feedback) diode laser, a phase modulator, and a semiconductor optical amplifier (SOA), both pulsed by modulating their drive currents (for discussion of the MO architecture see [8]). The 1063-nm DFB is electrically driven to deliver 60 ns pulses (FWHM) with a repetition rate in the range 10-1000 kHz. A majority of the measurements presented here were performed at 100 kHz with the exception of those incorporating a bulk phase modulator, which were performed at 20 kHz. The SOA is modulated at the same rate as the DFB, but with a much shorter pulse duration, typically in the 1.5-20 ns range. The results presented here were taken with the MO pulse duration set to 8.4 ns. The timing of the SOA with respect to the DFB is optimized to yield the most stable single frequency operation and time envelope. The fiber-coupled phase modulator for generating the chirp is placed between the DFB and the SOA. The two amplifier stages comprise 3 m of single mode 11-µm core, 0.075 NA, Yb-doped double-clad, polarization-maintaining fiber from Nufern (PLMA-YDF-10/125), pumped with 976 nm pump diodes. The fiber has about 4.8 dB/m pump absorption near 976 nm and about 1 dB/m core absorption near 1063 nm. A 10/90 tap coupler is inserted before the second stage to monitor the SBS. The fiber modulator was Photline NIR-MPX-LN-0.1. The maximum peak RF drive voltage, at which it was operated in this experiment, exceeded its rated voltage of 20 V by a factor of seven.
The driver for the phase modulator consists of a pulse amplifier with a narrow bandpass filter (50 MHz resonance frequency) at the output. The filter serves two purposes: impedance matching and converting an amplified pulse into a damped sine wave. By timing a maximum or minimum of the modulator drive voltage to coincide with the MO pulse, as is shown in Fig. 2, the time dependence of the phase approximates a parabola over the duration of the pulse yielding a nearly linear chip.
Fig. 2 Measured phase modulator drive voltage and seed laser pulse intensity profile (peak normalized), reflecting relative time position inside the modulator.
3. Frequency chirp
As mentioned in the previous section, an approximately linear frequency chip is produced by driving the phase modulator with a damped 50 MHz sine wave. Figure 3 shows the fiber-coupled modulator drive voltage and its derivative, both normalized by the nominal Vπ of the modulator (Vπ is the voltage that produces a phase shift of one π), which is 2.5 V for the fiber modulator used. Clearly, increasing the modulator phase amplitude by increasing the drive voltage amplitude increases the chirp, which, in turn, results in more SBS suppression. However, beyond certain point further increase in voltage becomes limited by the driver output capability or modulator damage. In the case of the fiber-coupled modulator, we were limited to a drive amplitude of around 150 volts. Specifically, we observed a significant loss of transmission through the modulator when the voltage is increased above 150 V - 250 V, with the onset varying significantly between a few modulator units that we tested. The loss in transmission appear to be instantaneous and reversible (after brief operation). However, we did not conduct life-time study, instead choosing to limit the amplitude to below 150 V to avoid any possibility of damage. The underlying mechanism for this behavior is not understood at the present time. However, we can speculate that for the electric fields developed in the modulator the ferroelectric domain reversal either by the electric field directly [16] or by ultrasound induced piezoelectrically [17] may be a concern. For the bulk modulator, which will be detailed later, the chirp was limited by the driver capability.
Fig. 3 Fiber modulator phase (drive voltage normalized by nominal Vπ = 2.5 V) and its derivative corresponding to the instantaneous frequency shift. The dashed vertical lines indicate an area of approximately linear chirp where the light pulse was placed.
Another way to increase the chirp is to increase the modulation frequency. Since the instantaneous frequency is the derivative of the phase, increasing the modulator drive frequency also yields larger chirp, provided, the pulse duration does not exceed half of the oscillation period of the drive voltage. However, the chirp becomes increasingly non-linear (sinusoidal) as this limit is approached and spectral broadening reaches a maximum at the limit. If areas of the maximum/minimum in the frequency shift are allowed to overlap with the pulse, this results in a distinct peaking at the extremes of the spectral shift and corresponding peaking in the SBS gain spectrum. However, if the MO pulse duration is allowed to be shortened simultaneously, further increase in chirp may be possible with potential benefit to SBS, provided other non-linearities can be kept at bay.
