Abstract

Coherent combination of laser beams from 37 fiber amplifiers in a tiled aperture configuration has been achieved thanks to an innovative iterative process. The high efficiency as well as the speed of the phase control demonstrated the relevance of the method for phase locking of a large array of fiber lasers.

© 2017 Optical Society of America

1. Introduction

Coherent beam combining (CBC) is extensively investigated for the delivery of high power laser radiation in a high quality beam. Some applications are related to wireless energy transmission [1] or to laser propulsion [2] but more recently CBC was considered also as a mean to make new particles accelerator thanks to high intensity ultrashort pulses at high average power with fiber amplifiers [3]. CBC techniques are also investigated to improve optical receiver in space optical communications [4] and to improve resolution in imaging [5]. Laser sources for CBC are based on a master oscillator feeding an array of parallel power amplifiers (MOPA). The amplified beams can be superimposed by a cascade of beam splitters or by a diffractive optical element (DOE) or just put together to form a dense array (tiled aperture). Efficient coherent light combining requires active stabilization of the optical path lengths in the MOPA structure, usually by means of electro-optic modulators inserted prior to the amplifiers. Various techniques have been proposed so far and implemented to phase-lock the laser fields so that they coherently added whatever the variation in their optical path through the array of amplifiers. In one class of methods, phase differences are measured, in the space domain or in the time domain, and then compensated by the modulators. In another class, a phase sensitive measurement is performed on the output and is maximized thanks to an iterative optimization process which monitor the modulators. For a review of the most popular methods see reference [6]. In terms of output power the record breaking performance of 100 kW dates back to 2009 and was obtained with seven chains of zig-zag slab solid-state amplifiers [7]. More recent achievements have been based on optical fiber laser technology to benefit from their high wall-plug efficiency and to get rid of wavefront distortions occurring in free space amplifiers. Unfortunately the fiber laser average power in single transverse mode operation is currently limited to a few kilowatts and it seems difficult to go beyond that power because of fundamental limitations. It means that a number of fiber lasers must be combined to reach performances close to or beyond the solid-state technology record. Regarding fiber laser array, the published experimental studies targeted either CBC at high average power or CBC of a large number of laser beams. In the former ones C.X. Yu et al. achieved phase-locking of a linear array of 8 fiber amplifiers and reported the highest performance with a total power of 4 kW [8]. In the latter ones, the number of laser fields which was synchronized in a tiled aperture amounts to a maximum of 64 fiber outputs [9]. Note that the phase control of fiber output array with large size were only obtained with passive fibers (no gain), at low power level so that it begs the question, does the technic still relevant for actual fiber MOPA architecture with amplifiers phase noise, with thermal effects at high power, with low coherence length radiation, etc. The record breaking experiments on that matter used phase diagnostics based on spatial interference patterns although other phasing techniques have been theoretically shown to be suited to a large number of channels [10–12].

In this letter we report the realization of a MOPA fiber laser with an unprecedented number of real fiber amplifier channels (37). We demonstrated the efficient coherent combining (94%) of the 37 laser outputs thanks to a phase-intensity mapping (PIM) device associated with an optimization loop, an innovative technique which was used here for the first time with laser amplifiers.

2. Phase-locking with PIM in an optimization loop

For the sake of completeness we introduce here the principle of the phasing method. Details can be found in [13] together with a preliminary proof of principle experiment. The new PIM method differs from the other techniques in the sense that it does not rely on direct phase measurements (interferometry, heterodyning, LOCSET), it does need neither some additional phase perturbations, nor a reference wave. The PIM device consists in a modified phase-contrast imaging set-up with an adapted amplitude and phase filtering. An array of photodiodes, with the same number of elements and same spatial distribution as the beam array is located at the output of the PIM device. It converts the filtered laser intensity pattern into a series of voltage which feeds an iterative optimization algorithm, based on projection methods (like Gerschberg and Saxton algorithm [14]). The algorithm uses the analytical description of the coherent filtering leading to the PIM for computation of the phase corrections which are then applied on the laser fields. It is an error reduction approach which requires a few iterations of the process to get compensation of the initial phase deviation across the beam network leading to phase-locking of the laser fields array. It was numerically demonstrated that the number of iterations to reach phase-synchrony and a combining efficiency η greater than 96% is of the order of 15 to 21 on average. The combining efficiency is given by:

