Abstract

We introduce orthogonally coded modulations for active coherent beam combining (CBC), and show how using Walsh codes enables the increase of the number of combined channels. Analytical, numerical, and experimental results are presented and compared to the standard multifrequency dithering technique, demonstrating that at least 5 times more fibers can be combined using the same modulation frequency. The modulation format excluded, no particular changes in the system need to be introduced and the benefits of active coherent beam combing, such as atmospheric turbulence compensation capability, are kept unchanged. Finally, we point out that this approach can be applied in partially CBC.

© 2014 Optical Society of America

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2013

V. P. Gapontsev, “Advances in power scaling of fiber lasers,” Proc. SPIE 8601, 8601–8613 (2013).

2012

2011

P. Bourdon, K. Cadoret, L. Lombard, A. Azarian, G. Canat, B. Bennaï, D. Goular, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent combining of low peak power pulsed fiber amplifiers with 80  ns pulse duration,” Proc. SPIE 7914, 79140W (2011).
[CrossRef]

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5  μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36, 523–525 (2011).
[CrossRef]

L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, and P. Georges, “Coherent beam combining of two femtosecond fiber chirped-pulse amplifiers,” Opt. Lett. 36, 621–623, (2011).
[CrossRef]

Y. Ma, X. Wang, J. Leng, H. Xiao, X. Dong, J. Zhu, W. Du, P. Zhou, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination of 1.08  kW fiber amplifier array using single frequency dithering technique,” Opt. Lett. 36, 951–953 (2011).
[CrossRef]

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Active phase locking of fiber amplifiers using sine-cosine single-frequency dithering technique,” Appl. Opt. 50, 3330–3336 (2011).
[CrossRef]

C. Yu, S. Augst, S. Redmond, K. Goldizen, D. Murphy, A. Sanchez, and T. Fan, “Coherent combining of a 4  kW, eigth-element fiber amplifier array,” Opt. Lett. 36, 2686–2689 (2011).
[CrossRef]

C. Wirth, O. Schmidt, I. Tsybin, T. Schreiber, R. Eberhardt, J. Limpert, A. Tunnermann, K. Ludewigt, M. Gowin, E. ten Have, and M. Jung, “High average power spectral beam combining of four amplifiers to 8.2  kW,” Opt. Lett. 36, 3118–3120 (2011).
[CrossRef]

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

T. Weyrauch, M. A. Vorontsov, G. W. Carhart, L. A. Beresnev, A. P. Rostov, E. E. Polnau, and J. J. Liu, “Experimental demonstration of coherent beam combining over a 7  km propagation path,” Opt. Lett. 36, 4455–4457 (2011).
[CrossRef]

2010

2009

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE. J. Sel. Topics Quantum Electron. 15, 248–256 (2009).
[CrossRef]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

2007

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 480–486 (2007).
[CrossRef]

2006

Augst, S.

Azarian, A.

P. Bourdon, K. Cadoret, L. Lombard, A. Azarian, G. Canat, B. Bennaï, D. Goular, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent combining of low peak power pulsed fiber amplifiers with 80  ns pulse duration,” Proc. SPIE 7914, 79140W (2011).
[CrossRef]

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5  μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36, 523–525 (2011).
[CrossRef]

Baker, J.

B. Pulford, T. Shay, J. Baker, A. Flores, C. Robin, C. Vergien, C. Zeringue, D. Gallant, A. D. Sanchez, C. Lu, and A. Lucero, “Phase locking an array of fiber amplifiers onto a remote object,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD), (Optical Society of America, 2010), paper CThO5.

Baker, J. T.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Barthelemy, A.

Bellanger, C.

Benham, V.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Bennaï, B.

P. Bourdon, K. Cadoret, L. Lombard, A. Azarian, G. Canat, B. Bennaï, D. Goular, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent combining of low peak power pulsed fiber amplifiers with 80  ns pulse duration,” Proc. SPIE 7914, 79140W (2011).
[CrossRef]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Beresnev, L. A.

Bourderionnet, J.

Bourdon, P.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5  μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36, 523–525 (2011).
[CrossRef]

P. Bourdon, K. Cadoret, L. Lombard, A. Azarian, G. Canat, B. Bennaï, D. Goular, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent combining of low peak power pulsed fiber amplifiers with 80  ns pulse duration,” Proc. SPIE 7914, 79140W (2011).
[CrossRef]

L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, and P. Georges, “Coherent beam combining of two femtosecond fiber chirped-pulse amplifiers,” Opt. Lett. 36, 621–623, (2011).
[CrossRef]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Brignon, A.

