Abstract

In this paper, the influence of aberrations on coherent polarization beam combining (CPBC) of fiber laser beams is analyzed in detail for the first time to our knowledge. The expression of the coherently polarization combined output power is obtained, which contains the geometry and nongeometry factors of the CPBC system. The geometry and nongeometry aberrations are numerically studied to investigate their effects on the combining efficiency. It is found that to ensure the combining efficiency of a CPBC unit (we studied) to be more than 90%, the overlap error (the beams in the polarization beam combiner cannot be superposed entirely) should be controlled to be less than 0.45, the tilt error should be less than 2π/15rad, and the RMS value of the phase error should be limited to be within λ/10. The generalized methodology that we present offers a good reference for investigating the CPBC system in an extensive way.

© 2012 Optical Society of America

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2010 (2)

2009 (5)

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 and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[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]

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[CrossRef]

B. Wang, E. Mies, M. Minden, and A. Sanchez, “All-fiber 50 W coherently combined passive laser array,” Opt. Lett. 34, 863–865 (2009).
[CrossRef]

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zerinque, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High power phase locking of a fiber amplifier array,” Proc. SPIE 7195, 71951M (2009).
[CrossRef]

2008 (3)

2007 (3)

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Topics Quantum Electron. 13, 546–551 (2007).
[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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

S. J. Augst, J. Ranka, T. Y. Fan, and A. Sanchez, “Beam combining of ytterbium fiber amplifiers,” J. Opt. Soc. Am. B 24, 1707–1715 (2007).
[CrossRef]

2006 (3)

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, 201118 (2005).
[CrossRef]

2003 (1)

J. Anderegg, S. Broanan, M. Weber, H. Komine, and M. Wickham, “8-watt coherently phased 4-element fiber array,” Proc. SPIE 4974, 1–6 (2003).
[CrossRef]

1995 (1)

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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

J. Anderegg, S. Broanan, M. Weber, H. Komine, and M. Wickham, “8-watt coherently phased 4-element fiber array,” Proc. SPIE 4974, 1–6 (2003).
[CrossRef]

Andrews, J. R.

Aschenbach, K.

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

Augst, S. J.

Baker, J. T.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zerinque, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High power phase locking of a fiber amplifier array,” Proc. SPIE 7195, 71951M (2009).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14, 12022–12027 (2006).
[CrossRef]

Barty, C. P. J.

Beach, R. J.

Benham, V.

Bennaï, 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 and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Beresnev, L. A.

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[CrossRef]

Bourdon, P.

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 and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Bratcher, A.

Broanan, S.

J. Anderegg, S. Broanan, M. Weber, H. Komine, and M. Wickham, “8-watt coherently phased 4-element fiber array,” Proc. SPIE 4974, 1–6 (2003).
[CrossRef]

Bronder, T. J.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zerinque, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High power phase locking of a fiber amplifier array,” Proc. SPIE 7195, 71951M (2009).
[CrossRef]

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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

Canat, G.

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 and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Carhart, G. W.

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[CrossRef]

Chen, Z.

Cheung, E.

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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

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, 201118 (2005).
[CrossRef]

Culpepper, M. A.

Dawson, J. 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, 201118 (2005).
[CrossRef]

Epp, P.

Fan, T. Y.

Gallant, D.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zerinque, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High power phase locking of a fiber amplifier array,” Proc. SPIE 7195, 71951M (2009).
[CrossRef]

Goodno, G. 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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, B. Weiss, S. Redmond, W. Long, R. Simpson, E. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31, 1247–1249 (2006).
[CrossRef]

Goular, D.

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 and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

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]

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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

Heebner, J. E.

Hickey, L. M. B.

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Topics Quantum Electron. 13, 546–551 (2007).
[CrossRef]

Horley, R.

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Topics Quantum Electron. 13, 546–551 (2007).
[CrossRef]

Howland, D.

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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, B. Weiss, S. Redmond, W. Long, R. Simpson, E. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31, 1247–1249 (2006).
[CrossRef]

Jaouën, Y.

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 and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Jeong, Y.

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Topics Quantum Electron. 13, 546–551 (2007).
[CrossRef]

Jolivet, V.

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 and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Kansky, J. E.

