Abstract

In this manuscript, we theoretically and experimentally investigate the influence of mode mismatch errors on active coherent polarization beam combining (CPBC) system. Firstly, by incorporating a piezo-mounted mirror (PMM) to generate artificial tilt phase aberrations, we design an experimental system to theoretically and experimentally investigate the influence of mode-mismatch errors induced by tilt phase aberrations on the combining efficiency of CPBC system. Further, by employing a spatial light modulator (SLM) to impose higher-order phase aberrations, the impact of mode-mismatch errors induced by higher-order phase aberrations on the CPBC system is also studied specifically. In the situation of adding each man-made aberration, experimental results correspond well with the theoretical ones. By theoretical and experimental analysis, we also show that the combining efficiency of the CPBC system is susceptible to the phase mismatch errors among different channels while has high tolerance on the intensity mismatch errors, which is compatible with the analysis in other CBC configurations. Besides, experimental results also show that the combining efficiency of the CPBC system is independent on the modulation frequency of dynamical tilt phase aberrations. Our analysis and designs provide useful approaches to diagnose the influence of mode-mismatch errors on CPBC system and optimize the whole CPBC system specifically.

© 2014 Optical Society of America

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2014 (4)

2013 (6)

2012 (1)

2011 (5)

2010 (3)

2009 (3)

2008 (3)

2007 (3)

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

S. Wielandy, “Implications of higher-order mode content in large mode area fibers with good beam quality,” Opt. Express 15(23), 15402–15409 (2007).
[Crossref] [PubMed]

J. Lhermite, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Passive phase locking of an array of four fiber amplifiers by an all-optical feedback loop,” Opt. Lett. 32(13), 1842–1844 (2007).
[Crossref] [PubMed]

2006 (2)

2005 (1)

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase—locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86(20), 201118 (2005).
[Crossref]

2002 (1)

Adams, L. N.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. Shih, D. M. Shimabukuro, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0901008 (2014).
[Crossref]

Alley, T. G.

Anderegg, J.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Asman, C. P.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Augst, S. J.

Baker, J. T.

Barthelemy, A.

Barty, C. P. J.

Beach, R. J.

Bellanger, C.

Benham, V.

Bourderionnet, J.

Bratcher, A.

Breitkopf, S.

Brignon, A.

Brosnan, S.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Chen, D. D.

Chen, Z.

Chen, Z. L.

Cheung, E. C.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Chua, C. F.

Corcoran, C. J.

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase—locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86(20), 201118 (2005).
[Crossref]

Culpepper, M. A.

Dai, S. J.

Dajani, I.

Dawson, J. W.

Desfarges-Berthelemot, A.

Dong, X.

Du, W.

Durville, F.

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase—locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86(20), 201118 (2005).
[Crossref]

Eidam, T.

Fan, T. Y.

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]

T. Y. Fan, “The effect of amplitude (power) variations on beam combining efficiency for phased arrays,” IEEE J. Sel. Top. Quantum Electron. 15(2), 291–293 (2009).
[Crossref]

Flores, A. S.

Goldizen, K. C.

Goodno, G. D.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. Shih, D. M. Shimabukuro, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0901008 (2014).
[Crossref]

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]

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Gottschall, T.

Hädrich, S.

Hammons, D.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

He, B.

Heebner, J. E.

Ho, J. G.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. Shih, D. M. Shimabukuro, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0901008 (2014).
[Crossref]

Hu, M.

Injeyan, H.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Jauregui, C.

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
[Crossref]

Johnson, A. M.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. Shih, D. M. Shimabukuro, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0901008 (2014).
[Crossref]

Kermene, V.

Kienel, M.

Klenke, A.

Komine, H.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Lachinova, S. L.

Leng, J.

Leng, J. Y.

Lhermite, J.

Li, X.

Lim, Y. L.

Limpert, J.

Liu, H. K.

Liu, Z.

Liu, Z. J.

Long, W. H.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Lou, Q. H.

Lu, C. A.

Ma, P.

Ma, Y.

Ma, Y. X.

Machan, J. P.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. Shih, D. M. Shimabukuro, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0901008 (2014).
[Crossref]

McClellan, M.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

McNaught, S. J.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. Shih, D. M. Shimabukuro, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0901008 (2014).
[Crossref]

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Messerly, M. J.

Mies, E.

Minden, M.

Murphy, D. V.

Nelson, D. J.

Pax, P. H.

Peng, M. Y.

Phua, P. B.

Pilkington, D.

Primot, J.