η= (|kFk|k|Fk|)2

where Fk denotes the laser field number k among the N output beams of the amplifiers array. Thanks to the fact that the number of parallel measurements serving for the optimization scales as the number of laser beams in the tiled aperture of the laser, the phase-locking speed evolves very weakly with the size of the beams array [Fig. 1]. For a 9-laser configuration and a threshold residual phase error set at λ/30, corresponding to 96% combining efficiency, phase-locking is reached after only 15 iterations (averaged on 200 initial phase conditions). For an array as large as 20-by-20 laser beams, the optimization remains quick (around 20 iterations, see Fig. 1). It is worth emphasizing that, whatever the number of lasers in the array, the convergence speed is weakly affected by initial phase conditions, which is of interest in the case of large laser arrays.

 figure: Fig. 1

Fig. 1 Evolution of the convergence speed given as an average number of iterations needed to reach a phase-locking level of 96% for different array sizes (average on 200 sets of random initial phases) . Bars denote standard deviation.

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3. Fiber laser with 37 parallel fiber amplifiers

The homemade laser system was seeded by a 100 mW laser diode of 250 MHz bandwidth at 1064nm. A LiNbO3 electro-optic modulator broadened the laser signal spectrum in order to mitigate stimulated Brillouin scattering in the amplifiers. An ytterbium doped fiber amplifier (YDFA) served for pre-amplification of the signal which was then launched in a custom polarization-maintaining 1:48 waveguide splitter. 37 outputs of the beam splitter carrying an almost equal power were connected to the inputs of a set of ytterbium-doped polarization maintaining fiber amplifiers each of them comprising an electro-optic modulator followed by two stages of amplification. Each YDFA delivered more than 5W of laser power. A photograph of the laser source is given in Fig. 2.

 figure: Fig. 2

Fig. 2 Photograph of the laser with 37 YDFAs

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Close to 200 W of linearly polarized laser radiation was delivered by the laser amplifier array. The fiber outputs of the amplifiers were arranged in a triangular lattice distribution with a high accuracy in position and pointing. The exiting beams were collimated by a lens array [Fig. 3(a)] to form a tiled aperture of 120 mm in diameter with a fill-factor of 75% and a pointing error of one tenth of single beam divergence. An anti-reflection coated plate set in the main laser stream with a 45° tilt angle was used to collect a small fraction (2.10−3 in power) of the light beam for the phasing system. Several other beam splitters provided beam replicas for imaging of the beam’s near field and far field and for the purpose of beam diagnostics. The PIM device include a custom reflective phase plate realized by thin layer deposition on a small disc area of a glass plate. An image of the plate recorded with a ZYGO optical surface profiler is given on Fig. 3(b) where the highly reflective and dephasing disc appears in black in the center. The set of laser fields filtered by the device was sent onto a Si photodiode (PD) array with a similar arrangement. A photograph of the PD’s is shown on Fig. 3(c). The photo-currents were digitized in parallel and sent as input data to a processing unit where the optimization algorithm was implemented. The output data obtained at the end of each computation corresponded to the phase correction. They were transformed into voltages for command of the electro-optic phase modulators placed at the input of each YDFA. An interface permitted to switch on and off the servo and to display the feedback signals, the phasing dynamics, etc.

 figure: Fig. 3

Fig. 3 a) drawing of the array of fiber collimators forming the laser beam. (b) Surface profile image of the phase plate used in the PIM device. (c) Photograph of the photodiodes array.

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4. Results and discussion

When the laser system was operated in open loop, the phase relationships between the light fields from the different amplifiers were randomly distributed and varied continuously because of differential thermal effects, mechanical vibrations, etc. in the fiber network. Consequently, the far field pattern of the laser beam array was broad and characterized by a speckled structure which varied in time. A typical recording is presented on Fig. 4(a). Another signature of the phase fluctuations was traced by the signal of a PD inserted in the center part of the far field. It was proportional to the coherently combined beam intensity and varied according to time, as can be seen on the left part of Fig. 5(a), whilst remaining at a low level. Then the servo loop was closed and the figure of the far field abruptly switched to a main intense and narrow peak in the center of the pattern surrounded by six weak side lobes typical of triangular lattice. An example of recording is shown in Fig. 4(b). The gain in peak intensity between Figs. 4(a) and 4(b) is not visible because, in the latter case, the beam attenuation was increased to avoid saturation of the camera sensor.

 figure: Fig. 4

Fig. 4 a) Far field pattern of the laser beam in open loop. (b) Far field pattern of the 37 laser source in closed loop. (c) Theoretical figure of the beam array in perfectly phase-locked condition. All figures are normalized and cannot be compared in terms of relative intensity.