Cadoret, K.

P. Bourdon, K. Cadoret, L. Lombard, A. Azarian, G. Canat, B. Bennaï, D. Goular, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent combining of low peak power pulsed fiber amplifiers with 80  ns pulse duration,” Proc. SPIE 7914, 79140W (2011).
[CrossRef]

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5  μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36, 523–525 (2011).
[CrossRef]

Canat, G.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5  μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36, 523–525 (2011).
[CrossRef]

P. Bourdon, K. Cadoret, L. Lombard, A. Azarian, G. Canat, B. Bennaï, D. Goular, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent combining of low peak power pulsed fiber amplifiers with 80  ns pulse duration,” Proc. SPIE 7914, 79140W (2011).
[CrossRef]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Carhart, G. W.

Chang, W.-Z.

Chen, G.

Cheung, E. C.

S. P. Palese, E. C. Cheung, G. D. Goodno, C.-C. Shih, and M. E. Weber, “Coherent combining of pulsed fiber amplifiers in the nonlinear chirp regime,” in Advanced Solid-State Photonics (ASSP), OSA Technical Digest (CD), (Optical Society of America, 2012), paper AM3A.4.

Clarkson, W. A.

Daniault, L.

Desfrages-Berthelemot, A.

Dong, X.

Druon, F.

Du, W.

Eberhardt, R.

Fan, T.

Flores, A.

B. Pulford, T. Shay, J. Baker, A. Flores, C. Robin, C. Vergien, C. Zeringue, D. Gallant, A. D. Sanchez, C. Lu, and A. Lucero, “Phase locking an array of fiber amplifiers onto a remote object,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD), (Optical Society of America, 2010), paper CThO5.

François, J.

Gallant, D.

B. Pulford, T. Shay, J. Baker, A. Flores, C. Robin, C. Vergien, C. Zeringue, D. Gallant, A. D. Sanchez, C. Lu, and A. Lucero, “Phase locking an array of fiber amplifiers onto a remote object,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD), (Optical Society of America, 2010), paper CThO5.

Galvanauskas, A.

Gao, K.

Gapontsev, V. P.

V. P. Gapontsev, “Advances in power scaling of fiber lasers,” Proc. SPIE 8601, 8601–8613 (2013).

Georges, P.

Goldizen, K.

Goodno, G. D.

S. P. Palese, E. C. Cheung, G. D. Goodno, C.-C. Shih, and M. E. Weber, “Coherent combining of pulsed fiber amplifiers in the nonlinear chirp regime,” in Advanced Solid-State Photonics (ASSP), OSA Technical Digest (CD), (Optical Society of America, 2012), paper AM3A.4.

Goular, D.

P. Bourdon, K. Cadoret, L. Lombard, A. Azarian, G. Canat, B. Bennaï, D. Goular, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent combining of low peak power pulsed fiber amplifiers with 80  ns pulse duration,” Proc. SPIE 7914, 79140W (2011).
[CrossRef]

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5  μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36, 523–525 (2011).
[CrossRef]

L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, and P. Georges, “Coherent beam combining of two femtosecond fiber chirped-pulse amplifiers,” Opt. Lett. 36, 621–623, (2011).
[CrossRef]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Gowin, M.

Guo, S.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE. J. Sel. Topics Quantum Electron. 15, 248–256 (2009).
[CrossRef]

Hanna, M.

Jaouën, Y.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5  μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36, 523–525 (2011).
[CrossRef]

P. Bourdon, K. Cadoret, L. Lombard, A. Azarian, G. Canat, B. Bennaï, D. Goular, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent combining of low peak power pulsed fiber amplifiers with 80  ns pulse duration,” Proc. SPIE 7914, 79140W (2011).
[CrossRef]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Jolivet, V.

P. Bourdon, K. Cadoret, L. Lombard, A. Azarian, G. Canat, B. Bennaï, D. Goular, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent combining of low peak power pulsed fiber amplifiers with 80  ns pulse duration,” Proc. SPIE 7914, 79140W (2011).
[CrossRef]

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5  μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36, 523–525 (2011).
[CrossRef]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Jung, M.

