Abstract

Phase-difference detection based on a double position sensing detector (PSD) configuration for coherent combination is proposed in this paper. The exact phase difference can be extracted from two PSD signals by using an algorithm, which can be used as the driven signal added to the phase modulator for phase-difference compensation. Numerical calculation considering practical experimental conditions was performed to show that the method is of great potential for coherent combination.

© 2008 Optical Society of America

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  1. T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567-577 (2005).
    [CrossRef]
  2. J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U (2006).
    [CrossRef]
  3. S. J. Augst, J. K. Ranka, T. Y. Fan, and A. Sanchez, “Beam combining of ytterbium fiber amplifiers,” J. Opt. Soc. Am. B 24, 1707-1715 (2007).
    [CrossRef]
  4. G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
    [CrossRef]
  5. D. C. Jones, A. M. Scott, S. Clark, C. Stace, and R. G. Clarke, “Beam steering of a fibre bundle laser output using phased array techniques,” Proc. SPIE. 5335, 125-131 (2004).
    [CrossRef]
  6. T. M. Shay, V. Benham, Jeffrey 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. Top. Quantum Electron. 13, 480-486 (2007).
    [CrossRef]
  7. T. M. Shay, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express 14, 12188-12195 (2006).
    [CrossRef] [PubMed]
  8. 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]
  9. J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. J. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE 6306, 63060G (2006).
    [CrossRef]
  10. C. Xingchun, Z. Shengbao, Z. Shanghong, L. Yunxia, and X. Jie, “Research on the phase-detecting method for coherent combining beams in fiber laser array,” Optoelectron. Lett. 3, 455-458 (2007).
    [CrossRef]
  11. C. S. Vikram and H. J. Caufield, “Interference fringe analysis based on centroid detection,” Appl. Opt. 46, 5137-5141 (2007).
    [CrossRef] [PubMed]
  12. http://www.sales.hamamatsu.com/en/products/solid-state-division/position-sensitive-detectors.php.
  13. C. S. Vikram and H. John Caufield, “Position-sensing detector for logical operations in incoherent light,” Opt. Eng. 44, 115201 (2005).
    [CrossRef]
  14. C. D. Nabors, “Effects of phased errors on coherent emitter arrays,” Appl. Opt 33, 2284-2289 (1994).
    [CrossRef] [PubMed]

2007

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

T. M. Shay, V. Benham, Jeffrey 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. Top. Quantum Electron. 13, 480-486 (2007).
[CrossRef]

C. Xingchun, Z. Shengbao, Z. Shanghong, L. Yunxia, and X. Jie, “Research on the phase-detecting method for coherent combining beams in fiber laser array,” Optoelectron. Lett. 3, 455-458 (2007).
[CrossRef]

C. S. Vikram and H. J. Caufield, “Interference fringe analysis based on centroid detection,” Appl. Opt. 46, 5137-5141 (2007).
[CrossRef] [PubMed]

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

2006

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]

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

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U (2006).
[CrossRef]

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

2005

C. S. Vikram and H. John Caufield, “Position-sensing detector for logical operations in incoherent light,” Opt. Eng. 44, 115201 (2005).
[CrossRef]

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567-577 (2005).
[CrossRef]

2004

D. C. Jones, A. M. Scott, S. Clark, C. Stace, and R. G. Clarke, “Beam steering of a fibre bundle laser output using phased array techniques,” Proc. SPIE. 5335, 125-131 (2004).
[CrossRef]

1994

C. D. Nabors, “Effects of phased errors on coherent emitter arrays,” Appl. Opt 33, 2284-2289 (1994).
[CrossRef] [PubMed]

Anderegg, J.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U (2006).
[CrossRef]

Asman, C. P.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

Augst, S. J.

Baker, J. T.

Baker, Jeffrey T.

T. M. Shay, V. Benham, Jeffrey 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. Top. Quantum Electron. 13, 480-486 (2007).
[CrossRef]

Benham, V.

T. M. Shay, V. Benham, Jeffrey 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. Top. Quantum Electron. 13, 480-486 (2007).
[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]

Brosnan, S.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U (2006).
[CrossRef]

Caufield, H. J.

Caufield, H. John

C. S. Vikram and H. John Caufield, “Position-sensing detector for logical operations in incoherent light,” Opt. Eng. 44, 115201 (2005).
[CrossRef]

Cheung, E.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U (2006).
[CrossRef]

Cheung, E. C.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

Clark, S.