The instantaneous frequency of the master oscillator was measured by recording a heterodyne signal on a fast photodiode and taking a Hilbert transform [18]. In the absence of the modulator, both DFB laser and the SOA contribute a measurable chirp due to the carrier density and temperature dependence of the index of refraction of the semiconductors [19]. Figure 4 shows the measured instantaneous frequency of the DFB laser with the modulator turned on and turned off. As seen from the figure, the instantaneous frequency induced by the modulator mirrors the derivative of the drive voltage given in Fig. 3. Also seen in the figure is a negative chirp for the majority of the DFB laser pulse duration. To maximize the combined chirp of the MO, SOA was timed to coincide with the negative slope of the instantaneous frequency contributed by the modulator (dashed lines in Fig. 4). However, if needed, our MO configuration allows for easy inversion of the chirp by timing the optical pulse to coincide with the positive rather than the negative slope of the the instantaneous frequency (see Fig. 3). There are competing physical arguments for using positive or negative chirp. As noted by [15], when the chirp broadening exceeds the Brillouin shift, a positive chirp may lead to seeding of SBS with Rayleigh scattering. On the other hand for short pulses self-phase modulation (SPM) adds a positive chirp which would lead to spectral narrowing in the negative chirp case.
Fig. 4 Heterodyne measurement of the instantaneous frequency of the pulse-driven DFB laser with and without driving the phase modulator (42 V peak-to-peak modulator voltage). Dashed lines indicate the section later gated with an SOA.
The instantaneous frequency of the entire MO (DFB, modulator and SOA) was measured in the same fashion: taking the Hilbert transform of the heterodyne signal. The results are shown in Figs. 5 and 6. As is seen in Fig. 6, the chirp changes linearly with the modulator peak-to-peak voltage (R2 = 99.9% of the linear regression shown). Due to the bandwidth limitation of our heterodyne measurement it was not possible to perform complete pulse frequency measurement at the maximum modulator driver output. Therefore, this value was obtained by linear extrapolation. Thus, by tuning the modulator driver output voltage, the master oscillator produced pulses with −0.11 GHz/ns chirp with the modulator off and up to 1.19 GHz/ns chirp at a maximum driver voltage dictated by an increasing transmission loss in the modulators we tested. A practical way to increase the chirp beyond this limit would be to use two or more modulators in sequence. In fact, new laser designs in our lab that utilize both of the scaling approaches, two modulators in sequence and higher frequency with a shorter laser pulse, achieve spectral broadening significantly in excess of the Brillouin shift and what was demonstrated in this experiment.
Fig. 5 Heterodyne measurement of the instantaneous frequency of the master oscillator (DFB laser, modulator and SOA) for 42 V peak-to-peak modulator driving voltage. Dashed line is the linear regression of the measurement.
Fig. 6 Measured master oscillator chirp as the function of the modulator driver peak-to-peak voltage.
4. Transient SBS gain
Transient SBS gain measurements were conducted on the system described above with the second stage gain fiber unpumped. Light from a tunable CW DFB diode laser was launched into the second amplifier stage in the counter-propagating direction to probe the SBS gain induced in the fiber by forward-propagating laser pulses. The SBS Stokes wave was then detected with a photodiode through a 10/90 tap coupler inserted in front of the second stage gain fiber (see Fig. 1). The resulting SBS signal was time-gated with respect to the forward-propagating pulse, such that the measured signal was derived from the first meter of the second stage gain fiber. This limited the effect of attenuation in the unpumped gain fiber. The CW DFB laser was frequency-scanned to map out the SBS gain spectra. The strength of the SBS signal was recorded versus the relative wavelength offset from the SBS peak center wavelength for different chirp rates. The signal measured with the CW laser sufficiently far from the SBS resonance was taken to be unity gain.