J. E. Kansky, C. X. Yu, and D. V. Murphy, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE 6306, 63060G (2006).
[CrossRef]

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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, B. Weiss, S. Redmond, W. Long, R. Simpson, E. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31, 1247–1249 (2006).
[CrossRef]

J. Anderegg, S. Broanan, M. Weber, H. Komine, and M. Wickham, “8-watt coherently phased 4-element fiber array,” Proc. SPIE 4974, 1–6 (2003).
[CrossRef]

Lachinova, S. L.

Liu, L.

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[CrossRef]

Liu, Z.

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]

P. Zhou, Z. Liu, X. Xu, and Z. Chen, “Numerical analysis of the effects of aberrations on coherent combined fiber laser beams,” Appl. Opt. 47, 3350–3359 (2008).
[CrossRef]

Lombard, L.

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 and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Long, W.

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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

Lu, C. A.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zerinque, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High power phase locking of a fiber amplifier array,” Proc. SPIE 7195, 71951M (2009).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14, 12022–12027 (2006).
[CrossRef]

Lucero, A.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zerinque, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High power phase locking of a fiber amplifier array,” Proc. SPIE 7195, 71951M (2009).
[CrossRef]

Ma, H.

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.

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]

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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, B. Weiss, S. Redmond, W. Long, R. Simpson, E. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31, 1247–1249 (2006).
[CrossRef]

McNaught, S. 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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, B. Weiss, S. Redmond, W. Long, R. Simpson, E. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31, 1247–1249 (2006).
[CrossRef]

Messerly, J. M.

Mies, E.

Minden, M.

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 and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Murphy, D. V.

J. E. Kansky, C. X. Yu, and D. V. Murphy, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE 6306, 63060G (2006).
[CrossRef]

Nelson, D.

Nilsson, J.

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Topics Quantum Electron. 13, 546–551 (2007).
[CrossRef]

Pax, P. H.

Payne, D. N.

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Topics Quantum Electron. 13, 546–551 (2007).
[CrossRef]

Pilkington, D.

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 and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Pulford, B.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zerinque, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High power phase locking of a fiber amplifier array,” Proc. SPIE 7195, 71951M (2009).
[CrossRef]

Ranka, J.

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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, B. Weiss, S. Redmond, W. Long, R. Simpson, E. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31, 1247–1249 (2006).
[CrossRef]

Robin, C. A.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zerinque, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High power phase locking of a fiber amplifier array,” Proc. SPIE 7195, 71951M (2009).
[CrossRef]

Sahu, J. K.

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Topics Quantum Electron. 13, 546–551 (2007).
[CrossRef]

Sanchez, A.

Sanchez, A. D.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zerinque, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High power phase locking of a fiber amplifier array,” Proc. SPIE 7195, 71951M (2009).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14, 12022–12027 (2006).
[CrossRef]

Schuster, G. L.

Shay, T. M.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zerinque, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High power phase locking of a fiber amplifier array,” Proc. SPIE 7195, 71951M (2009).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14, 12022–12027 (2006).
[CrossRef]

Shverdin, M. Y.

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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, B. Weiss, S. Redmond, W. Long, R. Simpson, E. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31, 1247–1249 (2006).
[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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, B. Weiss, S. Redmond, W. Long, R. Simpson, E. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31, 1247–1249 (2006).
[CrossRef]

Spring, J.

Sridharan, A. K.

Stappaerts, E. A.

Tiemann, B. G.

Turner, P. W.

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Topics Quantum Electron. 13, 546–551 (2007).
[CrossRef]

Uberna, R.

Vasseur, O.

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 and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Vergien, C. L.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zerinque, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High power phase locking of a fiber amplifier array,” Proc. SPIE 7195, 71951M (2009).
[CrossRef]

Vorontsov, M. A.

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[CrossRef]

M. A. Vorontsov and S. L. Lachinova, “Laser beam projection with adaptive array of fiber collimators. I. Basic considerations for analysis,” J. Opt. Soc. Am. A 25, 1949–1959(2008).
[CrossRef]

Wang, B.

Wang, X.

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]

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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, B. Weiss, S. Redmond, W. Long, R. Simpson, E. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31, 1247–1249 (2006).
[CrossRef]

J. Anderegg, S. Broanan, M. Weber, H. Komine, and M. Wickham, “8-watt coherently phased 4-element fiber array,” Proc. SPIE 4974, 1–6 (2003).
[CrossRef]

Weiss, B.

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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

Weyrauch, T.

