ARL-TR-7979 ● MAR 2017

US Army Research Laboratory

Stimulated Brillouin Scattering (SBS)

Suppression and Long Delivery Fibers at the 

Multikilowatt Level with Chirped Seed Lasers

by Jeffrey O White, Mark Harfouche, John Edgecumbe,

Naresh Satyan, George Rakuljic, and Amnon Yariv

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ARL-TR-7979 ● MAR 2017

US Army Research Laboratory

Stimulated Brillouin Scattering (SBS)

Suppression and Long Delivery Fibers at the 

Multikilowatt Level with Chirped Seed Lasers

by Jeffrey O White

Sensors and Electron Devices Directorate, ARL

Mark Harfouche and Amnon Yariv

Department of Electrical Engineering, California Institute of 

Technology, Pasadena, CA 

John Edgecumbe

Nufern, East Granby, CT 

Naresh Satyan and George Rakuljic

Telaris, Inc., Santa Monica, CA 

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4. TITLE AND SUBTITLE

Stimulated Brillouin Scattering (SBS) Suppression and Long Delivery Fibers at 

the Multikilowatt Level with Chirped Seed Lasers

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Jeffrey O White, Mark Harfouche, John Edgecumbe, Naresh Satyan, 

George Rakuljic, and Amnon Yariv

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US Army Research Laboratory

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ARL-TR-7979

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

In a high-power fiber amplifier, a frequency-chirped seed interrupts the coherent interaction between the laser and Stokes 

waves, raising the threshold for stimulated Brillouin scattering (SBS). Moving the external mirror of a vertical cavity surfaceemitting diode laser 0.2 μm in 10 μs can yield a frequency chirp of 5 × 1017 Hz/s at a nearly constant output power. Optoelectronic feedback loops can linearize the chirp and stabilize the output power. The simple and deterministic variation of 

phase with time preserves temporal coherence, in the sense that it is straightforward to coherently combine multiple amplifiers 

despite a large path-length mismatch. The seed bandwidth, as seen by the counterpropagating SBS, also increases linearly 

with fiber length, resulting in a nearly length-independent SBS threshold. Experimental results at the 1.6-kW level with a 

19-m delivery fiber are presented. A numerical simulation is also presented.

15. SUBJECT TERMS

fiber amplifier, stimulated Brillouin scattering, SBS, frequency-chirped seed, temporal coherence

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19a. NAME OF RESPONSIBLE PERSON

Jun Zhang

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iii

Contents

List of Figures iv

List of Tables iv

Acknowledgments v

1. Introduction 1

2. Chirped Diode Laser (ChDL) Technology 2

3. SBS Suppression 2

4. Experiment 3

5. Modeling 5

6. Discussion 12

7. Conclusions 13

8. References 14

List of Symbols, Abbreviations, and Acronyms 16

Distribution List 17
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iv

List of Figures

Fig. 1 Experimental setup with chirped diode laser (ChDL), distributed 

feedback Bragg (DFB) laser, electro-optic modulator (EOM), 

photodiodes (PDs), cladding mode stripper (CMS), and end cap..........3

Fig. 2 Oscilloscope traces representing the output power (upper trace) and 

backward power (lower trace), taken at an output power of 1.6 kW. 

The data points in Fig. 3 are averages of the bold portions of the 

traces. .....................................................................................................4

Fig. 3 Backward power vs. output power for various chirps and for a seed 

with a bandwidth of 40 GHz produced by random phase modulation. 

The dashed line represents a ratio of 10–4

..............................................5

Fig. 4 Pump and laser powers vs. position in the fiber at t = 0 ........................7

Fig. 5 Fractional inversion vs. position in the fiber at t = 0, at a pump power 

of 1.8 kW ...............................................................................................7

Fig. 6 Simulated conditions inside the fiber at a pump power of 1.8 kW. 