As anticipated, the width of the transient gain (Figs. 7 and 8) increases linearly with the frequency chirp (R2 = 99.9% for linear regression shown in Fig. 8) and is, as expected, approximately given by the product of the chirp rate and the pulse duration. The SBS gain spectrum reaches a full width half maximum of 9.4 GHz at the maximum chirp of −1.19 GHz/ns. At the same time, the logarithm of the peak SBS gain is approximately inversely proportional to the chirp rate (Fig. 9). For comparison a transient gain calculation is also shown in Fig. 9 and its details are discussed in the following section.
Fig. 7 Measured transient SBS gain spectra for 8.4 ns pulse duration, 0.58 µJ pulse energy and 11-µm core diameter double-clad Yb fiber.
Fig. 8 Full width at half maximum of the logarithm of SBS gain versus frequency chirp for 8.4 ns pulse duration, 0.58 µJ pulse energy and 11 µm diameter core double-clad Yb fiber.
Fig. 9 Experimental and calculated logarithm of the peak SBS gain versus inverse of chirp for 8.4 ns pulse duration, 11-µm diameter core double-clad Yb fiber and three pulse energies: 0.29 µJ, 0.43 µJ and 0.58 µJ.
5. Transient SBS gain calculation
To perform the transient SBS gain calculation versus chirp shown in Fig. 9, we start with a one-dimensional form of the slow envelope approximation [2,20]:
where v is group velocity, Ep is the forward propagating (pump, i.e. the signal of interest) field envelope, Es is the Stokes field envelope, ρ is the material density fluctuation (the sound wave), Γ is the Brillouin resonance width, k1 and k2 are gain coefficients for the sound and the light waves respectively and f is a noise source term that describes thermal excitation of acoustic waves. f is usually treated as Gaussian random process (white noise) characterized by a parameter Q [20]:where k is the Boltzmann constant, T is the temperature, ρ0 is material density (2210 kg m−3 [1]), vs is the speed of sound (5960 m s−1 [1]) and A and Δz are the cross section area and the length of the interaction region respectively. Gaussian random process has constant power spectral density equal to Q. It should be noted that there are two alternative definitions of complex intensities in Eq. (1-3), for instance [2,20]. We follow the convention of [2]. Thus, Eq. (4) was converted to this convention. The gain coefficients k1 and k2 can be expressed in terms of SBS parameters that are typically found experimentally, resonance width, Γ, and steady state gain g0 [2]:where γ is the electrostrictive coupling constant, n is the index of refraction, c is speed of light and λ is the wavelength. Thus, we can write [2]: where ε0 is the vacuum permittivity. We have not performed CW SBS measurements to determine Γ and g0 for the fiber used. The literature values for both vary over a wide range, g0 = (2-5) 1011 m/W [1,21] and Γ = 2π (58-68) MHz for Ytterbium active fibers at 1064 nm [22,23]. While our transient gain measurement is not sufficient to uniquely determine both parameters, upper range values for both, g0 = 5 1011 m/W and Γ = 2π 68 MHz, better describe our experimental results. Therefore, these values will be assumed throughout.In the case of the transient gain measurement, further simplifications can be made. Since the measured gain is low and Yb absorption also low (~1 dB/m), the pump pulse can be assumed to be undepleted and Eq. (1) can be replaced with:
Next, we can ignore the thermal noise term, f, in the Eq. (3), since the CW Stokes seed of approximately 1 mW results in gain which is significantly larger than this term. One can see this by evaluating both right hand side terms of Eq. (3). For 0.58 µJ, 8.4 ns pump, 1 mW Stokes and 300 K, the first term evaluates to 8.6 103 kg m−3 s−1 and the second term evaluates to 4.8 kg m−3 s−1. We have taken into account that only the spectral components of the noise term f that fall within the Brillouin resonance width would contribute. Ignoring f also leads to ρ*(0,z) = 0 initial condition, which can be seen by examining Eq. (3) in the absence of pump light.