Kermene, V.

Leng, J.

Limpert, J.

Liu, J. J.

Liu, Z.

Lombard, L.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5  μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36, 523–525 (2011).
[CrossRef]

P. Bourdon, K. Cadoret, L. Lombard, A. Azarian, G. Canat, B. Bennaï, D. Goular, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent combining of low peak power pulsed fiber amplifiers with 80  ns pulse duration,” Proc. SPIE 7914, 79140W (2011).
[CrossRef]

L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, and P. Georges, “Coherent beam combining of two femtosecond fiber chirped-pulse amplifiers,” Opt. Lett. 36, 621–623, (2011).
[CrossRef]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Lu, C.

B. Pulford, T. Shay, J. Baker, A. Flores, C. Robin, C. Vergien, C. Zeringue, D. Gallant, A. D. Sanchez, C. Lu, and A. Lucero, “Phase locking an array of fiber amplifiers onto a remote object,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD), (Optical Society of America, 2010), paper CThO5.

Lu, C. A.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Lucero, A.

B. Pulford, T. Shay, J. Baker, A. Flores, C. Robin, C. Vergien, C. Zeringue, D. Gallant, A. D. Sanchez, C. Lu, and A. Lucero, “Phase locking an array of fiber amplifiers onto a remote object,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD), (Optical Society of America, 2010), paper CThO5.

Ludewigt, K.

Ma, H.

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Active phase locking of fiber amplifiers using sine-cosine single-frequency dithering technique,” Appl. Opt. 50, 3330–3336 (2011).
[CrossRef]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE. J. Sel. Topics Quantum Electron. 15, 248–256 (2009).
[CrossRef]

Ma, Y.

Ming, H.

Moreau, B.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Mottay, E.

Murphy, D.

Nilsson, J.

O’Connor, M.

M. O’Connor and B. Shiner, “Highpower fiber lasers for industry and defense,” in High Power Laser Handbook, H. Injeyan and G. D. Goodno, ed. (McGraw-Hill, 2011), Chap. 18, pp. 517–532.

Palese, S. P.

S. P. Palese, E. C. Cheung, G. D. Goodno, C.-C. Shih, and M. E. Weber, “Coherent combining of pulsed fiber amplifiers in the nonlinear chirp regime,” in Advanced Solid-State Photonics (ASSP), OSA Technical Digest (CD), (Optical Society of America, 2012), paper AM3A.4.

Pilkington, D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Polnau, E. E.

Pourtal, E.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Primot, J.

Pulford, B.

B. Pulford, T. Shay, J. Baker, A. Flores, C. Robin, C. Vergien, C. Zeringue, D. Gallant, A. D. Sanchez, C. Lu, and A. Lucero, “Phase locking an array of fiber amplifiers onto a remote object,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD), (Optical Society of America, 2010), paper CThO5.

Redmond, S.

Richardson, D. J.

Robin, C.

B. Pulford, T. Shay, J. Baker, A. Flores, C. Robin, C. Vergien, C. Zeringue, D. Gallant, A. D. Sanchez, C. Lu, and A. Lucero, “Phase locking an array of fiber amplifiers onto a remote object,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD), (Optical Society of America, 2010), paper CThO5.

Rostov, A. P.

Sanchez, A.

Sanchez, A. D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 480–486 (2007).
[CrossRef]

B. Pulford, T. Shay, J. Baker, A. Flores, C. Robin, C. Vergien, C. Zeringue, D. Gallant, A. D. Sanchez, C. Lu, and A. Lucero, “Phase locking an array of fiber amplifiers onto a remote object,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD), (Optical Society of America, 2010), paper CThO5.

Schmidt, O.

Schreiber, T.

Shay, T.

B. Pulford, T. Shay, J. Baker, A. Flores, C. Robin, C. Vergien, C. Zeringue, D. Gallant, A. D. Sanchez, C. Lu, and A. Lucero, “Phase locking an array of fiber amplifiers onto a remote object,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD), (Optical Society of America, 2010), paper CThO5.