Temperature at the center of the core (upper curve) and the 

cladding/coating interface (lower curve). The Brillouin frequency is 

shown by the solid curve referred to the right hand axis. ......................8

Fig. 7 Stokes power vs. position in the fiber vs. z, after the last transit, and a 

sliding average taken over 5 cm.............................................................9

Fig. 8 Magnitude squared density fluctuation vs. z, after the last transit, and a 

sliding average taken over 5 cm.............................................................9

Fig. 9 Magnitude squared density fluctuations averaged over z vs. time for 

one quarter of a transit .........................................................................10

Fig. 10 SBS power at z = 0 vs. time, for 2 transits, and a sliding average taken 

over 0.24 ns..........................................................................................10

Fig. 11 Histogram of PPS zz = 00, tt sampled at the grid spacing of 2 ps for 8 

transits. The average power is 0.2 W...................................................11

Fig. 12 Average Stokes power vs. output laser power calculated for various 

chirps. The solid lines are calculated with the full temperature 

dependence. The symbols are calculated as though the entire fiber 

were at 300 K. The dotted line is calculated at the fastest chirp with a 

lower pump attenuation of 0.6 dB/m. The dashed line indicates the 

SBS threshold.......................................................................................11

List of Tables

Table 1 Simulation parameters ...........................................................................6
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v

Acknowledgments

We are grateful to Dr Vijaysekhar Jayaraman and Dr Christopher Burgner for 

providing the microelectromechanical system (MEMS)-vertical-cavity, surfaceemitting lasers (VCSELs).

This work was supported by the High-Energy Laser Joint Technology Office under 

contract 13-SA-0509. Some of the work done at the California Institute of 

Technology was funded by the US Army Research Office under grant W911NF11-2-0081. Development of the MEMS-VCSEL at Praevium Research was 

supported by Thorlabs.
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INTENTIONALLY LEFT BLANK.
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1

1. Introduction

One obstacle in the scaling of high-power fiber lasers arises because of nonlinear 

effects (e.g., stimulated Brillouin scattering [SBS]) due to the large intensity times 

length product. Efforts to raise the power threshold include 1) reducing the 

Brillouin gain by combining materials with positive and negative elasto-optic 

coefficients1 or tailoring the acoustic index to avoid guiding the acoustic wave,

2,3

2) reducing the effective Brillouin gain by using a seed linewidth much wider than 

the Brillouin bandwidth,

4–6 3) enlarging the Brillouin bandwidth relative to the seed 

linewidth,

7–9 4) lowering the laser intensity by enlarging the fiber core, and 

5) minimizing the required active fiber length by pumping at the wavelength of 

maximum absorption and doping as heavily as possible. Conventional approaches 

to broadening the seed linewidth reduce the coherence length, making it difficult to 

coherently combine multiple fiber amplifiers. For example, a seed bandwidth of 

40 GHz (coherence length in fiber = 5 mm) will require path-length matching of 

much less than 1 mm to maintain high coherence. 

In previous work, we have shown that chirped seed amplification (CSA) in 

conjunction with acousto-optic frequency shifters and feedback circuitry can 

maintain coherence between 2 fiber amplifiers, despite path-length differences of 

10–50 cm.10,11 The maximum path-length difference is limited to cc∆ννmax⁄ββββ, 

where Δννmax is the maximum available frequency shift, ββ is the chirp, and cc/ is 

the speed of light in the fiber. It is also limited by the intrinsic coherence length of 

the unchirped laser. The laser we describe in this report has an unchirped bandwidth 

of 40 MHz (full width at half maxixum [FWHM]), therefore a coherence length of

5 m.

In a tiled geometry, this ability to control the phase electronically can be used to 

predistort an emitted wavefront to compensate for atmospheric turbulence. CSA 

also leads to an SBS threshold that is fiber length independent in the long fiber 

limit. This approach is compatible with the other techniques for suppressing SBS, 

except those that increase the Brillouin linewidth. The present work describes the 

use of CSA with a microelectromechanical system (MEMS)-vertical-cavity,

surface-emitting laser (VCSEL) seed to scale the output power of a ytterbium (Yb)

fiber amplifier to 1.6 kW, while at the same time allowing a delivery fiber of 19 m. 

