Abstract

A new approach is proposed for the adaptive phase-locking of a set of parallel laser beams. It is based on an optical conversion of phase differences in the array into an intensity pattern which feeds an optimization algorithm for iterated adjustments of the phase modulators. A numerical analysis and proof of principle experiment support the method and demonstrate its speed.

© 2015 Optical Society of America

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References

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  1. A. Brignon, Coherent Laser Beam Combining (Wiley-VCH, 2013).
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    [Crossref] [PubMed]
  3. S. McNaught, C. Asman, H. Injeyan, A. Jankevics, A. Johnson, G. Jones, H. Komine, J. Machan, J. Marmo, M. McClellan, R. Simpson, J. Sollee, M. Valley, M. Webera, and S. Weiss, “100kW coherently combined Nd:YAG MOPA laser array,” in Frontiers in Optics (OSA, 2009), paper FthD2.
  4. 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]
  5. P. Honzatko, Y. Baravets, F. Todorov, P. Peterka, and M. Becker, “Coherently combined power of 20 W at 2000 nm from a pair of thulium-doped fiber lasers,” Laser Phys. Lett. 10(9), 095104 (2013).
    [Crossref]
  6. H. Chosrowjan, H. Furuse, M. Fujita, Y. Izawa, J. Kawanaka, N. Miyanaga, K. Hamamoto, and T. Yamada, “Interferometric phase shift compensation technique for high-power, tiled-aperture coherent beam combination,” Opt. Lett. 38(8), 1277–1279 (2013).
    [Crossref] [PubMed]
  7. 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]
  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).
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    [Crossref] [PubMed]
  11. H. Yang and X. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43(3), 630–635 (2011).
    [Crossref]
  12. T. Kim and G. Popescu, “Laplace field microscopy for label-free imaging of dynamic biological structures,” Opt. Lett. 36(23), 4704–4706 (2011).
    [Crossref] [PubMed]
  13. S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14(9), 3792–3805 (2006).
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  14. R. Horisaki, Y. Ogura, M. Aino, and J. Tanida, “Single-shot phase imaging with a coded aperture,” Opt. Lett. 39(22), 6466–6469 (2014).
    [Crossref] [PubMed]
  15. F. Zernike, “Phase contrast, a new method for the observation of transparent objects,” Physica 7, 686–698 (1942).
  16. F. Jeux, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Efficient passive phasing of an array of 20 ring fiber lasers,” Laser Phys. Lett. 11(9), 095003 (2014).
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2014 (2)

R. Horisaki, Y. Ogura, M. Aino, and J. Tanida, “Single-shot phase imaging with a coded aperture,” Opt. Lett. 39(22), 6466–6469 (2014).
[Crossref] [PubMed]

F. Jeux, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Efficient passive phasing of an array of 20 ring fiber lasers,” Laser Phys. Lett. 11(9), 095003 (2014).
[Crossref]

2013 (2)

P. Honzatko, Y. Baravets, F. Todorov, P. Peterka, and M. Becker, “Coherently combined power of 20 W at 2000 nm from a pair of thulium-doped fiber lasers,” Laser Phys. Lett. 10(9), 095104 (2013).
[Crossref]

H. Chosrowjan, H. Furuse, M. Fujita, Y. Izawa, J. Kawanaka, N. Miyanaga, K. Hamamoto, and T. Yamada, “Interferometric phase shift compensation technique for high-power, tiled-aperture coherent beam combination,” Opt. Lett. 38(8), 1277–1279 (2013).
[Crossref] [PubMed]

2011 (4)

2010 (1)

2006 (3)

1997 (1)

1984 (1)

1942 (1)

F. Zernike, “Phase contrast, a new method for the observation of transparent objects,” Physica 7, 686–698 (1942).

Aino, M.

Augst, S. J.

Baker, J. T.

Baravets, Y.

P. Honzatko, Y. Baravets, F. Todorov, P. Peterka, and M. Becker, “Coherently combined power of 20 W at 2000 nm from a pair of thulium-doped fiber lasers,” Laser Phys. Lett. 10(9), 095104 (2013).
[Crossref]

Barthelemy, A.

F. Jeux, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Efficient passive phasing of an array of 20 ring fiber lasers,” Laser Phys. Lett. 11(9), 095003 (2014).
[Crossref]

Becker, M.

P. Honzatko, Y. Baravets, F. Todorov, P. Peterka, and M. Becker, “Coherently combined power of 20 W at 2000 nm from a pair of thulium-doped fiber lasers,” Laser Phys. Lett. 10(9), 095104 (2013).
[Crossref]

Bellanger, C.