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 figure: Fig. 5

Fig. 5 (a) Peak intensity in the center of the far field according to time, initially in open loop state and then in closed loop operation. The inset is a recording on 100s showing the peak intensity stability when the loop is closed. (b) Comparison between theoretical and experimental profiles of a cross-section of the array far field.

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In fact there was an almost twenty fold enhancement in the far field on-axis average intensity as indicated by Fig. 5(a) where one can see the change between the OFF and ON states of the servo. The shape of the far field was very close to the expected theoretical pattern [Fig. 4(c)] and indicated that the 37 beams were phase-locked.

As a further comparison we show on Fig. 5(b) the cross section of the far field recorded in closed loop together with the plot of the profile computed for an ideal phased array. The two traces perfectly overlap on a large amplitude range and even the first modulation ring of very small intensity was visible in the background around the main peak, as expected for a perfect phase-locking. We also estimated the combining efficiency from measurements of the on-axis far-field peak intensity. The collected data led to a mean value of 94% for the combining efficiency corresponding to a residual phase error of λ/25. The combining fluctuations according to time amounted to 2% rms. A complementary assessment of the phasing performance was achieved by the common measurement of the power ratio in the bucket. It represents the fraction of power within a given far field angle compared with a reference ideal top hat beam with uniform phase. The reference beam here was of circular cross-section with a diameter D such that it covers entirely the hexagonal beam array. The fraction of the output laser power within a solid angle of 1.22 λ/D was measured in two ways. Firstly with a circular hard aperture followed by a power meter inserted in the far field and secondly with a high dynamics calibrated camera recording the full far field pattern which data were further processed. Both methods gave very close values corresponding to a PIB = 36%. The measured performance is in very good agreement with the expected value considering the experimental tolerance on the different optical and mechanical parameters of the whole laser set-up. The phase-locking dynamic has been characterized by measuring the rise time of the combined power after closing the servo loop. On average, within 1ms, 95% of the maximum combined power was reached indicating a phase-locking bandwidth of about 1 kHz. Note that this is by no way a fundamental limit because the electronics of the servo was based on standard on-the-shelve components and far from being optimized. The number of iteration loops required to get phase-locking was found to be 15 on average, a rather low value for a 37-elements array, in agreement with the numerical simulations (16 (+/−2) iterations theoretically expected). It has to be noted that PIM technique is strong enough to keep the phase-locked running even when up to 10 beams of the array failed, without any change in the algorithm.

5. Conclusion

A new phasing technique has been implemented on a fiber laser with a parallel array of ytterbium doped fiber amplifiers in a MOPA architecture. The method is based on the use of a phase-intensity mapping (PIM) device associated to an original iterative algorithm. The adaptive process brings laser fields with a random phase distribution to phase synchronization in about 20 iterations, with a continuous hill climbing dynamics. Fast convergence comes from the number of input data ( = number of detectors), which is identical to the number of beams to be combined, and from the efficiency of the algorithm based on projection methods. This new CBC technique does require neither a reference beam nor additional amplitude or phase modulations/perturbations. The reported experiments with a set of 37 fiber amplifiers demonstrated the efficiency of the approach for coherent summation of the laser fields delivered by a large number of fiber amplifiers, setting a new record in terms of fiber laser number. Almost 200W of total output power were phase-locked with a combining efficiency as high as 94%. Because of the fast optimization process, weakly dependent on the number of laser sources involved, the synchronization of the 37 laser beams took only 1ms limited by the non-optimized processing unit. The method can be applied to the phase-locking of pulsed laser fields as the ones associated with ultrashort laser pulses coming from femtosecond laser amplifiers. It can work as well with ultra-wide bandwidth signals with an appropriate design of the PIM device.

Acknowledgment

The authors acknowledge the CILAS Company for its technical support and funding.

