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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 18 — Aug. 29, 2011
  • pp: 17053–17058
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Collective coherent phase combining of 64 fibers

Jérome Bourderionnet, Cindy Bellanger, Jérome Primot, and Arnaud Brignon  »View Author Affiliations


Optics Express, Vol. 19, Issue 18, pp. 17053-17058 (2011)
http://dx.doi.org/10.1364/OE.19.017053


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Abstract

A new architecture for active coherent beam combining of a large number of fibers is demonstrated. The approach is based on a self-referenced quadriwave shearing interferometer and active control with arrays of electro-optic ceramic modulators. Coherent phase combining of 64 independent amplified fibers is obtained. This is to our knowledge the highest reported number of combined fibers. A Strehl ratio degradation less than 2dB is achieved with a residual phase error <λ/10 rms.

© 2011 OSA

1. Introduction

Fiber lasers provide an attractive means of reaching high-output laser power because of their advantages in terms of compactness, reliability, efficiency, and beam quality. Even given these advantages, it is desirable to increase the system power or energy levels beyond what is possible with a single-mode fiber laser. This becomes of particular interest for applications that requires a narrow-linewidth source with polarized emission. A promising technique is based on coherent beam combining (CBC), where all the fiber lasers operate at the same wavelength and are phase-locked so that their fields add coherently in the far field. Active phase locking involves phase detection and active compensation of phase errors [1

1. T. Y. Fan, “Laser beam combining for high-power, high radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005). [CrossRef]

,2

2. C. Labaune, D. Hulin, A. Galvanauskas, and G. Mourou, “On the feasibility of a fiber-based inertial fusion laser driver,” Opt. Commun. 281(15-16), 4075–4080 (2008). [CrossRef]

]. This technique brings additional functionalities such as beam deflection and beam shaping. This can be useful to correct a wavefront distorted by a passage through atmosphere, or to point a receiver in free-space communication [3

3. W. M. Neubert, K. H. Kudielka, W. R. Leeb, and A. L. Scholtz, “Experimental demonstration of an optical phased array antenna for laser space communications,” Appl. Opt. 33(18), 3820–3830 (1994). [CrossRef] [PubMed]

5

5. H. Bruesselbach, S. Wang, M. Minden, D. C. Jones, and M. Mangir, “Power-scalable phase-compensating fiber array transceiver for laser communications through the atmosphere,” J. Opt. Soc. Am. B 22(2), 347–353 (2005). [CrossRef]

].

Many different approaches have been proposed for active phase locking such as the the heterodyne detection phase control technique [6

6. S. J. Augst, T. Y. Fan, and A. Sanchez, “Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers,” Opt. Lett. 29(5), 474–476 (2004). [CrossRef] [PubMed]

,7

7. S. Demoustier, C. Bellanger, A. Brignon, and J. P. Huignard, “Coherent beam combining of 1.5µm Er-Yb doped fiber amplifiers,” Fiber Int. Opt. 27(5), 392–406 (2008). [CrossRef]

], the multi-dithering technique [8

8. T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14(25), 12015–12021 (2006). [CrossRef] [PubMed]

,9

9. B. Bennaï, L. Lombard, V. Jolivet, C. Delezoide, E. Pourtal, P. Bourdon, G. Canat, O. Vasseur, and Y. Jaouën, “Brightness scaling based on 1.55 µm fiber amplifiers coherent combining,” Fiber Int. Opt. 27(5), 355–369 (2008). [CrossRef]

], and stochastic parallel gradient descent (SPGD) algorithm phase control technique [10

10. L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront tip-tilt compensation,” Proc. SPIE 6708, 67080K, 67080K-12 (2007). [CrossRef]

]. Up to now the number of coherently combined fibers was limited to 48 [11

11. C. X. Yu, J. E. Kansky, S. E. J. Shaw, D. V. Murphy, and C. Higgs, “Coherent beam combining of a large number of PM fibers in 2-D fiber array,” Electron. Lett. 42(18), 1024–1025 (2006). [CrossRef]

].