Benham, V.

Bernet, S.

Bourderionnet, J.

Breitkopf, S.

Brignon, A.

Carhart, G. W.

Chosrowjan, H.

Culpepper, M. A.

Desfarges-Berthelemot, A.

F. Jeux, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Efficient passive phasing of an array of 20 ring fiber lasers,” Laser Phys. Lett. 11(9), 095003 (2014).
[Crossref]

Fan, T. Y.

Fujita, M.

Fürhapter, S.

Furuse, H.

Goldizen, K. C.

Hamamoto, K.

Honzatko, P.

P. Honzatko, Y. Baravets, F. Todorov, P. Peterka, and M. Becker, “Coherently combined power of 20 W at 2000 nm from a pair of thulium-doped fiber lasers,” Laser Phys. Lett. 10(9), 095104 (2013).
[Crossref]

Horisaki, R.

Izawa, Y.

Jesacher, A.

Jeux, F.

F. Jeux, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Efficient passive phasing of an array of 20 ring fiber lasers,” Laser Phys. Lett. 11(9), 095003 (2014).
[Crossref]

Kawanaka, J.

Kermene, V.

F. Jeux, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Efficient passive phasing of an array of 20 ring fiber lasers,” Laser Phys. Lett. 11(9), 095003 (2014).
[Crossref]

Kim, T.

Klenke, A.

Levi, A.

Li, X.

H. Yang and X. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43(3), 630–635 (2011).
[Crossref]

Limpert, J.

Lombard, L.

Lu, C. A.

Maurer, C.

Miyanaga, N.

Murphy, D. V.

Nelson, D. J.

Ogura, Y.

Peterka, P.

P. Honzatko, Y. Baravets, F. Todorov, P. Peterka, and M. Becker, “Coherently combined power of 20 W at 2000 nm from a pair of thulium-doped fiber lasers,” Laser Phys. Lett. 10(9), 095104 (2013).
[Crossref]

Pilkington, D.

Popescu, G.

Primot, J.

Redmond, S. M.

Ricklin, J. C.

Ritsch-Marte, M.

Sanchez, A.

Sanchez, A. D.

Seise, E.

Shay, T. M.

Spring, J.

Stark, H.

Tanida, J.

Todorov, F.

P. Honzatko, Y. Baravets, F. Todorov, P. Peterka, and M. Becker, “Coherently combined power of 20 W at 2000 nm from a pair of thulium-doped fiber lasers,” Laser Phys. Lett. 10(9), 095104 (2013).
[Crossref]

Toulon, B.

Tünnermann, A.

Vorontsov, M. A.

Ward, B.

Yamada, T.

Yang, H.

H. Yang and X. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43(3), 630–635 (2011).
[Crossref]

Yu, C. X.

Zernike, F.

F. Zernike, “Phase contrast, a new method for the observation of transparent objects,” Physica 7, 686–698 (1942).

J. Opt. Soc. Am. A (1)

Laser Phys. Lett. (2)

F. Jeux, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Efficient passive phasing of an array of 20 ring fiber lasers,” Laser Phys. Lett. 11(9), 095003 (2014).
[Crossref]

P. Honzatko, Y. Baravets, F. Todorov, P. Peterka, and M. Becker, “Coherently combined power of 20 W at 2000 nm from a pair of thulium-doped fiber lasers,” Laser Phys. Lett. 10(9), 095104 (2013).
[Crossref]

Opt. Express (3)

Opt. Laser Technol. (1)

H. Yang and X. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43(3), 630–635 (2011).
[Crossref]

Opt. Lett. (7)

T. Kim and G. Popescu, “Laplace field microscopy for label-free imaging of dynamic biological structures,” Opt. Lett. 36(23), 4704–4706 (2011).
[Crossref] [PubMed]

R. Horisaki, Y. Ogura, M. Aino, and J. Tanida, “Single-shot phase imaging with a coded aperture,” Opt. Lett. 39(22), 6466–6469 (2014).
[Crossref] [PubMed]

M. A. Vorontsov, G. W. Carhart, and J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient-descent optimization,” Opt. Lett. 22(12), 907–909 (1997).
[Crossref] [PubMed]

H. Chosrowjan, H. Furuse, M. Fujita, Y. Izawa, J. Kawanaka, N. Miyanaga, K. Hamamoto, and T. Yamada, “Interferometric phase shift compensation technique for high-power, tiled-aperture coherent beam combination,” Opt. Lett. 38(8), 1277–1279 (2013).
[Crossref] [PubMed]