References and links

1. Laser power beaming keeps drone fully charged http://optics.org/news/3/7/31, Space-based solar power https://en.wikipedia.org/wiki/Space-based_solar_power

2. Lee Billings, “$100-Million Plan Will Send Probes to the Nearest Star,” https://www.scientificamerican.com/article/100-million-plan-will-send-probes-to-the-nearest-star1/

3. G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics 7(4), 258–261 (2013). [CrossRef]  

4. D. J. Geisler, T. M. Yarnall, M. L. Stevens, C. M. Schieler, B. S. Robinson, and S. A. Hamilton, “Multi-aperture digital coherent combining for free-space optical communication receivers,” Opt. Express 24(12), 12661–12671 (2016). [CrossRef]   [PubMed]  

5. T. Gutzler, T. R. Hillman, S. A. Alexandrov, and D. D. Sampson, “Coherent aperture-synthesis, wide-field, high-resolution holographic microscopy of biological tissue,” Opt. Lett. 35(8), 1136–1138 (2010). [CrossRef]   [PubMed]  

6. A. Brignon, Coherent Laser Beam Combining (Wiley, 2013).

7. S. McNaught, C. Asman, H. Injeyan, A. Jankevics, A. Johnson, G. Jones, H. Komine, J. Machan, J. Marmo, M. MacClellan, R. Simpson, J. Sollee, M. Valley, M.Weber, and S. Weiss, “100 kW coherently combined Nd:YAG MOPA laser array,” in Frontiers in Optics (Optical Society of America, 2009), paper FThD2.

8. C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett. 36(14), 2686–2688 (2011). [CrossRef]   [PubMed]  

9. J. Bourderionnet, C. Bellanger, J. Primot, and A. Brignon, “Collective coherent phase combining of 64 fibers,” Opt. Express 19(18), 17053–17058 (2011). [CrossRef]   [PubMed]  

10. S. Redmond, K. Creedon, T. Y. Fan, A. Sanchez-Rubio, C. Yu, and J. Donnelly, “Active coherent combination using hill climbing based algorithms for fiber and semiconductor amplifiers,” in Coherent Laser Beam Combining, A. Brignon ed. (Wiley, 2013), pp. 114–117.

11. A. Azarian, P. Bourdon, L. Lombard, Y. Jaouën, and O. Vasseur, “Orthogonal coding methods for increasing the number of multiplexed channels in coherent beam combining,” Appl. Opt. 53(8), 1493–1502 (2014). [CrossRef]   [PubMed]  

12. R. Su, Z. Zhang, P. Zhou, Y. Ma, X. Wang, and X. Xu, “Coherent beam combining of a fiber lasers array based on cascaded phase control,” IEEE Photonics Technol. Lett. 28(22), 2585–2588 (2016). [CrossRef]  

13. D. Kabeya, V. Kermene, M. Fabert, J. Benoist, A. Desfarges-Berthelemot, and A. Barthelemy, “Active coherent combining of laser beam arrays by means of phase-intensity mapping in an optimization loop,” Opt. Express 23(24), 31059–31068 (2015). [CrossRef]   [PubMed]  

14. R. W. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).

References

  • View by:

