1616 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 25, NO. 16, AUGUST 15, 2013

Coherent Power Combining of Chirped-SeedErbium-Doped Fiber Amplifiers

Arseny Vasilyev, Eliot Petersen, Naresh Satyan, Member, IEEE, George Rakuljic,Amnon Yariv, Life Fellow, IEEE, and Jeffrey Owen White, Member, IEEE

Abstract— Using a rapidly-chirped (5 × 1014 Hz/s) continuous-wave optoelectronic swept-frequency seed laser and two 3 Werbium-doped fiber amplifiers, we demonstrate simultaneousstimulated Brillouin scattering suppression, coherent power com-bining, and electronic beam steering, without imposing strictpath-length matching requirements. Our platform presents aviable path toward high-power continuous-wave sources.

Index Terms— Optical phase locked loops, stimulated Brillouinscattering, Erbium-doped fiber amplifier, phase control.

I. INTRODUCTION

THE output power of continuous-wave (CW) optical fiberamplifiers is usually limited by stimulated Brillouin scat-

tering (SBS). Advances in the design of active fiber haveenabled increases in the SBS threshold power [1], [2]. Furtherincreases in the SBS threshold of a single amplifier aretraditionally obtained by broadening the linewidth of the seedlaser through phase-modulation [3], and therefore reducingits coherence length. Scaling of the output power of a singlefiber amplifier beyond ∼ 1 kW is typically limited by modalinstabilities instead of SBS [4], [5]. Coherent beam combiningof an SBS-suppressed amplifier array operating below themodal instability threshold therefore presents a promisingpathway towards the generation of high-power continuous-wave diffraction-limited beams. Due to the coherence lengthpenalty, efficient coherent combining of multiple amplifiersrequires careful path-length matching to sub-millimeter accu-racy, either in open-loop [6], or closed-loop [7] configurations.

In this letter we explore an architecture capable of SBS sup-pression and coherent combining without stringent mechanicalpath-length matching requirements. Our approach is to usea rapidly chirped (>1014 Hz/s) swept-frequency laser (SFL)seed to reduce the effective length over which SBS occurs[8], [9]. Path-length matching requirements are relaxed due tothe long coherence length (10s of meters) of semiconductorlaser based SFLs. Previous work focused on passive-fiber

Manuscript received April 13, 2013; revised June 13, 2013; accepted June20, 2013. Date of publication July 3, 2013; date of current version July 31,2013. This work was supported in part by the U.S. Army Research Officeunder Grant W911NF-11-2-0081 and in part by the High Energy Laser JointTechnology Office under Grant 11-SA-0405.

A. Vasilyev, N. Satyan, and A. Yariv are with the Department of AppliedPhysics and Material Science, California Institute of Technology, Pasadena,CA 91125 USA (e-mail: vasilyev@caltech.edu; naresh@caltech.edu;ayariv@caltech.edu).

E. Petersen and J. O. White are with the U.S. Army Research Lab-oratory, Adelphi, MD 20783 USA (e-mail: eliot.petersen.ctr@mail.mil;jeffrey.o.white6.civ@mail.mil).

G. Rakuljic is with Telaris Inc., Santa Monica, CA 90403 USA (e-mail:rakuljic@telarisinc.com).

Digital Object Identifier 10.1109/LPT.2013.2271784

Fig. 1. Schematic diagram of the heterodyne chirped-wave OPLL used inthe combining experiment. PD: photodetector.

phase-locking, coherent combining, and beam steering ofoptical waves chirping at a rate of 2∗1014 Hz/s [10]. Presently,we demonstrate simultaneous SBS suppression, coherent com-bining, and beam steering of chirped-seed fiber amplifiers(CSAs) with a frequency sweep rate of 5 ∗ 1014 Hz/s.

II. HETERODYNE PHASE-LOCKING OF CHIRPED WAVES

We first describe basic operation of the CSA coherent-combining system. An SFL is used to generate a linear chirp,with an instantaneous optical frequency given by ωL(t) =ω0 + ξ t, 0 ≤ t ≤ T, where ω0 is the initial optical frequency,ξ is the sweep rate, and T is the sweep time. The SFL is splitinto a single passive reference and multiple amplifier seeds.A difference in the lengths of the reference and amplifierchannel n results in a frequency difference ξlrn/c at thelocking point, where lrn is the path-length mismatch andc is the speed of light. An acousto-optic frequency shifter(AOFS) is placed before each amplifier to correct for both thefixed path-length mismatches as well as the dynamic lengthfluctuations arising from vibrations and temperature drift.These fluctuations are measured by interfering the amplifieroutput with the reference on a photodetector. The photocurrentis mixed with an electronic offset oscillator, generating anerror signal that is used to drive the frequency shifters.The resultant feedback system, shown in Fig. 1, is a heterodyneoptical phase-locked loop (OPLL). In the locked state, thesystem synchronizes the frequencies and phases of the multipleamplifier outputs, enabling coherent combining and beamsteering.