Shay, T. M.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 480–486 (2007).
[CrossRef]

T. M. Shay, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express 14, 12188–12195 (2006).
[CrossRef]

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S. P. Palese, E. C. Cheung, G. D. Goodno, C.-C. Shih, and M. E. Weber, “Coherent combining of pulsed fiber amplifiers in the nonlinear chirp regime,” in Advanced Solid-State Photonics (ASSP), OSA Technical Digest (CD), (Optical Society of America, 2012), paper AM3A.4.

Shiner, B.

M. O’Connor and B. Shiner, “Highpower fiber lasers for industry and defense,” in High Power Laser Handbook, H. Injeyan and G. D. Goodno, ed. (McGraw-Hill, 2011), Chap. 18, pp. 517–532.

Shou, T.

Si, L.

Siiman, L. A.

Su, R.

ten Have, E.

Tsybin, I.

Tunnermann, A.

Upton, E.

M. Wickham and E. Upton, “Optical energy transmission utilizing precise phase and amplitude control,” U. S. patent6,708,003 (14March2004).

Vasseur, O.

P. Bourdon, K. Cadoret, L. Lombard, A. Azarian, G. Canat, B. Bennaï, D. Goular, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent combining of low peak power pulsed fiber amplifiers with 80  ns pulse duration,” Proc. SPIE 7914, 79140W (2011).
[CrossRef]

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5  μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36, 523–525 (2011).
[CrossRef]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Vergien, C.

B. Pulford, T. Shay, J. Baker, A. Flores, C. Robin, C. Vergien, C. Zeringue, D. Gallant, A. D. Sanchez, C. Lu, and A. Lucero, “Phase locking an array of fiber amplifiers onto a remote object,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD), (Optical Society of America, 2010), paper CThO5.

Vorontsov, M. A.

Wagner, T. J.

T. J. Wagner, “Fiber laser beam combining and power scaling progress, Air Force Research Laboratory Laser Division,” Proc. SPIE 8237, 823718 (2012).
[CrossRef]

Wang, X.

Weber, M. E.

S. P. Palese, E. C. Cheung, G. D. Goodno, C.-C. Shih, and M. E. Weber, “Coherent combining of pulsed fiber amplifiers in the nonlinear chirp regime,” in Advanced Solid-State Photonics (ASSP), OSA Technical Digest (CD), (Optical Society of America, 2012), paper AM3A.4.

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M. Wickham and E. Upton, “Optical energy transmission utilizing precise phase and amplitude control,” U. S. patent6,708,003 (14March2004).

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Xiao, H.

Xu, L.

Xu, X.

Yu, C.

Zaouter, Y.

Zeringue, C.

B. Pulford, T. Shay, J. Baker, A. Flores, C. Robin, C. Vergien, C. Zeringue, D. Gallant, A. D. Sanchez, C. Lu, and A. Lucero, “Phase locking an array of fiber amplifiers onto a remote object,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD), (Optical Society of America, 2010), paper CThO5.

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V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 480–486 (2007).
[CrossRef]

IEEE. J. Sel. Topics Quantum Electron.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE. J. Sel. Topics Quantum Electron. 15, 248–256 (2009).
[CrossRef]

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Opt. Express

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C. Yu, S. Augst, S. Redmond, K. Goldizen, D. Murphy, A. Sanchez, and T. Fan, “Coherent combining of a 4  kW, eigth-element fiber amplifier array,” Opt. Lett. 36, 2686–2689 (2011).
[CrossRef]

C. Wirth, O. Schmidt, I. Tsybin, T. Schreiber, R. Eberhardt, J. Limpert, A. Tunnermann, K. Ludewigt, M. Gowin, E. ten Have, and M. Jung, “High average power spectral beam combining of four amplifiers to 8.2  kW,” Opt. Lett. 36, 3118–3120 (2011).
[CrossRef]

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5  μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36, 523–525 (2011).
[CrossRef]

L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, and P. Georges, “Coherent beam combining of two femtosecond fiber chirped-pulse amplifiers,” Opt. Lett. 36, 621–623, (2011).
[CrossRef]

Y. Ma, X. Wang, J. Leng, H. Xiao, X. Dong, J. Zhu, W. Du, P. Zhou, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination of 1.08  kW fiber amplifier array using single frequency dithering technique,” Opt. Lett. 36, 951–953 (2011).
[CrossRef]

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V. P. Gapontsev, “Advances in power scaling of fiber lasers,” Proc. SPIE 8601, 8601–8613 (2013).