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[CrossRef]

Wickham, 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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

J. Anderegg, S. Broanan, M. Weber, H. Komine, and M. Wickham, “8-watt coherently phased 4-element fiber array,” Proc. SPIE 4974, 1–6 (2003).
[CrossRef]

Xu, X.

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]

P. Zhou, Z. Liu, X. Xu, and Z. Chen, “Numerical analysis of the effects of aberrations on coherent combined fiber laser beams,” Appl. Opt. 47, 3350–3359 (2008).
[CrossRef]

Yu, C. X.

J. E. Kansky, C. X. Yu, and D. V. Murphy, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE 6306, 63060G (2006).
[CrossRef]

Zerinque, C.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zerinque, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High power phase locking of a fiber amplifier array,” Proc. SPIE 7195, 71951M (2009).
[CrossRef]

Zhou, P.

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]

P. Zhou, Z. Liu, X. Xu, and Z. Chen, “Numerical analysis of the effects of aberrations on coherent combined fiber laser beams,” Appl. Opt. 47, 3350–3359 (2008).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

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

IEEE J. Quantum Electron. (1)

R. Uberna, A. Bratcher, and B. G. Tiemann, “Coherent polarization beam combination,” IEEE J. Quantum Electron. 46, 1191–1196 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[CrossRef]

IEEE J. Sel. Topics Quantum Electron. (4)

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 and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Topics Quantum Electron. 15, 257–268 (2009).
[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]

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Topics Quantum Electron. 13, 546–551 (2007).
[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 solid-state laser arrays,” IEEE J. Sel. Topics Quantum Electron. 13, 460–472 (2007).
[CrossRef]

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

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

Opt. Express (2)

Opt. Lett. (2)

Proc. SPIE (3)

J. Anderegg, S. Broanan, M. Weber, H. Komine, and M. Wickham, “8-watt coherently phased 4-element fiber array,” Proc. SPIE 4974, 1–6 (2003).
[CrossRef]

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zerinque, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High power phase locking of a fiber amplifier array,” Proc. SPIE 7195, 71951M (2009).
[CrossRef]

J. E. Kansky, C. X. Yu, and D. V. Murphy, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE 6306, 63060G (2006).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Polarization state of two combined beam (a) phase undefined, (b) phase locked.

Fig. 2.
Fig. 2.

Principle diagram of one unit of the CPBC system.

Fig. 3.
Fig. 3.

Distributions of the combining efficiency along different normalized overlap error.

Fig. 4.
Fig. 4.

Distributions of the combining efficiency along different tilt angle and distance a=b=0mm, (b) a=b=5mm; (c) a=b=15mm, (d) θ1=θ, θ2=0.

Fig. 5.
Fig. 5.

Combining efficiency dependence on amplitude ratio r with (a) overlap error and (b) tilt error.

Fig. 6.
Fig. 6.

Combining efficiency dependence on phase error δwith (a) overlap error, (b) tilt error; (a=b=0, r=1), and (c) amplitude imbalance.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

E⃗i(x,y,z)=A⃗i(θi)exp((xxi)2+(yyi)2ωi2(z))×exp(i{ki[(xxi)2+(yyi)22Ri(z)+z]ψi+ψi0})(i=1,2),
ki=2πλi,Zi0=πωi02λi,ωi(z)=ωi01+(zZ)2,Ri(z)=Zi0(zZi0+Zi0z),Ai(θi)=Aicos(θ),ψ=arctan(zZi0)},
E⃗1(x,y)=A⃗1(θ1)exp[(xa2)2+(yb2)2ω2],
E⃗2(x,y)=A⃗2(θ2)exp[(x+a2)2+(y+b2)2ω2]exp(iδ),
ηeff=PomaxPideal.
Pideal=(A12+A22)exp(2(x2+y2)ω2)dxdy,
Pomax=12ψ(x,y)dxdy+12χ22χ22+χ12cos2δ+12χ12cos2δχ22+β12cos2δ,
ψ(x,y)=A12cos2(θ1)exp(2[(xa2)2+(yb2)2]ω2)+A22cos2(θ2)exp(2[(x+a2)2+(y+b2)2]ω2),
χ1=ψ(x,y)sin2ϕ(x,y)dxdy,χ2=ψ(x,y)cos2ϕ(x,y)dxdy,
tanϕ(x,y)=A2cos(θ2)A1cos(θ1)exp[2(ax+by)ω2],
ηoverall=ηk,N=2k,

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