Next, we note that the fiber transit time of 14.5 ns is longer than the pulse duration. Thus, we can introduce a simplification of treating the fiber as infinitely long. As a result we can see that our initial conditions and the drive term Ep in Eqs. (2) and (3) for two consecutive times t1 and t2 are only different by the shift of Ep by the distance (t2-t1)v. Thus, we can look for the solution to Eqs. (2) and (3) in the form:
At first glance Eqs. (9) and (10) look counter to what one would expect for the Stokes and sound waves. However, we have to remember that the phase velocity relationship was already used in the derivation of the Eqs. (1)-(3). ρ* and Es describe the evolution of the amplitude envelopes of each wave driven by the forward propagating Ep. Under the assumptions of undepleted pump and long fiber, it is easy to see that this growth should be the same (and following the pump pulse) for any two positions of the pump pulse in the fiber. In other words Stokes and sound amplitude envelop growth appear as propagation in the same direction as the pump pulse per Eqs. (9) and (10). Finally, for the still unconvinced we can note that solution in the form Eqs. (9) and (10) is found and satisfies the initial conditions. Substituting Eqs. (9) and (10) into the Eqs. (2) and (3) leads to a pair of ordinary differential equations: We can further scale ρ* by a constant as:to explicitly express the interaction in terms of g0 and Γ. Thus, from Eq. (7) and Eqs. (11)-(13) we have:Equations (14) and (15) can be solved with publicly available integrators such as zvod [24]. Taking g0 = 5 10−11 m/W and Γ = 2π*68 MHz, a core diameter of 11 µm, a pulse energy of 0.58 µJ, and a super Gaussian (exp(-αt8)) temporal profile with a 8.4-ns FWHM duration, we can calculate the transient gain for the same values of chirp as the experiment (Fig. 7) in the range −0.11 GHz/ns to −1.19 GHz/ns.
Figures 10 and 11 show the growth of the Stokes wave calculated for several values of chirp and two values of frequency offset from SBS line center, 0 and 250 MHz respectively. While these dynamics are not measured in our experiment, they are illustrative of the underlying physics. Comparing the results for the seed with 0 and 250 MHz offset from SBS line center, an intuitive picture emerges: amplification mostly occurs during the portion of the pump pulse when the instantaneous frequency is in resonance with the seed.
Fig. 10 Calculated growth of the Stokes wave over the duration of the forward propagating 0.58 µJ, 8.4 ns (FWHM) pulse for 11 µm core diameter fiber for several values of frequency chirp and 0 MHz frequency offset of the Stokes seed from the resonance center. The assumed 8.4 ns pulse profile is shown in black.
Fig. 11 Calculated growth of the Stokes wave over the duration of the forward propagating 0.58 µJ, 8.4 ns (FWHM) pulse for 11 µm core diameter fiber for several values of frequency chirp and 250 MHz frequency offset of the Stokes seed from the resonance center. The assumed 8.4 ns pulse profile is shown in black.
In our experiment, we only measure SBS gain for each value of chirp. In Figs. 10 and 11 this gain is calculated as the ratio of Stokes intensities after and before the arrival of the forward pulse. The calculated gain spectra are shown in Fig. 12 and are in good qualitative agreement with the experimental data displayed in Fig. 7.
Fig. 12 Calculated logarithm of SBS gain spectra for 11 µm core diameter, 0.58 µJ, 8.4 ns pulse for several values of frequency chirp.
As can be seen from the simulated spectra in Fig. 12, the transient SBS gain peak is broadened proportionally with increasing chirp rate and the maximum gain is reduced approximately exponentially. For a more direct comparison with the experiment the calculated logarithm of gain is also plotted against the inverse chirp rate in Fig. 9 for three pulse energies: 0.29 µJ, 0.43 µJ and 0.58 µJ. The calculation is in qualitative agreement with the experiment. However the gain values are somewhat underestimated at the low values of chirp.
