1308 OPTICS LETTERS / Vol. 35, No. 9 / May 1, 2010

Coherent beam combination with single frequencydithering technique

Yanxing Ma, Pu Zhou, Xiaolin Wang, Haotong Ma, Xiaojun Xu, Lei Si, Zejin Liu,* and Yijun ZhaoCollege of Opticelectric Science and Engineering, National University of Defense Technology, Changsha 410073, China

*Corresponding author: zejinliu@vip.sina.com

Received January 19, 2010; accepted March 9, 2010;posted March 18, 2010 (Doc. ID 122919); published April 20, 2010

The single frequency dithering technique for coherent beam combination with one single modulation fre-quency and without a reference beam is presented for the first time to our knowledge. Coherent beam com-bination of four fiber amplifiers is successfully demonstrated by using the single-dithering technique. Whenthe phase control system is in the closed loop, the fringe contrast of far-field intensity pattern is improved bymore than 85% from 8% in open loop, and the residual phase error is less than � /20. Experimental resultsreveal that the single-dithering technique has great potential in scaling to a large number of beamlets witha simple phase control system and low cost. © 2010 Optical Society of America

OCIS codes: 140.3298, 140.3290, 140.3580.

Coherent beam combination (CBC) of fiber laser/amplifiers based on a master oscillator power ampli-fier (MOPA) configuration is believed a promisingway to acquire a high brightness laser. In this tech-nique, active phasing is the key, and many ap-proaches have been proposed, i.e., the heterodyne de-tection phase control technique [1,2], multi-ditheringtechnique [3–6], and stochastic parallel gradient de-scent (SPGD) algorithm phase control technique[7–9]. CBC with the heterodyne detection phase con-trol technique requires a reference beam and a pho-todetector array with the same element numbers asthe beamlets in the whole MOPA system, and the sys-tem will become increasing complex and sophisti-cated when scaled to a large number of beamlets[10,11]. The SPGD algorithm needs only one photode-tector, but the implementing speed of the algorithmand control bandwidth will decrease with an increasein laser numbers [7,9]. The multi-dithering techniqueneeds one photodetector and phase control can beimplemented at a high speed, but every element inthe array requires an individual phase modulationfrequency and corresponded phase control module;accordingly the modulation frequency accumulates toextremely high value and becomes difficult to practi-cally implement with an increase in laser numbers[12]. In addition, when large numbers of beams arecoherently combined, the difficulty and cost of thecontrol system will also increase rapidly. In thepresent manuscript, we present the single frequencydithering technique based on the time division mul-tiplexing technique that has been widely applied inthe optical communication field to alleviate the abovedifficulties. We will show that phase control based onthe single frequency dithering technique has greatpotential to boost steady and robust CBC to a largenumber of laser beams with a simple phase controlsystem and low cost.

The scheme of the single frequency dithering tech-nique is shown in Fig. 1. The beam from the seed la-ser is split into k beams (four beams are given in thepicture) and coupled to k or k-1 optical phase modu-lators. The laser beams from the phase modulators

are amplified by k fiber amplifiers and sent to free-

0146-9592/10/091308-3/$15.00 ©

space via the collimators. The phase modulator isused to add the phase modulation signal and phaseerror control signal. The beam array emitted fromthe collimators is focused by a lens and a photodetec-tor is located at the focus plane. The electric signalfrom the photodetector is used to generate the opticalphase error control signal in the signal processingmodule. The whole laser array will be in phase-locked state when phase control signals are added tothe phase modulators.

The novelty of the single frequency dithering tech-nique is that only one modulation frequency and onephase control module are required, and the modula-tion signal and phase control signal are added to thedifferent phase modulator in turn. When one beam isworking with the modulation signal and phase con-trol signal, the phase control modules of other beamsremain unchanged.

The mathematical principle of the single frequencydithering technique can be briefly introduced as fol-lows [3–5]. Assuming that there are k beams in co-herent beam combining and the optical fields of allbeams are plane waves and are identically polarized,then the fields of beam i that are not phase modu-lated, Ei�t� are,

Ei�t� = Ei0 cos��Lt + �i� �where i = 1,2,3, . . . ,k�, �1�

where Ei0 and �i represent the field amplitude andthe optical phases of the beam i, and �L representsthe laser frequency.