D. C. Jones, A. M. Scott, S. Clark, C. Stace, and R. G. Clarke, “Beam steering of a fibre bundle laser output using phased array techniques,” Proc. SPIE. 5335, 125-131 (2004).
[CrossRef]

Clarke, R. G.

D. C. Jones, A. M. Scott, S. Clark, C. Stace, and R. G. Clarke, “Beam steering of a fibre bundle laser output using phased array techniques,” Proc. SPIE. 5335, 125-131 (2004).
[CrossRef]

Culpepper, M. A.

Epp, P.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U (2006).
[CrossRef]

Fan, T. Y.

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

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567-577 (2005).
[CrossRef]

Goodno, G. D.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

Hammons, D.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U (2006).
[CrossRef]

Hammonsm, D.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

Higgs, C.

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

Injeyan, H.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

Jie, X.

C. Xingchun, Z. Shengbao, Z. Shanghong, L. Yunxia, and X. Jie, “Research on the phase-detecting method for coherent combining beams in fiber laser array,” Optoelectron. Lett. 3, 455-458 (2007).
[CrossRef]

Jones, D. C.

D. C. Jones, A. M. Scott, S. Clark, C. Stace, and R. G. Clarke, “Beam steering of a fibre bundle laser output using phased array techniques,” Proc. SPIE. 5335, 125-131 (2004).
[CrossRef]

Kansky, J. E.

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. J. Shaw, R. C. Lawrence, and C. Higgs, “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. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U (2006).
[CrossRef]

Lawrence, R. C.

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

Long, W. H.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

Lu, C. A.

T. M. Shay, V. Benham, Jeffrey 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. Top. Quantum Electron. 13, 480-486 (2007).
[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]

McClellan, M.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

McNaught, S. J.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

Murphy, D. V.

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

Nabors, C. D.

C. D. Nabors, “Effects of phased errors on coherent emitter arrays,” Appl. Opt 33, 2284-2289 (1994).
[CrossRef] [PubMed]

Nelson, D.

Pilkington, D.

T. M. Shay, V. Benham, Jeffrey 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. Top. Quantum Electron. 13, 480-486 (2007).
[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]

Ranka, J. K.

Redmond, S.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

Sanchez, A.

Sanchez, A. D.

T. M. Shay, V. Benham, Jeffrey 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. Top. Quantum Electron. 13, 480-486 (2007).
[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]

Scott, A. M.

D. C. Jones, A. M. Scott, S. Clark, C. Stace, and R. G. Clarke, “Beam steering of a fibre bundle laser output using phased array techniques,” Proc. SPIE. 5335, 125-131 (2004).
[CrossRef]

Shanghong, Z.

C. Xingchun, Z. Shengbao, Z. Shanghong, L. Yunxia, and X. Jie, “Research on the phase-detecting method for coherent combining beams in fiber laser array,” Optoelectron. Lett. 3, 455-458 (2007).
[CrossRef]

Shaw, S. E. J.

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

Shay, T. M.

Shengbao, Z.

C. Xingchun, Z. Shengbao, Z. Shanghong, L. Yunxia, and X. Jie, “Research on the phase-detecting method for coherent combining beams in fiber laser array,” Optoelectron. Lett. 3, 455-458 (2007).
[CrossRef]

Simpson, R.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

Sollee, J.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

Spring, J.

Stace, C.

D. C. Jones, A. M. Scott, S. Clark, C. Stace, and R. G. Clarke, “Beam steering of a fibre bundle laser output using phased array techniques,” Proc. SPIE. 5335, 125-131 (2004).
[CrossRef]

Vikram, C. S.

C. S. Vikram and H. J. Caufield, “Interference fringe analysis based on centroid detection,” Appl. Opt. 46, 5137-5141 (2007).
[CrossRef] [PubMed]

C. S. Vikram and H. John Caufield, “Position-sensing detector for logical operations in incoherent light,” Opt. Eng. 44, 115201 (2005).
[CrossRef]

Ward, B.

Weber, M.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U (2006).
[CrossRef]

Weiss, S. B.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

Wickham, M.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammonsm, H. Injeyan, H. Komine, W. H. Long, Jr., 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. Top. Quantum Electron. 13, 460-472 (2007).
[CrossRef]

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U (2006).
[CrossRef]

Xingchun, C.