In this Paper, we present a new architecture based on a collective active phase control of a larger number of fibers. The setup involved an array of collimated fibers, arrays of electrooptic ceramic modulators and a self-referenced wavefront analyzer specifically developed for this application.

2. Experimental setup

The experimental setup is shown on Fig. 1
Fig. 1 Experimental setup. PC: Polarization Controller. PM EDFA: Polarization Maintaining Erbium Doped Fiber Amplifier. QWLSI: Quadriwave Lateral Shearing Interferometer.
. A continuous 1.55μm Distributed Feedback (DFB) laser is pre-amplified to 1W by a first Erbium-doped Polarization Maintaining Erbium-Doped Amplifier (PM-EDFA). The output is then split into 4 beams to feed 4 additional 1W PM-EDFAs. Each of the 4 outputs is further split into 16, leading to the 64 amplified fibered outputs. Sixteen modules of compact, 4-channels PLZT-based phase modulators are then inserted for phase feedback control before connection to the output laser head.

A schematic of one of the 16 four-channels phase modulators is given in Fig. 2
Fig. 2 Schematic of a phase modulator array (left) and (right).
(left). A pattern of interdigited electrodes is etched in a electro-optic ceramic (PLZT) using ultrasonic machining. The polarization axis of the input and the output PM fibers are aligned parallel to the applied electric field so as to provide the voltage-controlled phase shift. As seen in Fig. 2 (right), a 2π phase shift at 1.55µm is obtained for a 240Volts excursion for all of the 4 channels of one device. The response time of the device is in the 1-10µs range. The input fiber to output fiber insertion loss is better than 3 dB for each channel.

The lens array is then imaged onto a Quadriwave Lateral Shearing Interferometer (QWLSI) to perform phase measurement for each fiber. In a collective point of view, this can be seen as the analysis of a complex segmented wavefront, which stems from the juxtaposition of the quasi plane sub-wavefronts from each fiber. QWSLI, that has proven to be an efficient way to analyze complex stepped wavefronts [14

14. B. Toulon, J. Primot, N. Guérineau, R. Haïdar, S. Velghe, and R. Mercier, “Step-selective measurement by grating-based lateral shearing interferometry for segmented telescopes,” Opt. Commun. 279(2), 240–243 (2007). [CrossRef]

16

16. S. Mousset, C. Rouyer, G. Marre, N. Blanchot, S. Montant, and B. Wattellier, “Piston measurement by quadriwave lateral shearing interferometry,” Opt. Lett. 31(17), 2634–2636 (2006). [CrossRef] [PubMed]

], is adapted to a configuration dedicated to a collective phase detection for beam combining purposes [17

17. C. Bellanger, B. Toulon, J. Primot, L. Lombard, J. Bourderionnet, and A. Brignon, “Collective phase measurement of an array of fiber lasers by quadriwave lateral shearing interferometry for coherent beam combining,” Opt. Lett. 35(23), 3931–3933 (2010). [CrossRef] [PubMed]

]. After a calibration stage, this scheme allows a fast collective phase retrieval without external reference and is perfectly scalable to a much higher number of fiber.

The device is based on a 2D diffraction grating, rotated by 45° with respect to the fiber array orientation. This grating generates 4 laterally sheared replicas in two dimensions of the segmented wavefront. These replicas propagate to the Focal Plane Array (FPA) of a camera for detection. As shown in Fig. 3
Fig. 3 Principle of the self-referenced wavefront analysis technique based on the QWLSI. Right: part of the recorded interference pattern.
, the shearing between the 4 replicas is calculated to ensure a perfect overlap between replicas of adjacent beams on the FPA plane. The “green” replica of the left fiber overlap with the “blue” replica of the right fiber, the “black” replica of the bottom fiber overlap with the “red” replica of the top fiber, and so on. On each overlap area, we obtain a set of two-wave sinusoidal fringes, whose phase shift is in direct proportion with the phase step between the considered sub-wavefronts. Hence, the camera records a pattern that contains sets of vertical and horizontal fringes representative of the step between the fibers in 2 directions without correlation, allowing the reconstruction of the whole segmented wavefront by a simple spatial demodulation process. This operation can be very fast, allowing the combination of high power fiber amplifiers