  1. Laser power beaming keeps drone fully charged http://optics.org/news/3/7/31 , Space-based solar power https://en.wikipedia.org/wiki/Space-based_solar_power
  2. Lee Billings, “$100-Million Plan Will Send Probes to the Nearest Star,” https://www.scientificamerican.com/article/100-million-plan-will-send-probes-to-the-nearest-star1/
  3. G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics 7(4), 258–261 (2013).
    [Crossref]
  4. D. J. Geisler, T. M. Yarnall, M. L. Stevens, C. M. Schieler, B. S. Robinson, and S. A. Hamilton, “Multi-aperture digital coherent combining for free-space optical communication receivers,” Opt. Express 24(12), 12661–12671 (2016).
    [Crossref] [PubMed]
  5. T. Gutzler, T. R. Hillman, S. A. Alexandrov, and D. D. Sampson, “Coherent aperture-synthesis, wide-field, high-resolution holographic microscopy of biological tissue,” Opt. Lett. 35(8), 1136–1138 (2010).
    [Crossref] [PubMed]
  6. A. Brignon, Coherent Laser Beam Combining (Wiley, 2013).
  7. S. McNaught, C. Asman, H. Injeyan, A. Jankevics, A. Johnson, G. Jones, H. Komine, J. Machan, J. Marmo, M. MacClellan, R. Simpson, J. Sollee, M. Valley, M.Weber, and S. Weiss, “100 kW coherently combined Nd:YAG MOPA laser array,” in Frontiers in Optics (Optical Society of America, 2009), paper FThD2.
  8. C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett. 36(14), 2686–2688 (2011).
    [Crossref] [PubMed]
  9. J. Bourderionnet, C. Bellanger, J. Primot, and A. Brignon, “Collective coherent phase combining of 64 fibers,” Opt. Express 19(18), 17053–17058 (2011).
    [Crossref] [PubMed]
  10. S. Redmond, K. Creedon, T. Y. Fan, A. Sanchez-Rubio, C. Yu, and J. Donnelly, “Active coherent combination using hill climbing based algorithms for fiber and semiconductor amplifiers,” in Coherent Laser Beam Combining, A. Brignon ed. (Wiley, 2013), pp. 114–117.
  11. A. Azarian, P. Bourdon, L. Lombard, Y. Jaouën, and O. Vasseur, “Orthogonal coding methods for increasing the number of multiplexed channels in coherent beam combining,” Appl. Opt. 53(8), 1493–1502 (2014).
    [Crossref] [PubMed]
  12. R. Su, Z. Zhang, P. Zhou, Y. Ma, X. Wang, and X. Xu, “Coherent beam combining of a fiber lasers array based on cascaded phase control,” IEEE Photonics Technol. Lett. 28(22), 2585–2588 (2016).
    [Crossref]
  13. D. Kabeya, V. Kermene, M. Fabert, J. Benoist, A. Desfarges-Berthelemot, and A. Barthelemy, “Active coherent combining of laser beam arrays by means of phase-intensity mapping in an optimization loop,” Opt. Express 23(24), 31059–31068 (2015).
    [Crossref] [PubMed]
  14. R. W. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).

2016 (2)

D. J. Geisler, T. M. Yarnall, M. L. Stevens, C. M. Schieler, B. S. Robinson, and S. A. Hamilton, “Multi-aperture digital coherent combining for free-space optical communication receivers,” Opt. Express 24(12), 12661–12671 (2016).
[Crossref] [PubMed]

R. Su, Z. Zhang, P. Zhou, Y. Ma, X. Wang, and X. Xu, “Coherent beam combining of a fiber lasers array based on cascaded phase control,” IEEE Photonics Technol. Lett. 28(22), 2585–2588 (2016).
[Crossref]

2015 (1)

2014 (1)

2013 (1)

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics 7(4), 258–261 (2013).
[Crossref]

2011 (2)

2010 (1)

1972 (1)

R. W. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).

Alexandrov, S. A.

Augst, S. J.

Azarian, A.

Barthelemy, A.

Bellanger, C.

Benoist, J.

Bourderionnet, J.

Bourdon, P.

Brignon, A.

Brocklesby, B.

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics 7(4), 258–261 (2013).
[Crossref]

Desfarges-Berthelemot, A.

Fabert, M.

Fan, T. Y.

Geisler, D. J.

Gerchberg, R. W.

R. W. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).

Goldizen, K. C.

Gutzler, T.

Hamilton, S. A.

Hillman, T. R.

Jaouën, Y.

Kabeya, D.

Kermene, V.

Limpert, J.

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics 7(4), 258–261 (2013).
[Crossref]

Lombard, L.

Ma, Y.

R. Su, Z. Zhang, P. Zhou, Y. Ma, X. Wang, and X. Xu, “Coherent beam combining of a fiber lasers array based on cascaded phase control,” IEEE Photonics Technol. Lett. 28(22), 2585–2588 (2016).
[Crossref]

Mourou, G.

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics 7(4), 258–261 (2013).
[Crossref]

Murphy, D. V.

Primot, J.

Redmond, S. M.

Robinson, B. S.

Sampson, D. D.

Sanchez, A.

Schieler, C. M.

Stevens, M. L.

Su, R.