T. J. Wagner, “Fiber laser beam combining and power scaling progress, Air Force Research Laboratory Laser Division,” Proc. SPIE 8237, 823718 (2012).
[CrossRef]

P. Bourdon, K. Cadoret, L. Lombard, A. Azarian, G. Canat, B. Bennaï, D. Goular, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent combining of low peak power pulsed fiber amplifiers with 80  ns pulse duration,” Proc. SPIE 7914, 79140W (2011).
[CrossRef]

Other

M. Wickham and E. Upton, “Optical energy transmission utilizing precise phase and amplitude control,” U. S. patent6,708,003 (14March2004).

S. P. Palese, E. C. Cheung, G. D. Goodno, C.-C. Shih, and M. E. Weber, “Coherent combining of pulsed fiber amplifiers in the nonlinear chirp regime,” in Advanced Solid-State Photonics (ASSP), OSA Technical Digest (CD), (Optical Society of America, 2012), paper AM3A.4.

B. Pulford, T. Shay, J. Baker, A. Flores, C. Robin, C. Vergien, C. Zeringue, D. Gallant, A. D. Sanchez, C. Lu, and A. Lucero, “Phase locking an array of fiber amplifiers onto a remote object,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD), (Optical Society of America, 2010), paper CThO5.

M. O’Connor and B. Shiner, “Highpower fiber lasers for industry and defense,” in High Power Laser Handbook, H. Injeyan and G. D. Goodno, ed. (McGraw-Hill, 2011), Chap. 18, pp. 517–532.

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Figures (19)

Fig. 1.
Fig. 1.

Schematic view of the LOCSET technique.

Fig. 2.
Fig. 2.

Simulink simulation of 3 coherently combined fibers. (a) Setpoints, (b) PID controllers, (c) modulations, (d) optical system, and (e) synchronous detections.

Fig. 3.
Fig. 3.

Simulated phase fluctuations and corresponding power spectral density.

Fig. 4.
Fig. 4.

Near field of the array of three fibers and corresponding far field when the phases at the output of each fiber are 0.

Fig. 5.
Fig. 5.

Normalized interference signal and power spectral density of uncorrected and corrected phase differences.

Fig. 6.
Fig. 6.

Normalized interference signal and Δφ1 as a function of Δφ2. In red: the line of equation Δφ1+Δφ2=0(2π).

Fig. 7.
Fig. 7.

Experimental setup. EOM, Electro-optic modulator; DET, photodetector; Dashed lines, electronic part; Plain lines, optical part.

Fig. 8.
Fig. 8.

Far field intensity when the system is phase-locked.

Fig. 9.
Fig. 9.

Signal on the photodiode, blue when the counter-reacting loop is switched off and green when it is switched on with a phase shift between the modulations of 90°.

Fig. 10.
Fig. 10.

Quality of the beam combination as a function of the phase difference between the modulations.

Fig. 11.
Fig. 11.

Hadamard matrix of orders 0, 1, and 2.

Fig. 12.
Fig. 12.

I(t) in the case of a second Hadamard matrix with a period of 90 μs.

Fig. 13.
Fig. 13.

Four modulations built from a second order Hadamard matrix. Values on y axis is arbitrary. In red: the 4 time intervals corresponding on the change from a sine to a cosine (or inversely) as I(t) changes from +1, to 0 and Q(t) changes from 0 to +1.

Fig. 14.
Fig. 14.

Near field of the array of 9 fibers and corresponding far field when all the phases are equal to 0.

Fig. 15.
Fig. 15.

Normalized interference signal. The residual phase difference is around λ/25.

Fig. 16.
Fig. 16.

Near field of the array of 6 fibers, and corresponding far field, when all the phases are equal to 0.

Fig. 17.
Fig. 17.

Normalized interference signal. The residual phase difference is around λ/30.

Fig. 18.
Fig. 18.

Near field of each array of the 2 coherent subsystems at (a) λ1 and (b) λ2, and (c) the total near field.

Fig. 19.
Fig. 19.

Far field of the array of the 2 coherent subsystems and the obtained interference signal.