Pulford, B.

Qian, Q.

Qiu, J. R.

Redmond, S.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Redmond, S. M.

Robin, C.

Rothenberg, J. E.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. Shih, D. M. Shimabukuro, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0901008 (2014).
[Crossref]

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]

Rothhardt, J.

Saitou, T.

Sanchez, A.

Sanchez, A. D.

Sekiguchi, T.

Shay, T. M.

Shen, S. X.

Shih, C.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. Shih, D. M. Shimabukuro, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0901008 (2014).
[Crossref]

Shih, C. C.

Shimabukuro, D. M.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. Shih, D. M. Shimabukuro, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0901008 (2014).
[Crossref]

Shirakawa, A.

Shverdin, M. Y.

Si, L.

Siders, C. W.

Simpson, R.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Sollee, J.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Spring, J.

Sridharan, A. K.

Stappaerts, E. A.

Su, R.

Tan, L. H.

Tao, R.

Thielen, P. A.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. Shih, D. M. Shimabukuro, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0901008 (2014).
[Crossref]

Tiemann, B. G.

Tünnermann, A.

Uberna, R.

Ueda, K.

Vorontsov, M. A.

Wacks, M. P.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. Shih, D. M. Shimabukuro, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0901008 (2014).
[Crossref]

Wang, B. S.

Wang, X.

Wang, X. L.

Ward, B.

Weber, M.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Weber, M. E.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. Shih, D. M. Shimabukuro, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0901008 (2014).
[Crossref]

Wei, X. M.

Wei, Y. R.

Weiss, S. B.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

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G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
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Zhang, W. N.

Zhao, Y.

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P. Ma, X. Wang, Y. Ma, P. Zhou, and Z. Liu, “Analysis of multi-wavelength active coherent polarization beam combining system,” Opt. Express 22(13), 16538–16551 (2014).
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P. Ma, R. Tao, X. Wang, Y. Ma, R. Su, and P. Zhou, “Coherent polarization beam combination of four mode-locked fiber MOPAs in picosecond regime,” Opt. Express 22(4), 4123–4130 (2014).
[Crossref] [PubMed]

P. Ma, P. Zhou, H. Xiao, Y. Ma, R. Su, and Z. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photon. Technol. Lett. 25(19), 1936–1938 (2013).
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R. Tao, X. Wang, H. Xiao, P. Zhou, and L. Si, “Coherent beam combination of fiber lasers with a strongly confined tapered self-imaging waveguide: theoretical modeling and simulation,” Photon. Res. 1(4), 186–197 (2013).
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P. Ma, P. Zhou, X. Wang, Y. Ma, R. Su, and Z. Liu, “Influence of perturbative phase noise on active coherent polarization beam combining system,” Opt. Express 21(24), 29666–29678 (2013).
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X. L. Wang, P. Zhou, Y. X. Ma, J. Y. Leng, X. J. Xu, and Z. J. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett. 36(16), 3121–3123 (2011).
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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(6), 951–953 (2011).
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Zhu, J.

Appl. Opt. (2)

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Chin. Opt. Lett. (1)

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S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. Shih, D. M. Shimabukuro, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0901008 (2014).
[Crossref]

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
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IEEE Photon. Technol. Lett. (1)

P. Ma, P. Zhou, H. Xiao, Y. Ma, R. Su, and Z. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photon. Technol. Lett. 25(19), 1936–1938 (2013).
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J. Opt. Soc. Am. A (1)

Nat. Photonics (1)

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
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Opt. Express (10)

A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, “Coherent addition of fiber lasers by use of a fiber coupler,” Opt. Express 10(21), 1167–1172 (2002).
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J. W. Dawson, M. J. Messerly, R. J. Beach, M. Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. J. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Express 16(17), 13240–13266 (2008).
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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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R. Uberna, A. Bratcher, T. G. Alley, A. D. Sanchez, A. S. Flores, and B. Pulford, “Coherent combination of high power fiber amplifiers in a two-dimensional re-imaging waveguide,” Opt. Express 18(13), 13547–13553 (2010).
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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).
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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]

P. Ma, P. Zhou, X. Wang, Y. Ma, R. Su, and Z. Liu, “Influence of perturbative phase noise on active coherent polarization beam combining system,” Opt. Express 21(24), 29666–29678 (2013).
[Crossref] [PubMed]

P. Ma, R. Tao, X. Wang, Y. Ma, R. Su, and P. Zhou, “Coherent polarization beam combination of four mode-locked fiber MOPAs in picosecond regime,” Opt. Express 22(4), 4123–4130 (2014).
[Crossref] [PubMed]