A small-signal phase noise analysis about the steady-stateoperating point of the OPLL yields a Fourier-domain descrip-tion of the residual phase error between the reference andchannel n: [10]

δθrn( f ) = θr ( f ) − θn( f )

1 + K ( f )+ (lrn/c)[ j2π f θL( f )]

1 + K ( f ), (1)

where θr ( f ) and θn( f ) are phase noise terms that model lengthfluctuations in the reference and the n-th amplifier channel, and

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VASILYEV et al.: COHERENT POWER COMBINING OF CHIRPED-SEED ERBIUM-DOPED FIBER AMPLIFIERS 1617

Fig. 2. Schematic diagram of the dual-channel CSA coherent-combiningexperiment. PD: photodetector, PM: back-scattered power monitor.

θL( f ) is the phase noise (including residual chirp nonlinearity)of the SFL. We have neglected the phase noise contribution ofthe offset oscillator and assumed that the OPLL is operated at azero free-running frequency difference.1 The loop gain is givenby K ( f ) = Kel( f ) exp(− j2π f τd )/( j2π f ), where Kel ( f )is the frequency-dependent electronic gain, τd is the loopdelay, and the term 1/( j2π f ) models the phase-integratingcharacteristic of the frequency shifter. Eq. (1) describes theresidual phase error of a single OPLL. Assuming equal loopgains, the Fourier-domain combining phase error of a dualamplifier system, δθ12( f ) ≡ δθr2( f ) − δθr1( f ), is thereforegiven by

δθ12( f ) = θ1( f ) − θ2( f )

1 + K ( f )+ (l12/c)[ j2π f θL( f )]

1 + K ( f ), (2)

where l12 ≡ lr2 − lr1, the path-length mismatch between thetwo amplifier arms, determines the locked state combiningerror.

III. ACTIVE EXPERIMENT

A schematic of the dual-channel CSA coherent-combiningexperiment is shown in Fig. 2. An optoelectronic SFL [11]based on a 1550 nm vertical-cavity surface-emitting laseris linearly chirped over a bandwidth of 500 GHz in 1 ms,resulting in a sweep rate ξ/(2π) = 5 ∗ 1014 Hz/sec. At theend of the 1 ms sweep time, the laser is chirped in reverse atthe same rate, bringing it back to its original starting frequency.Channels 1 and 2 are boosted to powers of ∼ 3 W eachwith commercially available erbium-doped fiber amplifiers.We used polarization-maintaining fiber in the experiment, withthe active and passive segments possessing matched modefield diameters of 9.9 μm, and matched numerical aperturesof 0.125.

The back-scattered power from the 5 m final amplifier stageand the 45 m delivery fiber is recorded for each channel.

1This is achieved by adjusting the AOFS bias so that the free-runningfrequency shift is equal to the sum of ξ lrn/c and the offset oscillatorfrequency.

Fig. 3. Far-field intensity distributions of the individual channels and thelocked aperture. lr1 = −28.5 mm, and lr2 = 1.5 mm.

Fig. 4. Steering of the combined beam through emitter phase control. �θis the relative DDS phase.

We define the SBS threshold as the power level at whichthe ratio of the back-scattered power to the forward poweris 10−4. There is a three-fold increase in the SBS thresholdfor the 5 ∗ 1014 Hz/sec chirp rate, when compared to a single-frequency seed.

Synchronized direct digital synthesis (DDS) circuits areused as offset oscillators in the two heterodyne OPLLs.An offset frequency of 100 MHz is chosen to match thenominal acousto-optic frequency shift. The loop bandwidthwas limited by the AOFS driver to ∼ 60 kHz. A tiled apertureis formed using a 90◦ prism with reflecting legs, and itsfar-field distribution is imaged onto a phosphor-coated CCDcamera with a lens.