6. Fiber amplifier SBS threshold
To measure the fiber amplifier SBS threshold, the pump power of the second stage was gradually increased until the threshold condition was reached. The output from the first stage was kept fixed at 0.58 µJ. The tap in front of the second stage in the backward direction (see Fig. 1) was connected to a spectrum analyzer to observe both the signal scattering (Rayleigh and SBS) and the amplified spontaneous emission (ASE). For the purpose of these measurements, 10 dB above ASE was considered to be the SBS threshold condition (Fig. 13). Because the 10 dB value is arbitrary, we also present results for 20 dB to demonstrate that the resulting amplifier threshold power levels are affected only slightly by this substantial change in the threshold condition definition. This definition of threshold becomes problematic once the amplified pulse spectrum becomes sufficiently broad for Rayleigh and Brillouin peaks to overlap. However in our experiment the spectral width is less than the ~16 GHz Brillouin shift and we see only a slight overlap at the maximum chirp of −1.19 GHz/ns. We note an apparent SBS peak shift at the maximum chirp rate and pump power in Fig. 13. Since we used a negative chirp, seeding of SBS with Rayleigh scattered light is not possible and what other coherent interaction may contribute to this behavior is not clear to us. Other than attributing this change to the Rayleigh scattering and SBS peaks overlapping with increasing bandwidth, this behavior remains unexplained.
Fig. 13 Optical spectrum analyzer spectra at threshold, defined by the SBS peak height of 10 dB above the back-propagating ASE in the 2nd amplifier stage.
Because of the difficulty in defining the SBS threshold there are alternative definitions in the literature. One common approach (see for instance [15]) is to define the threshold by equality of SBS and Rayleigh spectral peak heights. The issue with this approach is that the Rayleigh peak also includes back reflections from other components in the amplifier such as pump combiners etc. Also the Rayleigh scattering from the fiber itself is dependent on the index non-uniformity and varies from fiber to fiber. Ultimately, none of these have physics linking them with the SBS process making this definition practical rather than physics-based. Our definition of threshold is based on the notion that SBS in a fiber amplifier is started form ASE. To substantiate this notion, we can again evaluate the right hand side terms in Eq. (3). Taking a typical value of 3 μW/nm near 1063 nm for our amplifier, we get 7.6 kg m−3 s−1 versus 4.8 kg m−3 s−1 for the thermal noise term f. The two terms are of the same order of magnitude, so strictly neither can be simply ignored. Since ASE grows with pump power we can expect one or the other term to dominate under different pumping conditions with ASE dominating at the higher pump powers. Additionally ASE propagating in the cladding may contribute to the initial growth of the acoustic wave.
Following the notion of SBS initiation with ASE we can associate SBS gain with our threshold definition. Because of the signal accumulation in the spectrum analyzer, the measured spectrum is averaged over the laser repetition rate period. The amplifier is continuously pumped, thus the ASE is present throughout the period. At the same time SBS only happens as the laser pulse traverses the amplifier. The majority of the SBS light only comes from the area near the output of the amplifier where the laser pulse is the most intense. Assuming that traversal of this area results in approximately 10 ns duration of the SBS signal, we can equate the 10 dB threshold definition on the spectrum analyzer to the maximum transient SBS gain of approximately 104 at the amplifier exit, also taking into consideration the 100 kHz laser repetition rate.
The measurements of the threshold dependence on chirp rate using the 10 dB threshold criterion are shown in Fig. 14 along with a 20 dB result for comparison. The 20 dB results show a very similar dependence on chirp as the 10 dB results, but obviously lie somewhat higher on the pulse energy scale. As can be seen from the 10 dB data, the threshold power and, thus, the amplifier power handling capability, have increased 8.8-fold at the maximum chirp of −1.19 GHz/ns in comparison to the unmodulated operation.