Experimentally, to avoid parasitic overlap due to Gaussian beam divergence and to adapt the fiber array size on the FPA size of the Xenics InGaAs camera we had, the microlens array plane is imaged onto the QWSLI with a magnitude ratio of 2:1. We hence obtain a beam array with a pitch of 750µm. To generate the replicas, we use a 2D diffraction grating with a 240 µm period, rotated by 45° towards the fiber array orientation and placed at 40 mm in front of the FPA. This leads to a lateral shearing of 500 µm and a perfect overlap of the replicas. For 64 beams, we obtained a pattern with 7x8 horizontal fringes sets and 8x7 vertical fringes sets. As the phase steps of the fibers evolves during the experiment in open loop, we could observe the scrolling of the fringes on the camera. After calibration, errors on phase retrieval, meaning the accuracy of the phase measurement setup, was measured to be 0.11 rad (λ/60) RMS with our device.

As an example for the numerical wavefront reconstruction, the intensity pattern of one line of vertical fringes set can be approximately written as:
I(x)=nrect(xnda)×cos(Ωx+Δϕn),
(1)
where a is the pupil width, d is the pitch, Ω is the fringes frequency, and Δφn denotes the phase shift between fibers n and n + 1. The first calculation step is a Fourier transform of I(x):
I˜(u)=12[nFT(rect(xnda))δ(uΩ)×eiΔφn+nFT(rect(xnda))δ(u+Ω)×eiΔφn]
(2)
where ~and FT denote Fourier transform operator, and δ is the Dirac function. ThenI˜(u)is numerically filtered by selecting the frequency content around Ω, and centered at zero frequency. This means to consider only the left-hand summation in the above equation, and to turn δ(u-Ω) into δ(u). Finally, a reverse Fourier transform is applied:
I˜filtered(u)=12[nFT(rect(xnda))δ(u)×eiΔϕn]TF1(I˜filtered)(x)=12[nrect(xnda)×eiΔϕn].
(3)
The phase map is finally obtained by taking the argument of the above expression, and fed back to drive the phase modulators. It is worth noting that this phase measurement method based on QWSLI could also be used with a hexagonal arrangement of fiber arrays by using a grating that generates three replica instead of four [17

17. C. Bellanger, B. Toulon, J. Primot, L. Lombard, J. Bourderionnet, and A. Brignon, “Collective phase measurement of an array of fiber lasers by quadriwave lateral shearing interferometry for coherent beam combining,” Opt. Lett. 35(23), 3931–3933 (2010). [CrossRef] [PubMed]

].

3. Experimental results

Figure 4
Fig. 4 Experimental (in blue) and theoretical (in red) far-field intensity profiles. Gray curve shows the Fourier transform of an individual output pupil.
shows in blue line the experimental far field pattern. This correspond to the best profile extracted from the live measurement in Fig. 5
Fig. 5 Single-frame excerpts from video recordings of the far field intensity pattern of the 64 combined fibers (Media 1), when the phase-lock loop is closed.
(Media 1). In red is shown the theoretical profile corresponding to an ideal in-phase coherent summation of the 64 beamlets in a squared lattice arrangement. Both are very close, with a slight deviation corresponding to a Strehl ratio (SR) degradation of 0.64. This means that the peak energy of the central lobe of the experimental far field pattern is 0.64 times the peak energy of the theoretical profile. During the recording of Fig. 5 (Media 1), we measured phase errors varying between λ/13 and λ/10 rms. In best case, the λ/13 rms phase error theoretically drops the SR by 0.8. We also measured a 0.52mrad rms pointing error, which, considering a 1.33mrad full-width half maximum beamlet divergence, leads to an additional × 0.85 SR reduction [18

18. G. D. Goodno, C. C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18(24), 25403–25414 (2010). [CrossRef] [PubMed]

]. The residual degradation is attributed to collimating errors of the output beamlets.