A numerical simulation of the experiment shows that the SBS threshold could be 

raised to 2 kW by optimizing the pump attenuation.
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2. Chirped Diode Laser (ChDL) Technology

Our work with chirped seeds began with a conventional VCSEL in which linear 

chirps up to 5 × 1015 Hz/s were produced by a time-varying current and an 

optoelectronic feedback circuit.

12 A 100 times faster chirp can be obtained by

moving the external mirror of a MEMS-VCSEL. Our laser is pumped with an 

850-nm diode and has a cavity length of 11 μm.13 The mirror can be moved 1 μm 

via the Coulomb force by changing the bias by 50 V. 

A chirp of 5 × 1017 Hz/s can be obtained by moving the mirror 0.2 μm in 10 μs. A 

highly linear chirp can be obtained by fine adjustment of the temporal voltage 

waveform. To maintain a constant seed power during the frequency sweep, the laser 

output passes through a semiconductor optical amplifier controlled by a feedback 

loop. 

The chirp is determined by passing part of the MEMS-VCSEL output through an 

unbalanced fiber Mach-Zehnder interferometer (free spectral range [FSR] = 

71.9 GHz), and calculating the instantaneous frequency of the resultant beat signal. 

The chirps (measured away from the turning points) are 5.2 × 1016, 1.0 × 1017, 

2.6 × 1017, and 5.2 × 1017 ±5% Hz/s for durations of 100, 50, 20, and 10 μs, 

respectively. The frequency spans are 5.2 THz (~20 nm at 1.06 μm), limited only 

by the Yb gain spectrum.

The frequency of the seed can be made to follow a triangular waveform in time, 

spanning up to 100 nm, larger than the entire Yb gain spectrum.

Error! Bookmark not 

defined. One issue is SBS occurring at the turning points in the waveform, where the 

chirp passes through zero. We have shown that 2 synchronized swept frequency 

sources combined with an electro-optic switch (Agiltron, Inc., Woburn, MA) can 

solve this problem.

14 In the present work, we alternate between a chirped seed and 

a conventional broadband seed, injecting the latter at the turning points. This 

reduces the duty cycle for coherent combining to approximately 70%, but it allows 

us to study the behavior of the SBS, without requiring a second chirped source. 

3. SBS Suppression

An intuitive explanation of the SBS suppression due to a chirped seed has been 

given in our previous work, and a numerical model has shown good agreement with 

experiment.15 If the chirp is linear and the Brillouin gain gg(νν) is Lorentzian, the 

gain for every frequency component of the Stokes wave will follow a Lorentzian in 

space. The Stokes frequency that comes into resonance in the middle of the fiber 

will have the largest gain when integrated over z. The FWHM gain for this 

component will be cc∆ννBB⁄(2ββn). For a Brillouin linewidth ΔννBB = 100 MHz
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(FWHM) and a chirp of ββ = 1017 Hz/s, this frequency component will experience 

gain over a distance of only approximately 0.1 m. 

To estimate the SBS threshold, one needs to look at the gain experienced by all 

frequencies present during one transit time. In the high chirp limit, the gain 

spectrum for this ensemble of Stokes frequencies, ggens, is effectively flattened and 

broadened to ββββ. While the frequency integral of ggens is unchanged by chirping, a 

large reduction in Stokes power can be realized because the small signal gain is 

exponential. A flat spectrum such as this yields the highest threshold for a given 

spectral width.

4. Experiment

We injected the seed laser described in Section 2 into a Yb amplifier with a 25-m 

final stage (Fig. 1). A mode field adapter was located between the tap and the pump 

combiner. The pump diodes operated at 976 nm with a maximum power of 1.8 kW. 

The amplifier output is typically limited by SBS in the final stage. The diameters 

of the core, cladding, low-index polymer and jacket are 25, 400, 450, and 550 μm. 