Fig. 14 SBS threshold (10 dB or 20 dB above ASE, see Fig. 13) versus master oscillator frequency chirp.
The results reported in reference [15] for 1 μs pulses also showed a 9-fold increase in threshold, but at a chirp rate 240 times lower than reported here. This seemingly lower effectiveness of chirp in our experiment is easy to understand if we note that the peak intensity in the core at the threshold is also 170 times higher in our case in comparison with the 1 µs pulse case in [15]. Overall, the comparison between the two experiments is a little tenuous, since the experiment in [15] is closer both in terms of implementation and SBS regime to the earlier CW work from that group [13,14] than to the experimental approach and conditions presented here. Nevertheless, even for such vastly different conditions and different definition of threshold between the two experiments, factors of 240 and 170 still suggest possibility of close to linear scaling with chirp. Obviously, only a more detailed theoretical analysis could make this conclusion less speculative.
The results of the model calculations are also shown in Fig. 14. As discussed earlier, the 10-dB threshold definition approximately corresponds to a maximum transient gain of 104. Similarly a 20- dB threshold approximately corresponds to a gain of 105. Using these gain values we calculate SBS threshold versus chirp with the approach described in the previous section. While the calculated threshold dependence on chirp rate is close to linear, the measured dependence is nonlinear and grows slower with chirp than the calculation. Overall, the threshold trend and power levels are predicted encouragingly well by this simple model giving some credence to the idea that SBS is initiated with ASE. It is worth noting that no adjustable parameter was used to obtain these calculation results.
The simplified transient gain model describes earlier, Eqs. (11) and (12), is not strictly valid for describing a pumped amplifier case. The undepleted pump approximation is no longer valid once we introduce amplifier gain, as well as ASE may or may not be the dominant Stokes seed, so that thermal fluctuations cannot strictly be ignored. However, as comparison with the experiment demonstrates, the model still provides reasonable results, albeit experimental threshold grows slower than linear as predicted by the model. There are two physical mechanisms omitted by the model that may be particularly relevant to the slower growth: pulse temporal profile evolution and self-phase modulation (SPM). At higher pulse energies pulse reshaping is expected to be more pronounced and may lead to pulse shortening with a corresponding increase in intensity and reduction in bandwidth, due to chirp linking pulse time envelop and spectrum. SPM introduces a positive chirp, which would be subtracted from the negative chirp of our seed. Either one of these effects or both may be responsible for the sub-linear increase in threshold with chirp observed in the measurements.
For a practical system, the SBS threshold as defined here is unlikely to be an operational limit of an amplifier as it would greatly depend on the power handling capabilities of the upstream components such as filters and isolators, which would be the most susceptible to damage due to back-propagating SBS light. Probably the weakest link is the master oscillator and the SOA in particular, as it is essentially an optical absorber when the SBS pulse would arrive. Because the SBS pulse experiences further amplification as it propagates up the amplifier chain, sufficient isolation is necessary to avoid damage, particularly between the MO and the first amplifier stage.
7. Removing chirp post amplification
A number of atmospheric lidar applications such as HSRL, Doppler and DIAL require spectral resolution better than 1 GHz. The deterministic manner in which we achieved the spectral broadening to suppress SBS offers an opportunity to reverse the process after amplification. In this proof-of-principal demonstration we added a bulk phase modulator at the output of the amplifier to reverse the chirp introduced in the MO to suppress SBS. A similar idea was reported earlier for a CW amplifier [25]. In that work, the RF modulation was used with a CW amplifier, imposing frequency side bands to achieve a modulation depth of 1.33 and a 1.33-fold increase in SBS threshold with subsequent spectral reconstruction post amplification.