To further quantify the beam combining efficiency of the system, we evaluated the ratio between the energy contained in the central lobe of the far field pattern and the total emitted energy. The central lobe width is determined by the first zeros of the theoretical far field pattern in Fig. 4. Experimentally, we measured 34% of the total emitted energy contained in the central lobe, compared to 44% for the perfect fibers combination in a square lattice arrangement.

Figure 5 (Media 1) shows the real-time far field intensity pattern recorded on the IR camera used for far field monitoring (see Fig. 1). In open loop configuration, when no phase correction is applied, the far field results from the interference of all the 64 beamlets, with fluctuating phases. This leads to a speckle-like pattern, with an overall envelope divergence corresponding to the Fourier transform of an individual near field beamlet, while the speckle grain divergence corresponds to the Fourier transform of the total near field pupil. On the other hand, when the phase loop is closed, we observe the constructive interference of all the 64 beams, leading to the intense central lobe, whose divergence is given by the inverse of the total output pupil size. It can be seen on the movie that the peak intensity of the central lobe, and therefore the SR, fluctuates in time. The mean SR was 0.59 with a standard deviation of 0.025, and a best value of 0.64 (Fig. 4). These fluctuations are due to our relatively low system bandwidth, which operated at 20Hz. Since the computation time is below 100μs, and the modulators response time is in the μs range, the system bandwidth is only limited by the QWLSI camera acquisition rate. This bandwidth was however enough to cophase the 64 fibers and to compensate the relative phase fluctuations of our 4 EDFAs in continuous regime, as well as phase fluctuations of the 64 independent fibers due to environmental perturbations.

4. Conclusion

We have demonstrated a new architecture for coherent beam combining of a large number of fibers based on the active control of the individual phase of each fiber. Collective techniques have been implemented including a self-referenced quadriwave shearing interferometer, arrays of high-speed phase modulators and collimated fiber arrays. Coherent phase combining of 64 independent amplified fibers has been demonstrated. The presented concept involving the measurement of the phase errors by the recording of a single image and the compact array arrangement of the modulators is intrinsically scalable to a much larger number of fibers. Further developments will involve a high-speed camera operating in the >kHz range bandwidth to cophase a large number of active fibers in the high power and pulsed regimes.

Acknowledgments

The authors acknowledge the French National Research Agency (ANR) for partial funding of this work within the Coherent Amplifying Network (CAN) Project led by Gérard Mourou. The authors also thank Fayçal Bouamrane, Thierry Bouvet and Sephan Megtert from Unité Mixte de Recherche CNRS/Thales.

References and links

1.

T. Y. Fan, “Laser beam combining for high-power, high radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005). [CrossRef]

2.

C. Labaune, D. Hulin, A. Galvanauskas, and G. Mourou, “On the feasibility of a fiber-based inertial fusion laser driver,” Opt. Commun. 281(15-16), 4075–4080 (2008). [CrossRef]

3.

W. M. Neubert, K. H. Kudielka, W. R. Leeb, and A. L. Scholtz, “Experimental demonstration of an optical phased array antenna for laser space communications,” Appl. Opt. 33(18), 3820–3830 (1994). [CrossRef] [PubMed]

4.

C. Stace, C. J. C. Harisson, R. G. Clarke, D. C. Jones, and A. M. Scott, “Fiber bundle lasers and their applications,” Paper B21, 1st Electro Magnetic Remote Sensing Defence Technical Conference, Edinburgh, United Kingdom (2004)

5.