Ninety percent of the pump power is absorbed in the first 5.6 m of the fiber, so our 

setup is equivalent to having a 19-m delivery fiber. The final stage fiber is 

nonpolarization-maintaining. The first 5 m is wound around a mandrel for cooling 

and to increase the loss for higher order modes. An endcap was spliced to the fiber 

and then cleaved to a length of 3.5 mm with an angle of 4.2°.

Fig. 1 Experimental setup with chirped diode laser (ChDL), distributed feedback Bragg 

(DFB) laser, electro-optic modulator (EOM), photodiodes (PDs), cladding mode stripper 

(CMS), and end cap

Three 100-MHz PDs monitor the power entering the final stage, the output power, 

and the backward power leaving the final stage. Mean values were obtained by 
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digitizing and averaging the PD output, and calibrating with subkilohertz

bandwidth thermal sensors. 

Oscilloscope traces taken with the fast PDs at an output power of 1.6 kW are shown 

in Fig. 2. The output power (top trace) has some unintentional modulation and 

transients that occur when switching between the 2 seeds. This modulation is also 

present on the power entering the final stage (not shown) and is due to wavelengthand polarization-dependent loss/gain and dispersion in the components between the 

seed laser and the preamplifier, including the electro-optic switch and the taps. 

The backward power (bottom trace) has the stochastic behavior characteristic of the 

initiation from spontaneous scattering. For the 2 slower chirps, the (+) and (–) 

chirps yielded the same backward power. For the 2 faster chirps, at the higher 

powers, the (+) chirp had significantly more backward power, as shown in Fig. 2. 

Oscilloscope traces were recorded and used to obtain the fraction of the backward 

power due to the (–) chirp. 

Fig. 2 Oscilloscope traces representing the output power (upper trace) and backward

power (lower trace), taken at an output power of 1.6 kW. The data points in Fig. 3 are averages 

of the bold portions of the traces.

The output power was varied by changing the current to the diodes pumping the 

final stage. The backward SBS power can then be plotted versus the output power 

(Fig. 3). Data for the 2 slower chirps are an average of (+) and (–) chirp. Data for 

the 2 faster chirps are for only the (–) chirp. 

Data taken with the 40-GHz seed alone are shown for comparison. We were unable 

to obtain more than 1.3 kW with the 40-GHz seed because spikes in the backward 

power would quickly trip the interlock. The highest output with the chirped seed, 
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1.6 kW, was limited by the available pump power. The backward power in all cases 

clearly shows a threshold behavior at the onset of SBS. We define threshold as the 

point where the backward power equals 10–4 times the output power. The threshold 

output power is increasing approximately linearly with chirp. 

Fig. 3 Backward power vs. output power for various chirps and for a seed with a 

bandwidth of 40 GHz produced by random phase modulation. The dashed line represents a 

ratio of 10–4

.

We have observed higher SBS for the (+) chirp with other co-pumped fiber 

amplifiers. A natural explanation for this would be that heating of the fiber produces 

a Brillouin frequency that decreases along the fiber length, so that the Stokes wave 

stays in resonance with the pump longer. In other words, the backward propagating 

Stokes wave sees an increase in the Brillouin frequency that offsets the increase in

the pump frequency. We have also observed that the (+) chirp yields less SBS with 

a 500-W counter-pumped Yb amplifier. The model described in Section 5 was 

developed in part to test this hypothesis.