A bulk phase modulator is needed to handle the significantly increased optical power levels post amplification. For this test we used an off-the-shelf device (4064 by NewFocus) with a Vπ of 240 V (versus 2.5 V for the fiber modulator). With our current driver version we were only able to achieve a little over a 4 kV p-to-p 50-MHz oscillation with a repetition rate of 20 kHz. A typical modulator driver voltage trace is shown in Fig. 15. Since the chirp achievable with our current bulk modulator was less than that of the fiber modulator, we had to reduce the chirp of the fiber device to match that of the bulk one. Further optimization of the driver and the modulator should allow scaling the chirp closer to the values we achieve with the fiber modulator.
Fig. 15 Bulk modulator phase (drive voltage normalized by nominal Vπ = 240 V) and its derivative corresponding to the instantaneous frequency. Dashed vertical lines indicate an area of approximately linear chirp where light pulse was placed.
Spectra with and without chirp and amplification, shown in Fig. 16, were taken with a scanning Fabry-Perot etalon (110 MHz resolution). The blue trace shows the 240 MHz bandwidth of the system with the MO operating at 20 kHz, 8.4 ns, both modulators turned off and the amplifier running at low power to avoid SBS. The green trace shows a spectral broadening of 2 GHz imposed by the fiber modulator, which was subsequently reversed in the red trace with the bulk modulator to recover the input 240-MHz spectral width. The amplifier was pumped to yield an output pulse energy of 7.9 µJ. With further optimizations of the bulk modulator and the driver, and a large core diameter final amplification stage a few 100s of µJ should be achievable with this approach. A hybrid approach, where a bulk amplifier final stage is used [26], can potentially allow even higher output pulse energy. Finally it is easy to imagine replacing the second modulator with a device compensating the group velocity of the pulse to compress it in time rather than spectrally. However, with our current chirp a grating compressor needed would be unrealistically large.
Fig. 16 Spectral compressions after amplification by inverting the chirp with the second (bulk) phase modulator. Spectrum before initial application of chirp in the MO (blue): width 240 MHz; after modulation but before compression (green): 2 GHz FWHM width; and after compression (red): width 240 MHz.
8. Conclusions
We demonstrated an approach for mitigating SBS in nanosecond fiber amplifiers using a near linear chirp generated by pulse driving a phase modulator. We observe a nearly 9-fold increase in the SBS threshold for a pulsed 2-stage Yb fiber amplifier at the maximum achieved chirp of −1.19 GHz/ns. We used a two-stage single mode fiber amplifier of modest 11 µm fiber core diameter to characterize the technique. We performed transient SBS gain measurement in the unpumped second stage fiber and SBS threshold measurements with the stage pumped. The results showed reasonable agreement with theoretical calculation performed with the slow envelope and undepleted pump approximations. We observe that the logarithm of the SBS gain is approximately inversely proportional to the frequency chirp. On the other hand the threshold in the pumped amplifier showed slower than linear dependence on chirp despite expecting a linear dependence from the theoretical model. Finally we demonstrated reversal of the chirp after amplification to recover 240 MHz linewidth. The demonstrated fiber laser architecture will be beneficial for pulsed lidar applications requiring narrowband signals, such as DIAL, Doppler and HSRL.
Acknowledgments
This work was supported by The Aerospace Corporation's Sustained Experimentation and Research for Program Applications and Independent Research and Development programs. The authors would also like to thank Dr. George Valley for reviewing the theoretical analysis and Dr. Fabio di Teodoro and Dr. Paul Steinvurzel for many fruitful discussions in the course of this work.
References and links
1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).