C. Xingchun, Z. Shengbao, Z. Shanghong, L. Yunxia, and X. Jie, “Research on the phase-detecting method for coherent combining beams in fiber laser array,” Optoelectron. Lett. 3, 455-458 (2007).
[CrossRef]

Yu, C. X.

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

Yunxia, L.

C. Xingchun, Z. Shengbao, Z. Shanghong, L. Yunxia, and X. Jie, “Research on the phase-detecting method for coherent combining beams in fiber laser array,” Optoelectron. Lett. 3, 455-458 (2007).
[CrossRef]

Appl. Opt

C. D. Nabors, “Effects of phased errors on coherent emitter arrays,” Appl. Opt 33, 2284-2289 (1994).
[CrossRef] [PubMed]

Appl. Opt.

IEEE J. Sel. Top. Quantum Electron.

T. M. Shay, V. Benham, Jeffrey 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. Top. Quantum Electron. 13, 480-486 (2007).
[CrossRef]

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567-577 (2005).
[CrossRef]

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http://www.sales.hamamatsu.com/en/products/solid-state-division/position-sensitive-detectors.php.

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Figures (10)

Fig. 1
Fig. 1

Schematic for phase-difference detection based on a double-PSD configuration for coherent combination.

Fig. 2
Fig. 2

Interference pattern in PSD1 for different ψ: (a)  ψ = 0 , (b)  ψ = π / 2 , (c)  ψ = π , (d)  ψ = 3 π / 2 .

Fig. 3
Fig. 3

Centroid position in PSD 1 and PSD 2 versus the phase difference.

Fig. 4
Fig. 4

Dependence of phase difference ψ extracted from the two PSD signals on the actual phase difference ψ.

Fig. 5
Fig. 5

Dependence of maximal shift of centroid position on the fringe number N.

Fig. 6
Fig. 6

Centroid position in PSD 1 and PSD 2 versus the phase difference when N = 1 , γ = 0.5 , and Δ = 2 cm .

Fig. 7
Fig. 7

Dependence of maximal shift of centroid position on fringe contrast.

Fig. 8
Fig. 8

Dependence of phase difference ψ extracted from the two PSD signals on the actual phase difference ψ when N = 1 , γ = 0.5 .

Fig. 9
Fig. 9

Interference pattern in PSD1 when N = 1.2 and ψ = 0 .

Fig. 10
Fig. 10

Dependence of phase difference ψ extracted from the two PSD signals on the actual phase difference ψ when N = 1.2 .

Equations (7)

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I 1 ( x ) = 1 + γ cos ( 2 N π x Δ + ψ ) ,
I 2 ( x ) = 1 + γ cos ( 2 N π x Δ + ψ + π 2 ) = 1 + γ sin ( 2 N π x Δ + ψ ) .
X ¯ 1 = Δ / 2 Δ / 2 x I 1 ( x ) d x Δ / 2 Δ / 2 I 1 ( x ) d x = γ Δ sin ψ [ cos ( π N ) π N sin ( π N ) ( π N ) 2 ] 2 [ 1 + γ cos ψ sin ( π N ) π N ] ,
X ¯ 2 = Δ / 2 Δ / 2 x I 2 ( x ) d x Δ / 2 Δ / 2 I 2 ( x ) d x = γ Δ cos ψ [ cos ( π N ) π N sin ( π N ) ( π N ) 2 ] 2 [ 1 + γ sin ψ sin ( π N ) π N ] .
X ¯ 1 γ Δ sin ψ cos ( π N ) 2 π N , X ¯ 2 γ Δ cos ψ cos ( π N ) 2 π N .
ψ = { arcsin [ 2 π N X ¯ 1 / γ Δ ] π arcsin [ 2 π N X ¯ 1 / γ Δ ] 2 π + arcsin [ 2 π N X ¯ 1 / γ Δ ] if     { X ¯ 1 < 0 , X ¯ 2 < 0 X ¯ 2 > 0 X ¯ 1 > 0 , X ¯ 2 < 0 and     N   is an odd number ,
ψ = { arcsin [ 2 π N X ¯ 1 / γ Δ ] π arcsin [ 2 π N X ¯ 1 / γ Δ ] 2 π + arcsin [ 2 π N X ¯ 1 / γ Δ ] if     { X ¯ 1 > 0 , X ¯ 2 > 0 X ¯ 2 < 0 X ¯ 1 < 0 , X ¯ 2 > 0 and   N   is an even number .

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