P. Ma, X. Wang, Y. Ma, P. Zhou, and Z. Liu, “Analysis of multi-wavelength active coherent polarization beam combining system,” Opt. Express 22(13), 16538–16551 (2014).
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S. Wielandy, “Implications of higher-order mode content in large mode area fibers with good beam quality,” Opt. Express 15(23), 15402–15409 (2007).
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C. Robin, I. Dajani, and B. Pulford, “Modal instability-suppressing, single-frequency photonic crystal fiber amplifier with 811 W output power,” Opt. Lett. 39(3), 666–669 (2014).
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S. H. Xu, Z. M. Yang, W. N. Zhang, X. M. Wei, Q. Qian, D. D. Chen, Q. Y. Zhang, S. X. Shen, M. Y. Peng, and J. R. Qiu, “400 mW ultrashort cavity low-noise single-frequency Yb³⁺-doped phosphate fiber laser,” Opt. Lett. 36(18), 3708–3710 (2011).
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L. H. Tan, C. F. Chua, and P. B. Phua, “Preserving a diffraction-limited beam in Ho:YAG laser using coherent polarization locking,” Opt. Lett. 37(22), 4621–4623 (2012).
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Y. F. Yang, M. Hu, B. He, J. Zhou, H. K. Liu, S. J. Dai, Y. R. Wei, and Q. H. Lou, “Passive coherent beam combining of four Yb-doped fiber amplifier chains with injection-locked seed source,” Opt. Lett. 38(6), 854–856 (2013).
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A. Klenke, S. Breitkopf, M. Kienel, T. Gottschall, T. Eidam, S. Hädrich, J. Rothhardt, J. Limpert, and A. Tünnermann, “530 W, 1.3 mJ, four-channel coherently combined femtosecond fiber chirped-pulse amplification system,” Opt. Lett. 38(13), 2283–2285 (2013).
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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(6), 951–953 (2011).
[Crossref] [PubMed]

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J. M. O. Daniel, N. Simakov, P. C. Shardlow, and W. A. Clarkson, “Effect of seed linewidth on few-moded fiber amplifiers,” Conference on Laser and Electro-Optics (CLEO): paper STu2N.7 (2014).
[Crossref]

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Figures (17)

Fig. 1
Fig. 1 The basic process of the polarization beam combination for (a) without phase control and (b) phase control.
Fig. 2
Fig. 2 Experimental setup of the two-channel CPBC system with artificial tilt aberrations. CO1-CO2: collimators; HWP: half wavelength plate; M1: all-reflectance mirror; M2: high- reflectance mirror (99.9:0.1); M3:40:60 beam splitter; PMM: piezo-mounted mirror; SG: signal generator; PBC1-PBC2: polarization beam combiners; PD: photo-detector; P1-P3: Power meters.
Fig. 3
Fig. 3 (a) The simplified schematic of the experimental setup and (b) coordinate systems for the laser beam propagating in different directions.
Fig. 4
Fig. 4 The time dependent energy collected in the PD in the situations of without phasing and with active phasing.
Fig. 5
Fig. 5 The far-field initial central positions and terminal central positions of beam 2 at different modulation depths.
Fig. 6
Fig. 6 (a) The comparison of theoretical and experimental combining efficiencies at different tilt aberrations and (b) the modulation frequency of tilt phase aberrations versus the combining efficiency of the experimental setup.
Fig. 7
Fig. 7 Experimental setup of the two-channel CPBC system with artificial higher order phase aberrations. CO1-CO2: collimators; HWP: half wavelength plate; NPBS: non-polarized beam splitter; SLM: spatial light modulator; BS1: 96:4 beam splitter; BS2: 40:60 beam splitter; IPD: intensity and phase measurable detector; PBC1-PBC2: polarization beam combiners; PD: photo-detector.
Fig. 8
Fig. 8 The time dependent energy collected in the PD in the circumstance of without and with active phasing.
Fig. 9
Fig. 9 The intensity distribution of the referenced beam is shown in figure (a) and the averaged phase distribution of the referenced beam is shown in figure (b).
Fig. 10
Fig. 10 The intensity and averaged phase distributions of the defocus phase modulated beam with different d are shown in figure (a) and (b), respectively.
Fig. 11
Fig. 11 The theoretical and experimental combining efficiencies of experimental setup with defocus phase aberrations in the situations of different modulation coefficient d.
Fig. 12
Fig. 12 The intensity and averaged phase distributions of the 0° astigmatism phase modulated beam with different d are shown in figure (a) and (b), respectively.
Fig. 13
Fig. 13 The theoretical and experimental combining efficiencies of experimental setup with 0° astigmatism phase aberrations in the situations of different modulation coefficients d.
Fig. 14
Fig. 14 The intensity and averaged phase distributions of the coma-y phase aberrations modulated beam with different d are shown in figure (a) and (b), respectively.
Fig. 15
Fig. 15 The theoretical and experimental combining efficiencies of experimental setup with coma-y phase aberrations in the circumstances of different modulation coefficients d.
Fig. 16
Fig. 16 The intensity and averaged phase distributions of the 0° trefoil phase aberrations modulated beam with different d are shown in figure (a) and (b), respectively.
Fig. 17
Fig. 17 The theoretical and experimental combining efficiencies of experimental setup with 0° trefoil phase aberrations in the circumstances of different modulation coefficients d.