Equations (17)

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error_signal_i(t)EiJ1(βi)[Ersin(φrφi)++k=1N1EkJ0(βj)sin(φkφi)],
error_signal_i(t)J1(β)[sin(φrφi)++k=1N1J0(β)sin(φkφi)].
sin(φrφi)φrφi=Δφisin(φkφi)φkφi=(φrφi)(φrφk)=ΔφiΔφk.
(J1(β)+(N1)J1(β)J0(β)J1(β)J0(β)J1(β)J0(β)J1(β)J0(β)J1(β)+(N1)J1(β)J0(β)J1(β)J0(β)J1(β)J0(β)J1(β)J0(β)J1(β)+(N1)J1(β)J0(β))(Δφ1Δφ2ΔφN1)=(000).
(Δφ1Δφ2ΔφN1)=(000).
I[cos(ωlt+φr)+cos(ωlt+φ1+βsin(ωmodt))+cos(ωlt+φ2+βsin(ωmodt+δ))]2,
Photocurrent32+cos(φrφ1)cos(βsin(ωmodt))+sin(φrφ1)sin(βsin(ωmodt))+cos(φrφ2)cos(βsin(ωmodt+δ))+sin(φrφ2)sin(βsin(ωmodt+δ))+cos(φ1φ2)cos(βsin(ωmodt))cos(βsin(ωmodt+δ))+sin(φ1φ2)cos(βsin(ωmodt))sin(βsin(ωmodt+δ))+cos(φ1φ2)sin(βsin(ωmodt))sin(βsin(ωmodt+δ))sin(φ1φ2)sin(βsin(ωmodt))cos(βsin(ωmodt+δ)).
sin(βsin(ωmodt))=[2n=1J2n1(β)sin((2n1)ωmodt)],cos(βsin(ωmodt))=[J0(β)+2n=1J2n(β)cos(2nωmodt)].
{error channel1:sin(φrφ1)(2J1(β))+sin(φrφ2)(2J1(β)cos(δ))+sin(φ1φ2)(2J1(β)J0(β)cos(δ)2J1(β)J0(α)),error channel2:sin(φrφ1)(2J1(β)cos(δ))+sin(φrφ2)(2J1(β))+sin(φ1φ2)(2J1(β)J0(β)cos(δ)+2J1(β)J0(β)).
{sin(φrφ1)φrφ1=Δφ1sin(φrφ2)φrφ2=Δφ2.
(2J1(β)2J1(β)J0(β)cos(δ)+2J1(β)J0(β)2J1(β)cos(δ)+2J1(β)J0(α)cos(δ)2J1(β)J0(α)2J1(β)cos(δ)+2J1(β)J0(α)cos(δ)2J1(β)J0(β)2J1(β)2J1(β)J0(β)cos(δ)+2J1(β)J0(β))(Δφ1Δφ2)=(00).
det=4J1(β)(1cos(δ)2)+4J1(β)2J0(β)(1cos(δ)2).
{first modulation:mod_1=sin(ωmodt),second modulation:mod_2=sin(ωmodt+δ),third modulation:mod_3=sin(ωmodt+δ),mod_3=mod_2sin(δ)sin(δ)+mod_1cos(δ)sin(δ)cos(δ)sin(δ).
ϕResidual=2ΔVRMSVMAX.
β×(I(t)×sin(ωmodt)+Q(t)×cos(ωmodt)),
I[cos(ωlt+φr)+cos(ωlt+φ1+mod1)+cos(ωlt+φ2+mod2)+cos(ωlt+φ3+mod3)+cos(ωlt+φ4+mod4)]2,
{Δt1:Δφ1+Δφ2+Δφ3+Δφ4=0,Δt2:{Δφ1(12J0(β))+Δφ2(2J0(β))+Δφ3(12J0(β))+Δφ4(2J0(β))=0,Δφ1(2J0(β))+Δφ2(12J0(β))+Δφ3(2J0(β))+Δφ4(12J0(β))=0,Δt3:{Δφ1(12J0(β))+Δφ2(12J0(β))+Δφ3(2J0(β))+Δφ4(2J0(β))=0,Δφ1(2J0(β))+Δφ2(2J0(β))+Δφ3(12J0(β))+Δφ4(12J0(β))=0,Δt4:{Δφ1(12J0(β))+Δφ2(2J0(β))+Δφ3(2J0(β))+Δφ4(12J0(β))=0,Δφ1(2J0(β))+Δφ2(12J0(β))+Δφ3(12J0(β))+Δφ4(2J0(β))=0,.

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