5. Modeling

The model described previously15 has been modified to include the effect of 

temperature on the speed of sound, which, in turn, affects the Brillouin frequency, 

bandwidth, and the strength of the thermal phonon “noise” from which the 

stimulated scattering grows. Changes in the Brillouin frequency are accompanied 

by changes in the acoustic wavevector, the acousto-optic coefficient, and the elastooptic coefficient.
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Our first step is to find the steady-state solution of the system consisting of pump 

diode, laser, and Yb inversion, with no 1) acoustic wave, 2) Stokes wave, or 3) seed 

modulation. The heat generated inside the fiber is used to calculate the temperature 

of the core and all of the temperature-dependent quantities. These are used as the 

initial conditions for solving equations describing the coupling among the 

modulated laser, Stokes wave, and acoustic field.* The assumption of pump waves 

that are constant in time is valid providing the Stokes wave remains small. In our 

simulation, the Stokes power is less than 1% of the pump power throughout the 

fiber, even at z = 21 m, where the ratio is highest. In practical amplifiers, the 

backward Stokes power is typically less than 1% of the seed laser power at the start 

of the final stage (z = 0), where the ratio is highest. 

The parameters used in the model are given in Table 1. All are values taken from 

literature, except that the electrostrictive coefficient had to be multiplied by a factor 

of 5 to bring the simulation into agreement with the data. The equations were solved 

on a grid with intervals related by ∆zz = cc∆tt/ . The number of grid points in z is 

given by NNzz = 8ββ 2 (i.e., approximately 8 timesthe time-bandwidth product), where 

the seed bandwidth is taken over one transit. At the highest chirp, the simulation takes 

103 s on an Intel Xeon 3.3-GHz central processing unit running MATLAB.

Table 1 Simulation parameters

Brillouin frequency (at 300 K) 16.2 GHz

Brillouin bandwidth (at 300 K) 58 MHz

Thermal Brillouin frequency shift 2.25 MHz/K

Silica heat capacity 700 J/(kg K)

Silica thermal conductivity 1.38 W/(mK)

Polymer thermal conductivity 0.2 W/(mK)

Thermal convection coefficient 250 W/(m2 K)

Ambient temperature 300 K

Fiber attenuation at 976 nm 1.8 dB/m

Yb absorption cross section at 976 nm 10.5 × 10-25 m2

Yb emission cross section at 976 nm 0.7 × 10-25 m2

Yb absorption cross section at 1064 nm 0.03 × 10-25 m2

Yb emission cross section at 1064 nm 2.5 × 10-25 m2

Yb excited state decay time 1 ms

Electrostrictive coefficient 4.5

Polarization factor 1.0 (linear)

 * To avoid an initial spike in the SBS, it is important that the laser wave inside the fiber be chirped at 

t = 0.
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The initial conditions for a pump power of 1.8 kW are shown in Figs. 4–6. These 

conditions are representative of the highest output power data point in Fig. 3.

Fig. 4 Pump and laser powers vs. position in the fiber at t = 0

The fractional inversion has a peak of 0.6 at z = 0 and maintains a value of at least 

0.012 throughout the fiber because of the small but finite absorption at 1.06 μm 

(Fig. 5).

Fig. 5 Fractional inversion vs. position in the fiber at t = 0, at a pump power of 1.8 kW

The temperature of the core was calculated by solving the radial heat equation, 

assuming that all of the heat is generated on axis and that the interface between the 

outer plastic surface and the surrounding air is represented by the thermal 

convection coefficient given earlier. We have no actual measurements of fiber 

temperature with which to compare, so this value was chosen to bring the 

temperature at the glass/plastic interface to a value of approximately 450 K, at the 

limit of long-term stability. The temperature reaches a peak at 0.4 m into the fiber
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(Fig. 6), where the Yb ions are cycling the fastest due to a combination of strong 

pump and stimulated emission. We also show the temperature at the glass/plastic 

interface, which is the most vulnerable point.

Fig. 6 Simulated conditions inside the fiber at a pump power of 1.8 kW. Temperature at 

the center of the core (upper curve) and the cladding/coating interface (lower curve). The 

Brillouin frequency is shown by the solid curve referred to the right hand axis.

The Brillouin frequency follows the same curve as the core temperature (Fig. 6). 