Equations (12)

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E 1 (x,y, z 1 )= 2 P 1 π . 1 w 1 ( z 1 ) .exp( x 2 + y 2 w 2 1 ( z 1 ) ) .exp( i φ 1 )
k= 2π λ ; Z 10 = π w 2 10 λ R 1 ( z 1 )= Z 10 ( z 1 / Z 10 + Z 10 / z 1 ); ψ 1 (z)=arctan( z 1 / Z 10 ) ψ 10 w( z 1 )= w 10 1+ ( z 1 / Z 10 ) 2 ; φ 1 =k[ x 2 + y 2 2 R 1 ( z 1 ) ]+k z 1 ψ 1 ( z 1 ) }
E 2 (x,y, z 2 )= 2 P 2 π . 1 w 2 ( ρ 2 ) .exp( ε 2 2 + η 2 2 w 2 2 ( ρ 2 ) ) .exp(i φ 2 )
Z 20 = π w 20 2 λ ; ε 2 =xcos δ θ x + z 2 sin δ θ x η 2 =xsin δ θ x sin δ θ y +ycos δ θ y z 2 cos δ θ x sin δ θ y ρ 2 =xcos δ θ y sin δ θ x +ysin δ θ y + z 2 cos δ θ y cos δ θ x w 2 ( ρ 2 )= w 20 1+ ( ρ 2 / Z 20 ) 2 ; R 2 ( ρ 2 )= Z 20 ( ρ 2 / Z 20 + Z 20 / ρ 2 ) ψ 2 ( ρ 2 )=arctan( ρ 2 / Z 0 ) ψ 20 ; φ 2 =k[ ε 2 2 + η 2 2 2 R 2 ( ρ 2 ) ]+k ρ 2 ψ 2 ( ρ 2 ) }
η eff = P 2max P 0
η eff = 1 2 Γ 1 d x d y + ( Γ 2 T d x d y ) 2 + ( Γ 3 d x d y ) 2 i=1 2 | E i | 2 d x d y
Γ 1 = T ps R o T hs | E 1 (x,y, z 1 ) | 2 + T ps T e T hs | E 2 (x,y, z 2 ) | 2 Γ 2 =2 T ps T hs R o T e | E 1 (x,y, z 1 ) || E 2 (x,y, z 2 ) |cos[ φ 1 φ 2 +ξ(t) ] Γ 3 = T ps R o T hs | E 1 (x,y, z 1 ) | 2 T ps T e T hs | E 2 (x,y, z 2 ) | 2 }
E 1 (x,y, z 1 )= I 1 (x,y, z 1 ) exp[ i ϕ 1 (x,y, z 1 ) ] E 2 (x,y, z 2 )= I 2 (x,y, z 2 ) exp[ i ϕ 2 (x,y, z 2 ) ]
η eff = 1 2 (1Δη) ϒ 1 d x d y + ( ϒ 2 T d x d y ) 2 + ( ϒ 3 d x d y ) 2 ϒ 1 d x d y
ϒ 1 = I 1 (x,y, Z 1 )+ I 2 (x,y, Z 2 ) ϒ 2 =2 I 1 (x,y, Z 1 ) I 2 (x,y, Z 2 ) cos[ ϕ 1 (x,y, Z 1 ) ϕ 2 (x,y, Z 2 )+ξ(t) ] ϒ 3 = I 1 (x,y, Z 1 ) I 2 (x,y, Z 2 ) }
η eff = P BS1 P PM P BS1 (1Δη)
Δ ψ PV =d ψ PA

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