2. R. W. Boyd, Nonlinear Optics (Elsevier Inc., 2008).
3. K. Shiraki, M. Ohashi, and M. Tateda, “SBS threshold of a fiber with a Brillouin frequency shift distribution,” J. Lightwave Technol. 14(1), 50–57 (1996). [CrossRef]
4. T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photonics Technol. Lett. 1(5), 107–108 (1989). [CrossRef]
5. J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen, “Increase of the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” J. Lightwave Technol. 19(11), 1691–1697 (2001). [CrossRef]
6. M. D. Mermelstein, “SBS threshold measurements and acoustic beam propagation modeling in guiding and anti-guiding single mode optical fibers,” Opt. Express 17(18), 16225–16237 (2009). [CrossRef] [PubMed]
7. Y. Aoki and K. Tajima, “Stimulated Brillouin scattering in a long single-mode fiber excited with a multimode pump laser,” J. Opt. Soc. Am. B 5(2), 358–363 (1988). [CrossRef]
8. F. Di Teodoro, J. Morais, T. S. McComb, M. K. Hemmat, E. C. Cheung, M. Weber, and R. Moyer, “SBS-managed high-peak-power nanosecond-pulse fiber-based master oscillator power amplifier,” Opt. Lett. 38(13), 2162–2164 (2013). [CrossRef] [PubMed]
9. C. Zeringue, I. Dajani, S. Naderi, G. T. Moore, and C. Robin, “A theoretical study of transient stimulated Brillouin scattering in optical fibers seeded with phase-modulated light,” Opt. Express 20(19), 21196–21213 (2012). [CrossRef] [PubMed]
10. N. A. Naderi, I. Dajani, and A. Flores, “High-efficiency, kilowatt 1034 nm all-fiber amplifier operating at 11 pm linewidth,” Opt. Lett. 41(5), 1018–1021 (2016). [CrossRef] [PubMed]
11. B. Anderson, A. Flores, R. Holten, and I. Dajani, “Comparison of phase modulation schemes for coherently combined fiber amplifiers,” Opt. Express 23(21), 27046–27060 (2015). [CrossRef] [PubMed]
12. C. Weitkamp, Lidar. Range-Resolved Optical Remote Sensing of Atmosphere (Springer, 2005).
13. J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express 20(14), 15872–15881 (2012). [CrossRef] [PubMed]
14. J. O. White, E. Petersen, J. Edgecumbe, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “A linearly chirped seed suppresses SBS in high-power fiber amplifiers, allows coherent combination, and enables long delivery fibers,” Proc. SPIE 8961, 896102 (2014). [CrossRef]
15. J. O. White, D. Engin, M. Akbulut, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “Chirped laser seeding for SBS suppression in a 100-W pulsed erbium fiber amplifier,” IEEE J. Quantum Electron. 51(6), 1–10 (2015). [CrossRef]
16. L. L. Pendergrass, “Ferroelectric microdomain reversal at room temperature in lithium niobate,” J. Appl. Phys. 62(1), 231–236 (1987). [CrossRef]
17. O. V. Bystrov and A. V. Golenishchev-Kutuzov, “Acoustically induced domain structure in lithium niobate,” JETP Lett. 61, 135 (1995).
18. N. E. Huang and Z. Wu, “A review on Hilbert‐Huang transform: Method and its applications to geophysical studies,” Rev. Geophys. 46(2), RG2006 (2008). [CrossRef]
19. M. Ito and T. Kimura, “Carrier density dependence of refractive index in AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 16(9), 910–911 (1980). [CrossRef]
20. R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990). [CrossRef] [PubMed]
21. M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997). [CrossRef]
22. I. Dajani, C. Vergien, C. Robin, and C. Zeringue, “Experimental and theoretical investigations of photonic crystal fiber amplifier with 260 W output,” Opt. Express 17(26), 24317–24333 (2009). [CrossRef] [PubMed]
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]
24. P. N. Brown, G. D. Byrne, and A. C. Hindmarsh, zvod.f on netlib.org, http://www.netlib.org/ode/zvode.f
25. H. Tünnermann, P. Jahn, V. Quetschke, J. Neumann, D. Kracht, and P. Wessels, “SBS mitigation via phase modulation and demodulation,” in CLEO: Science and Innovations (OSA, 2014), paper SW3N–2.
26. R. Zhu, J. Wang, J. Zhou, J. Liu, and W. Chen, “Single-frequency pulsed laser source with hybrid MOPA configuration,” Appl. Opt. 51(17), 3826–3831 (2012). [CrossRef] [PubMed]