The 0.3-GHz variation in ννB is significant with respect to ΔννB, but it is present only 

in a short length of fiber, so has a minimal effect on the net Brillouin gain. The 

effective “chirp” of νB is much less than that due to the chirped seed, so we do not

expect that temperature will affect the (+) and (–) chirps differently. We have 

estimated the effect on the Brillouin frequency of the compressive strain induced 

by the cooler cladding. We adapted an earlier treatment of a fiber at uniform 

temperature, but where the core and cladding have different coefficients of thermal 

expansion.16 Silica is unusual in that the speed of sound decreases with pressure, so 

the compressive strain lowers the Brillouin frequency. In the conditions discussed 

here, the effect of strain is minor.

The Brillouin bandwidth measured in a standard optical fiber at 1.32 μm has a small 

dependence on temperature in the region of 300–400 K.

17–19 Lacking data on our 

particular fiber, we take the bandwidth to be constant at 58 MHz.

20

The results of a simulation of 4 transits of the fiber for a chirp of 

β = 5.2 × 1017 Hz/s are shown in Figs. 7–10. Longer simulations gave essentially 

the same results. The z-dependence of the laser power at the end of the last transit 

is unchanged from that shown in Fig. 4. The z-dependence of the Stokes power at 

the end of the last transit is shown in Fig. 7. One can see that the Stokes power at 

z = 0 is 3–4 orders of magnitude larger than the spontaneous level at z = 25 m. Even 

so, the stochastic behavior is dominant, as opposed to the case where the SBS is far 

above threshold (see, e.g., Fig. 1).15
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Fig. 7 Stokes power vs. position in the fiber vs. z, after the last transit, and a sliding average 

taken over 5 cm

In the near-threshold condition, the z-dependence of the magnitude squared density 

fluctuation also has the random appearance characteristic of the noise throughout 

most of the fiber (Fig. 8). 

Fig. 8 Magnitude squared density fluctuation vs. z, after the last transit, and a sliding 

average taken over 5 cm

The time-dependent results from the simulation are shown in Figs. 9 and 10. Due 

to the chirp, |ρρ|

2 averaged over z increases by only 3 orders of magnitude over the 

spontaneous level (Fig. 9). The rise time here is approximately one phonon lifetime 

and shows that the simulation is behaving according to intuition. 
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Fig. 9 Magnitude squared density fluctuations averaged over z vs. time for one quarter of 

a transit

In these near-threshold conditions, the output laser power (1.66 kW) has temporal 

fluctuations on the order of only 1%, so we do not show it here. The Stokes power 

leaving the fiber, PS(z=0), reaches a pseudo-steady-state within one fiber transit 

time (Fig. 10). 

Fig. 10 SBS power at z = 0 vs. time, for 2 transits, and a sliding average taken over 0.24 ns

Knowledge of the peak SBS power is important for protecting upstream 

components in the amplifier. The statistics can be seen with a histogram of the 

instantaneous SBS power sampled at 2-ps intervals for 8 transits (Fig. 11). 
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Fig. 11 Histogram of PPS (zz = 00, tt) sampled at the grid spacing of 2 ps for 8 transits. The 

average power is 0.2 W.

A compilation of simulation results is shown in Fig. 12, for comparison with

Fig. 3. The average of the Stokes power was taken over the final 3 transits, to avoid 

the initial transient. One can see that the threshold scales linearly with chirp, in this 

regime. The effect of neglecting the heating in the fiber and the subsequent shift in 

Stokes frequency is shown by the square symbols. For these power levels and 

chirps, neglecting the temperature dependence is of no consequence. For shorter 

fibers, the suppression of SBS due to a temperature variation is well known.Error!

Bookmark not defined. The large difference between the spatial variation of Brillouin 

frequency and that of the seed (Fig. 6) suggests that the temperature gradient will 

not introduce any additional SBS for the (+) chirp, and none was observed in our 

simulations.