H. Bruesselbach, S. Wang, M. Minden, D. C. Jones, and M. Mangir, “Power-scalable phase-compensating fiber array transceiver for laser communications through the atmosphere,” J. Opt. Soc. Am. B 22(2), 347–353 (2005). [CrossRef]

6.

S. J. Augst, T. Y. Fan, and A. Sanchez, “Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers,” Opt. Lett. 29(5), 474–476 (2004). [CrossRef] [PubMed]

7.

S. Demoustier, C. Bellanger, A. Brignon, and J. P. Huignard, “Coherent beam combining of 1.5µm Er-Yb doped fiber amplifiers,” Fiber Int. Opt. 27(5), 392–406 (2008). [CrossRef]

8.

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14(25), 12015–12021 (2006). [CrossRef] [PubMed]

9.

B. Bennaï, L. Lombard, V. Jolivet, C. Delezoide, E. Pourtal, P. Bourdon, G. Canat, O. Vasseur, and Y. Jaouën, “Brightness scaling based on 1.55 µm fiber amplifiers coherent combining,” Fiber Int. Opt. 27(5), 355–369 (2008). [CrossRef]

10.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront tip-tilt compensation,” Proc. SPIE 6708, 67080K, 67080K-12 (2007). [CrossRef]

11.

C. X. Yu, J. E. Kansky, S. E. J. Shaw, D. V. Murphy, and C. Higgs, “Coherent beam combining of a large number of PM fibers in 2-D fiber array,” Electron. Lett. 42(18), 1024–1025 (2006). [CrossRef]

12.

http://www.suss-microoptics.com/

13.

C. Bellanger, A. Brignon, B. Toulon, J. Primot, F. Bouamrane, T. Bouvet, S. Megtert, L. Quetel, and T. Allain, “Design of a fiber-collimated array for beam combining,” Opt. Eng. 50(2), 025005 (2011). [CrossRef]

14.

B. Toulon, J. Primot, N. Guérineau, R. Haïdar, S. Velghe, and R. Mercier, “Step-selective measurement by grating-based lateral shearing interferometry for segmented telescopes,” Opt. Commun. 279(2), 240–243 (2007). [CrossRef]

15.

B. Toulon, G. Vincent, R. Haïdar, N. Guérineau, S. Collin, J. L. Pelouard, and J. Primot, “Holistic characterization of complex transmittances generated by infrared sub-wavelength gratings,” Opt. Express 16(10), 7060–7070 (2008). [CrossRef] [PubMed]

16.

S. Mousset, C. Rouyer, G. Marre, N. Blanchot, S. Montant, and B. Wattellier, “Piston measurement by quadriwave lateral shearing interferometry,” Opt. Lett. 31(17), 2634–2636 (2006). [CrossRef] [PubMed]

17.

C. Bellanger, B. Toulon, J. Primot, L. Lombard, J. Bourderionnet, and A. Brignon, “Collective phase measurement of an array of fiber lasers by quadriwave lateral shearing interferometry for coherent beam combining,” Opt. Lett. 35(23), 3931–3933 (2010). [CrossRef] [PubMed]

18.

G. D. Goodno, C. C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18(24), 25403–25414 (2010). [CrossRef] [PubMed]

OCIS Codes
(140.3290) Lasers and laser optics : Laser arrays
(140.3298) Lasers and laser optics : Laser beam combining

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: June 27, 2011
Revised Manuscript: August 8, 2011
Manuscript Accepted: August 11, 2011
Published: August 16, 2011

Citation
Jérome Bourderionnet, Cindy Bellanger, Jérome Primot, and Arnaud Brignon, "Collective coherent phase combining of 64 fibers," Opt. Express 19, 17053-17058 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-18-17053