Assuming that t represents time, andt0 , t1 , t2 , . . . , tn represent the different moment, and

Fig. 1. (Color online) The scheme of the single-dithering

technique.

2010 Optical Society of America

May 1, 2010 / Vol. 35, No. 9 / OPTICS LETTERS 1309

when t0� t� t1, the modulation signal is added tobeam 1 and its field can be written as

E1�t� = E10 cos��Lt + �1 + � sin��t��, �2�

where � and � represent the phase modulation am-plitude and frequency of beam 1 respectively. All theother beams are unmodulated and their field hold un-changed.

The optical fields from all beams are overlapped onthe photodetector so that the total optical intensity is

I�t� =� �0

�0��

l=1

k

El�t����j=1

k

Ej�t�� , �3�

where �0, �0 represent the magnetic and permeabili-ties of free space.

The photodetector current is

iPD�t� = RPD · S ·� �0

�0��

l=1

k

El�t����j=1

k

Ej�t�� , �4�

where RPD represents the responsivity of the photo-detector, and S represents the photodetector area.

The phase control signal is extracted from the pho-tocurrent by demodulating. When the photocurrent ismultiplied by sin��t� and integrated over a time, ,we will get the phase control signal of the beam 1 asfollows,

V1 =1

�

0

iPD�t� · sin��t�dt. �5�

Substituting Eqs. (1), (2), and (4) into Eq. (5), usingthe trigonometric identity and the Fourier series ex-pansions for cosine and sine of � sin��t�, neglectingthe term oscillating at optical frequencies, and let-ting be long enough for integration, but shortenough for phase control, we can obtain

V1 = RPD · S · E10 · J1���� �0

�0��

j=2

k

Ej0 sin��j − �1�� .

�6�

V1 is the phase control signal of beam 1 and isadded to the corresponding phase modulator, whilethe phase error control signal of the other beams arezeros. When t1� t� t2, the phase modulation signaland the real-time phase error control signal areadded to beam 2, and the phase control signal ofbeam 1 holds unchanged as the signal generated att= t1, and the phase control signals added to the re-maining beams retain zeros. When ti−1� t� ti �i�k�,the phase control signal of beam i is

Vi = RPD · S · Ei0 · J1���� �0

�0��j=1j�i

k

Ej0 sin��j − �i� ,

�7�

and the phase control signals of other beams hold un-changed as the signal generated at t= ti−1. When i

k, let m= i mod k, and add the modulation signal

and phase control signals to beam m, and otherbeams hold the previous phase control signal. If onlyT= ti+k− ti is short enough so that the phases of allbeams have not been disturbed but longer than theintegration time , the phase error between differentbeams will be compensated by repeating the aboveoperations for the different beams in turn.

To demonstrate the feasibility of the single fre-quency dithering technique, we have done the experi-ment of coherent beam combination of four beams.The experimental setup is shown in Fig. 2. The seedlaser is a distributed feedback (DFB) polarizationmaintaining Yb-doped fiber laser with 1083 nmwavelength and 25 kHz linewidth. The laser beamfrom the seed laser through the optical isolator issplit into four beams and coupled to four LiNbO3phase modulators. The laser beams from the phasemodulators are coupled to four optical isolators be-fore being sent to four polarization maintained fiberamplifiers whose output power can be tuned to bemore than 1 W. The output beams from amplifiers aresent to free space via four collimators arranged in arectangle array (as an insert shown in Fig. 2). The ra-dius of the collimator is 2 mm, and the distance be-tween collimators is about 12 mm in x direction and 8mm in y direction. The focus length of collimators ismore than 10 m. The output beams from collimatorstravel 10 m and are sampled by a cubic beam splitter.After the splitter, part of the beam is sent to a focus-ing lens with 1 m focus length that images the cen-tral lobe of the far field onto a homemade pinholewith 50 �m radius and a photodetector is located im-mediately behind the pinhole. The photodetectoris a PDA36A-EC Si amplifier detector with400 nm–1100 nm response wavelength and 1.2 MHzbandwidth when the gain is at 10 dB, produced byTHORLABS Corporation. The electric signal trans-formed by the photodetector is used to produce thephase control signal in the signal processing circuitbased on a field programmable gate array (FPGA) de-signed by us. The FPGA is programmed with a singlefrequency dithering control algorithm. The signalprocessing circuit works on 50 MHz and provides a60 kHz sine wave as the phase modulation signal.Another part of the beam after the splitter is also fo-cused by a lens. An IR CCD camera is set at the focalplane and can be used to diagnose the far-field beamprofile of the combined beam.