Fig. 12 Average Stokes power vs. output laser power calculated for various chirps. The solid 

lines are calculated with the full temperature dependence. The symbols are calculated as 

though the entire fiber were at 300 K. The dotted line is calculated at the fastest chirp with a 

lower pump attenuation of 0.6 dB/m. The dashed line indicates the SBS threshold.
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6. Discussion

The experimentally observed, chirp-sign-dependent SBS is not explained by the 

previous simulation. The temperature dependence introduces an effect on the SBS 

of the correct sign but of insufficient magnitude to explain the data. Other sources 

of chirp-sign-dependent SBS could be the temperature-induced strain caused by a 

lateral temperature gradient in the fiber. Our estimate of the effect, borrowing from 

the analysis in Dragic et al.16 indicates that this is unlikely. 

The most likely source of the chirp asymmetry is seeding of the Stokes wave by a 

Fresnel reflection of the laser from the endcap.21 This will occur when 2ββββ > ΔννB. 

For a 25-m fiber, this effect will begin to occur for chirps ββ > 6.6 × 1016 Hz/s. 

The effect was large enough for us to notice at ββ = 2.6 × 1017 Hz/s. The problem 

can be resolved by reducing the reflections from the end cap or by using a sawtooth 

negative chirp, such as in White et al.

14

The pump wavelength and attenuation for our amplifier was chosen to minimize 

the length of the final stage. With CSA, longer fibers are less of an issue. If the 

amplifier were designed with a longer fiber in mind, the optimal pump attenuation 

would be lower, for purposes of lowering the fiber temperature and reducing the 

gggggg Brillouin gain product. A simulation of an amplifier with 0.6 dB/m shows that 

the threshold could be raised to 2 kW in this fashion without requiring an increase 

in chirp (Fig. 12).

Several other engineering steps could be taken to perfect the CSA technique. In the 

current configuration, the seed power is stabilized with a feedback circuit driven by 

a photodetector located close to the MEMS-VCSEL. If the power fluctuations at 

the output of the amplifier (Fig. 2) are a concern, they can be minimized by using 

for feedback a photodetector located at the amplifier output, or at the tap in Fig. 1. 

Of course the bandwidth will be limited by the transit time of the feedback loop.

The same could be said if unwanted phase fluctuations at the output of the amplifier 

are a concern. In the current configuration, the linear chirp is produced by a 

feedback circuit that samples the phase of the MEMS-VCSEL. Propagation through 

dispersive elements will reduce the linearity, and degrade the coherent combining 

of multiple amplifiers. Nonlinearities in the output chirp can also be minimized by 

extending the feedback circuit to incorporate the entire chain. 

Designing an amplifier specifically for use with a chirped seed would begin with a 

measurement of the wavelength- and polarization-dependent dispersion and gain of 

the components in the amplifier chain. Based on those results, one can design or 

select broadband components that are wavelength independent over a 20-nm range, 

or that compensate for each other over that range, for example.
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7. Conclusions

We have demonstrated that a 1-mW, 1.06-μm MEMS-VCSEL can be scaled with 

a Yb fiber amplifier to the multikilowatt level using CSA. The significance of a 

linearly chirped seed is that it allows multiple amplifiers to be coherently combined 

without strict path length matching, which allows long delivery fibers. Our setup is 

equivalent to a 6-m amplifier and a 19-m delivery fiber. Our 1.6-kW result is the 

most power so far transmitted through a large mode area fiber of such length. A 

simulation indicates that 2 kW could be obtained from a 25-m amplifier if the pump 

attenuation were optimized.
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8. References

1. Dragic PD, Ballato J, Morris S, Hawkins T. Pockels’ coefficients of alumina 

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List of Symbols, Abbreviations, and Acronyms

ChDL chirped diode laser 

CMS cladding mode stripper

CSA chirped seed amplification 

DFB distributed feedback Bragg 

EOM electro-optic modulator 

FWHM full width at half maximum

MEMS microelectromechanical system

PD photodiode 

SBS stimulated Brillouin scattering 

VCSEL vertical-cavity, surface-emitting laser

Yb ytterbium
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