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References

  1. T. Y. Fan, “Laser beam combining for high-power, high radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005). [CrossRef]
  2. C. Labaune, D. Hulin, A. Galvanauskas, and G. Mourou, “On the feasibility of a fiber-based inertial fusion laser driver,” Opt. Commun. 281(15-16), 4075–4080 (2008). [CrossRef]
  3. W. M. Neubert, K. H. Kudielka, W. R. Leeb, and A. L. Scholtz, “Experimental demonstration of an optical phased array antenna for laser space communications,” Appl. Opt. 33(18), 3820–3830 (1994). [CrossRef] [PubMed]
  4. C. Stace, C. J. C. Harisson, R. G. Clarke, D. C. Jones, and A. M. Scott, “Fiber bundle lasers and their applications,” Paper B21, 1st Electro Magnetic Remote Sensing Defence Technical Conference, Edinburgh, United Kingdom (2004)
  5. H. Bruesselbach, S. Wang, M. Minden, D. C. Jones, and M. Mangir, “Power-scalable phase-compensating fiber array transceiver for laser communications through the atmosphere,” J. Opt. Soc. Am. B 22(2), 347–353 (2005). [CrossRef]
  6. S. J. Augst, T. Y. Fan, and A. Sanchez, “Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers,” Opt. Lett. 29(5), 474–476 (2004). [CrossRef] [PubMed]
  7. S. Demoustier, C. Bellanger, A. Brignon, and J. P. Huignard, “Coherent beam combining of 1.5µm Er-Yb doped fiber amplifiers,” Fiber Int. Opt. 27(5), 392–406 (2008). [CrossRef]
  8. T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14(25), 12015–12021 (2006). [CrossRef] [PubMed]
  9. B. Bennaï, L. Lombard, V. Jolivet, C. Delezoide, E. Pourtal, P. Bourdon, G. Canat, O. Vasseur, and Y. Jaouën, “Brightness scaling based on 1.55 µm fiber amplifiers coherent combining,” Fiber Int. Opt. 27(5), 355–369 (2008). [CrossRef]
  10. L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront tip-tilt compensation,” Proc. SPIE 6708, 67080K, 67080K-12 (2007). [CrossRef]
  11. C. X. Yu, J. E. Kansky, S. E. J. Shaw, D. V. Murphy, and C. Higgs, “Coherent beam combining of a large number of PM fibers in 2-D fiber array,” Electron. Lett. 42(18), 1024–1025 (2006). [CrossRef]
  12. http://www.suss-microoptics.com/
  13. C. Bellanger, A. Brignon, B. Toulon, J. Primot, F. Bouamrane, T. Bouvet, S. Megtert, L. Quetel, and T. Allain, “Design of a fiber-collimated array for beam combining,” Opt. Eng. 50(2), 025005 (2011). [CrossRef]
  14. B. Toulon, J. Primot, N. Guérineau, R. Haïdar, S. Velghe, and R. Mercier, “Step-selective measurement by grating-based lateral shearing interferometry for segmented telescopes,” Opt. Commun. 279(2), 240–243 (2007). [CrossRef]
  15. B. Toulon, G. Vincent, R. Haïdar, N. Guérineau, S. Collin, J. L. Pelouard, and J. Primot, “Holistic characterization of complex transmittances generated by infrared sub-wavelength gratings,” Opt. Express 16(10), 7060–7070 (2008). [CrossRef] [PubMed]
  16. S. Mousset, C. Rouyer, G. Marre, N. Blanchot, S. Montant, and B. Wattellier, “Piston measurement by quadriwave lateral shearing interferometry,” Opt. Lett. 31(17), 2634–2636 (2006). [CrossRef] [PubMed]
  17. C. Bellanger, B. Toulon, J. Primot, L. Lombard, J. Bourderionnet, and A. Brignon, “Collective phase measurement of an array of fiber lasers by quadriwave lateral shearing interferometry for coherent beam combining,” Opt. Lett. 35(23), 3931–3933 (2010). [CrossRef] [PubMed]
  18. G. D. Goodno, C. C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18(24), 25403–25414 (2010). [CrossRef] [PubMed]

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