R. Su, Z. Zhang, P. Zhou, Y. Ma, X. Wang, and X. Xu, “Coherent beam combining of a fiber lasers array based on cascaded phase control,” IEEE Photonics Technol. Lett. 28(22), 2585–2588 (2016).
[Crossref]

Tajima, T.

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics 7(4), 258–261 (2013).
[Crossref]

Vasseur, O.

Wang, X.

R. Su, Z. Zhang, P. Zhou, Y. Ma, X. Wang, and X. Xu, “Coherent beam combining of a fiber lasers array based on cascaded phase control,” IEEE Photonics Technol. Lett. 28(22), 2585–2588 (2016).
[Crossref]

Xu, X.

R. Su, Z. Zhang, P. Zhou, Y. Ma, X. Wang, and X. Xu, “Coherent beam combining of a fiber lasers array based on cascaded phase control,” IEEE Photonics Technol. Lett. 28(22), 2585–2588 (2016).
[Crossref]

Yarnall, T. M.

Yu, C. X.

Zhang, Z.

R. Su, Z. Zhang, P. Zhou, Y. Ma, X. Wang, and X. Xu, “Coherent beam combining of a fiber lasers array based on cascaded phase control,” IEEE Photonics Technol. Lett. 28(22), 2585–2588 (2016).
[Crossref]

Zhou, P.

R. Su, Z. Zhang, P. Zhou, Y. Ma, X. Wang, and X. Xu, “Coherent beam combining of a fiber lasers array based on cascaded phase control,” IEEE Photonics Technol. Lett. 28(22), 2585–2588 (2016).
[Crossref]

Appl. Opt. (1)

IEEE Photonics Technol. Lett. (1)

R. Su, Z. Zhang, P. Zhou, Y. Ma, X. Wang, and X. Xu, “Coherent beam combining of a fiber lasers array based on cascaded phase control,” IEEE Photonics Technol. Lett. 28(22), 2585–2588 (2016).
[Crossref]

Nat. Photonics (1)

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics 7(4), 258–261 (2013).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Optik (Stuttg.) (1)

R. W. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).

Other (5)

A. Brignon, Coherent Laser Beam Combining (Wiley, 2013).

S. McNaught, C. Asman, H. Injeyan, A. Jankevics, A. Johnson, G. Jones, H. Komine, J. Machan, J. Marmo, M. MacClellan, R. Simpson, J. Sollee, M. Valley, M.Weber, and S. Weiss, “100 kW coherently combined Nd:YAG MOPA laser array,” in Frontiers in Optics (Optical Society of America, 2009), paper FThD2.

S. Redmond, K. Creedon, T. Y. Fan, A. Sanchez-Rubio, C. Yu, and J. Donnelly, “Active coherent combination using hill climbing based algorithms for fiber and semiconductor amplifiers,” in Coherent Laser Beam Combining, A. Brignon ed. (Wiley, 2013), pp. 114–117.

Laser power beaming keeps drone fully charged http://optics.org/news/3/7/31 , Space-based solar power https://en.wikipedia.org/wiki/Space-based_solar_power

Lee Billings, “$100-Million Plan Will Send Probes to the Nearest Star,” https://www.scientificamerican.com/article/100-million-plan-will-send-probes-to-the-nearest-star1/

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Figures (5)

Fig. 1
Fig. 1 Evolution of the convergence speed given as an average number of iterations needed to reach a phase-locking level of 96% for different array sizes (average on 200 sets of random initial phases) . Bars denote standard deviation.
Fig. 2
Fig. 2 Photograph of the laser with 37 YDFAs
Fig. 3
Fig. 3 a) drawing of the array of fiber collimators forming the laser beam. (b) Surface profile image of the phase plate used in the PIM device. (c) Photograph of the photodiodes array.
Fig. 4
Fig. 4 a) Far field pattern of the laser beam in open loop. (b) Far field pattern of the 37 laser source in closed loop. (c) Theoretical figure of the beam array in perfectly phase-locked condition. All figures are normalized and cannot be compared in terms of relative intensity.
Fig. 5
Fig. 5 (a) Peak intensity in the center of the far field according to time, initially in open loop state and then in closed loop operation. The inset is a recording on 100s showing the peak intensity stability when the loop is closed. (b) Comparison between theoretical and experimental profiles of a cross-section of the array far field.

Equations (1)

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η=  ( | k F k | k | F k | ) 2

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