In the experiment, when the control system is inopen loop, the single frequency dithering technique isnot performed and the phases of beams randomlyfluctuate due to phase fluctuations in each fiber chan-

Fig. 2. (Color online) The experimental setup of coherent

beam combination of four beams.

1310 OPTICS LETTERS / Vol. 35, No. 9 / May 1, 2010

nel induced by amplifiers, air cooling machines, andmechanical quivering. The power encircled in thetarget-pinhole fluctuates and the intensity pattern atthe observing plane keeps shifting. The long-exposure far-field intensity distribution is shown inFig. 3(a), and its fringe contrast is calculated to beless than 8%, where the fringe contrast is defined bythe formula �Imax−Imin� / �Imax+Imin�, where Imax andImin are the maximum optical intensity and the adja-cent minimum on the intensity pattern, respectively.When the control system is in closed loop, the phasecontrol algorithm is implemented and the phasemodulation and control signal are added to the modu-lators of each beam by the signal processing circuit inturn, and the phase noises are compensated effi-ciently. The intensity pattern at the observing planeis clear and steady, and the long-exposure far-field in-tensity distribution is shown in Fig. 3(b) and itsfringe contrast is calculated to be more than 85%.The theoretical far-field pattern of the ideally phasedfour laser arrays that are arranged according to theabove real data is computed and presented in Fig.3(c). It is found that the experimental result is inagreement with the theoretical one.

The fidelity of coherent beam combination and thephase fluctuation suppressing result can be furtherstudied using the time series signals and the spectraldensity of energy encircled in the pinhole shown inFig. 4. When the control loop is open, the normalizedenergy encircled in the pinhole fluctuates between 0and 1 randomly. When the control loop is closed, theenergy encircled in the pinhole can be locked steadilyto be more than 0.9 for most of the time, the residualphase error less than � /20, and the spectral densityabout 30 dB lower than in open-loop below 200 Hz,which denotes a remarkable increase in energy en-circled in the main lobe. The phase that fluctuatesless than � /20 will be not compensated because itgoes beyond the noise floor of the used phase controlsystem. According to the measuring result that thephase fluctuating frequency of a fiber amplifier at260 W output power in a relatively quiet laboratoryenvironment is well below 100 Hz [13], we believe co-herent beam combination of fiber amplifiers usingthe single-dithering technique also has the potentialto be scaled to a high output power.

Along with the number of beams in combination in-creasing, the time division will become higher andthe control bandwidth of the single frequency dither-

Fig. 3. (Color online) Long-exposure far-field intensitypattern of the combined laser beam (a) open-loop (b) closed-loop (c) theoretical pattern.

ing will decrease. However, increasing the frequencyof the modulation signal can alleviate this difficulty.

In summary, we present the single frequency dith-ering technique for coherent beam combination forthe first time, and it is demonstrated by the experi-ment of coherent beam combination of four fiber laserbeams. The fringe contrast of the long-exposure co-herent combined beam profile is improved to 85% inclosed loop from 8% in open loop. Excellent stabilityagainst environmental disturbances has been demon-strated, and phase noises below 200 Hz have been ef-ficiently compensated. Along with increase of the fre-quency of the phase modulation signal, we believethat the single-dithering technique may have the po-tential to boost CBC using dithering-based-phase-control to a larger number of lasers with the simplephase control circuit, low cost, and compact systemconfiguration.

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Fig. 4. (Color online) Time series signals and spectral den-sity of energy encircled in the pinhole in open loop andclosed loop (a) time series signals (b) spectral density.