Intensity distributions of the individual channels, as wellas that of the locked aperture are shown in Fig. 3. The pathlengths are nominally matched, with l12 = 30 mm. This levelof path-length matching is easily achieved. We observe, in thelocked state, a two-fold narrowing of the central lobe and anassociated increase in the peak lobe intensity. The phases ofthe individual emitters track the phases of the DDS oscillators,and we are therefore able to electronically steer the combinedbeam. Intensity distributions corresponding to relative DDSphases of �θ = 0, π/2, π , and 3π/2 radians are shown inFig. 4.

We extract the time-dependent phase differences betweenthe reference and amplifier channels from the two pho-todetector signals using the in-phase and quadrature (I/Q)

1618 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 25, NO. 16, AUGUST 15, 2013

Fig. 5. I/Q-demodulated phase differences between the amplifier channelsand the reference. �θ is the relative DDS phase.

TABLE I

OPLL PHASE ERRORS AND PHASE-NOISE-LIMITED FRINGE VISIBILITIES

demodulation technique described in [10]. The I/Q phasescorresponding to the four values of �θ are shown Fig. 5.As expected, the OPLL phases, and hence the phases of theindividual chirped waves track the DDS setpoint.

To characterize system performance, we consider three path-length matching cases, summarized in Table I. The I/Q tech-nique yields the residual phase errors, δθr1(t) and δθr2(t). Thetime-domain combining phase error is then given by δθ12(t) =δθr2(t)−δθr1(t). The standard deviations σxy =

√〈δθ2

xy(t)〉t ofall three phase errors, along with the phase-noise-limited fringevisibilities are listed in Table I. The visibilities are calculatedfrom the standard deviations σ12 using a Gaussian phase noisemodel, as described in the appendix.

The first case (nominally path-length-matched) has thelowest combining error, which is consistent with Eq. (2).The second and third cases have nearly identical amplifierpath-length mismatches and exhibit nearly identical combiningphase errors. This is consistent with the prediction that theresidual combining error is determined solely by the mismatchbetween the amplifier channels.

The phase-noise-limited fringe visibility for the path-length-matched case is almost 99%, yet the fringe visibility in Fig. 3is only about 80%. We believe the discrepancy is due to thewavefront distortions introduced by the collimators and theprism reflectors.

IV. CONCLUSION

We have implemented and characterized a 1550 nm CSAcoherent-combining system. The 5∗1014 Hz/sec chirp resultedin a three-fold increase of the SBS threshold, when comparedto a single-frequency seed. We demonstrated efficient phase-locking and electronic beam steering of two 3 W erbium-dopedfiber amplifier channels. We achieved temporal phase noiselevels corresponding to fringe visibilities exceeding 90% atpath-length mismatches of ≈ 500 mm, and exceeding 98%at a path-length mismatch of 30 mm. We expect that thedemonstrated coherent combining approach will scale well to

a larger number of channels, since the combination of coherentsignal gain and incoherent phase errors leads to a higherinterferometric visibility with increasing number of opticalbeams [12].

APPENDIX

PHASE-NOISE-LIMITED FRINGE VISIBILITY

We consider the case of a tiled aperture formed bytwo emitters with equal intensities. We assume that theemitters are phase-locked with a residual phase errorδθ12(t). The far-field intensity at location rrr is then givenby I ∝ 〈|1 + e jθ12(rrr)+ jδθ12(t)|2〉t = 2 + 2e−σ 2

12/2 cos θ12(rrr),where θ12(rrr) is the mean phase difference between the beamsat the point rrr and 〈〉t denotes an average over time. Weassumed that δθ12(t) is a zero-mean Gaussian random variablewith variance σ 2

12, so that 〈e jδθ12(t)〉t = e−σ 212/2. Intensity

extrema are found at points of constructive and destructiveinterference, with cos θ12(rrr) = ±1. The fringe visibilityis therefore given by V ≡ (Imax − Imin )/(Imax + Imin) =e−σ 2

12/2. Strictly speaking, this derivation applies only tosingle frequency beams, since in the chirped case thepropagation phase θ12 is a function of both rrr and t . However,the frequency ranges considered in this work are ∼ 0.25% ofthe nominal lasing frequency, so the result above applies.

ACKNOWLEDGMENT

The authors thank Zhi Yi Yang at the U.S. Army ResearchLaboratory for his expert technical assistance.

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