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]

E. Seise, A. Klenke, S. Breitkopf, J. Limpert, and A. Tünnermann, “88 W 0.5 mJ femtosecond laser pulses from two coherently combined fiber amplifiers,” Opt. Lett. 36(19), 3858–3860 (2011).
[Crossref] [PubMed]

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]

Physica (1)

F. Zernike, “Phase contrast, a new method for the observation of transparent objects,” Physica 7, 686–698 (1942).

Other (2)

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

S. McNaught, C. Asman, H. Injeyan, A. Jankevics, A. Johnson, G. Jones, H. Komine, J. Machan, J. Marmo, M. McClellan, R. Simpson, J. Sollee, M. Valley, M. Webera, and S. Weiss, “100kW coherently combined Nd:YAG MOPA laser array,” in Frontiers in Optics (OSA, 2009), paper FthD2.

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Figures (9)

Fig. 1
Fig. 1 Schematic drawing of the phase-locking system with a computer controlled phase modulator array PMs. The beam splitter BS sends a weak fraction of the laser beam array into a phase intensity mapping device (PIM) that shapes the intensity of the array pattern owing to the relative phase of the input beamlets (input wavefront). The PIM outputs are detected by a photodiode array (PDs) and their signals feed an algorithm to compute the appropriate commands for the PMs. A few iterations of the electro-optic loop lead to phase-locking of the output beam array.
Fig. 2
Fig. 2 Schematic picture of the approach for compensation of the phase difference in the laser beam array by adaptive control of the phase modulators (PMs). The light path is represented in blue lines and light fields are in red characters while numerical values and their path are written in black. Transmission through the PIM device performs a linear transformation (T) of the input laser fields [F(n)] in the outputs [Em]. The photodiodes (PDs) give only the modulus of [Em]. The target phases Arg(E) are assigned to the measured fields before computation of the corresponding input fields [Fs]. The computed phases Arg(Fs) serve to the command the PMs in order to apply an opposite sign phase correction to the laser beams.
Fig. 3
Fig. 3 Phase locking dynamics of 5x5 = 25 laser beam array for various random choices of the initial phases (in dashed lines). The corresponding evolutions of the phase standard deviation across the array are plotted in solid lines.
Fig. 4
Fig. 4 Order parameter (phase-locking efficiency) versus the number of iterations computed for beam arrays of increasing size (from 3x3 to 22x22). Complete phasing of the array is fast and evolves only smoothly when the beam network gets larger. Averaging on more than 100 realizations of the random initial phases has been achieved for each set.
Fig. 5
Fig. 5 Number of iterations to reach perfect phase-locking (η = 0.99) versus the number of beams in the array. Data have been averaged on 200 initial conditions. Vertical bars represent the variance of the simulation results.
Fig. 6
Fig. 6 Assessment of the impact of detection noise on the phase-locking dynamics and steady-state for a 5x5 beam array. The phase-locking level is in dashed lines and the rms phase difference in the array is in solid lines. Performances computed with noiseless detection are in blue, with SNR = 10 in red and SNR = 7 in green. The initial random phase distribution was kept similar for the three simulations.
Fig. 7
Fig. 7 Schematic drawing of the experimental set-up. SLM1 shape the laser beam in a 4X4 beamlet array with random phases. SLM2 applies the phase modulations computed by the processing unit. The Phase intensity mapping device is based on an imaging telescope with an amplitude and phase filtering performed in the far field pattern by SLM3. The shape of the filter is given on the left together with its transmittance profile in amplitude and phase.
Fig. 8
Fig. 8 (a) Far field pattern of the 4x4 laser beam array recorded in the initial state for the beam phases. (b) Far field pattern recorded after 15 iterations of the phase-locking system.
Fig. 9
Fig. 9 Measurement of the phase-locking efficiency (dashed line) versus the iteration steps of the synchronization system. The beam array was 4x4 with a random phase pattern in the initial condition. The system quickly set the fields’ phase to a common value. Fast oscillations on top of the trace are artefacts. Theoretical evolution of the synchronization derived from simulation is plotted in red solid line for comparison. Convergence speeds are in good agreement. Points A and B corresponds to the far field patterns in Fig. 8(a) and Fig. 8(b) respectively.

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T klmn =β. δ klmn + 1 N 2 . ( 2γw π p ) 2 .(jβ).sinc( (km).2.γ N ).sinc( (ln).2.γ N )

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