Abstract

We present a mathematical model and provide an analysis of optical beam director systems composed of adaptive arrays of fiber collimators (subapertures), referred to here as conformal optical systems. Performances of the following two system architectures are compared: A conformal-beam director with mutually incoherent output laser beams transmitted through fiber collimators (beamlets), and a corresponding coherent system whose beamlets can be coherently combined (phase locked) at a remote target plane. The effect of the major characteristics of the conformal systems on the efficiency of laser beam projection is evaluated both analytically and through numerical simulations. The characteristics considered here are the number of fiber collimators and the subaperture and conformal aperture fill factors, as well as the accuracy of beamlet pointing.

© 2008 Optical Society of America

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  1. A. Labeyrie, “Coherent arrays,” in Proceedings of Conference on Optical Telescopes of the Future (ESO/CERN, 1978), pp. 375-385.
  2. E. K. Hege, J. M. Beckers, P. A. Strittmatter, and D. W. McCarthy, “Multiple mirror telescope as a phased array telescope,” Appl. Opt. 24, 2565-2576 (1985).
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    [CrossRef] [PubMed]
  4. M. Minden, “Coherent coupling of a fiber amplifier array,” in Thirteenth Annual Solid State and Diode Laser Technology Review, SSDLTR 2000 Tech. Digest (Air Force Research Laboratory, 2000).
  5. H. Bruesselbach, S. Wang, M. Minden, D. C. Jones, and M. Mangir, “Power-scalable phase-compensating fiber-array transceiver for laser communications through the atmosphere,” J. Opt. Soc. Am. B 22, 347-353 (2005).
    [CrossRef]
  6. M. A. Vorontsov, “Adaptive photonics phase-locked elements (APPLE): System architecture and wavefront control concept,” Proc. SPIE 5895, 589501 (2005).
    [CrossRef]
  7. P. Sprangle, J. Penano, and A. Ting, “Incoherent combining of high-power fiber lasers for long-range directed energy applications. Interim Rept. May-June 2006,” NRL/MR/6790-06-8963 (Naval Research Laboratory, 2006).
  8. 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]
  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. T. M. Shay, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express 14, 12188-12195 (2006).
    [CrossRef] [PubMed]
  11. V. P. Gapontsev, “New milestones in the development of super high power fiber lasers,” presented at the Photonics West, OE/LASE 2006, San Jose, Calif., January 21-26, 2006.
  12. S. L. Lachinova and M. A. Vorontsov, “Laser beam projection with adaptive array of fiber collimators. II. Analysis of atmospheric compensation efficiency,” J. Opt. Soc. Am. A 25, 1960-1973 (2008).
    [CrossRef]
  13. We assume that the coordinate vector r in Eqs. belongs to the target plane and all beamlets are projected onto the on-axis target plane without changes.
  14. S. Thaniyavarn, “Wavelength-independent polarization converter,” U.S. patent 4,691,984 (8 September 1987).
  15. See http://www.eospace.com/.
  16. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).
  17. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  18. L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
    [CrossRef]
  19. S. W. Sparrold, J. P. Mills, R. A. Paiva, T. D. Arndt, K. S. Ellis, and D. J. Knapp, “Beam steering optical arrangement using Risley prisms with surface contours for aberration correction,” U.S. patent 6,344,937 (5 February 2002).
  20. B. D. Duncan, P. J. Bos, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42, 1038-1047 (2003).
    [CrossRef]
  21. P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268-298 (1996).
    [CrossRef]
  22. P. F. McManamon and W. Thompson, “Phased array of phased arrays (PAPA) laser systems architecture,” in 2002 IEEE Aerospace Conference Proceedings (IEEE, 2002), Vol. 3, pp. 1465-1472.
  23. S. Serati, H. Masterson, and A. Linnenberger, “Beam combining using a phased array of phased arrays (PAPA),” in 2004 IEEE Aerospace Conference Proceedings (IEEE, 2004), Vol. 3, 1722-1729.
  24. L. A. Beresnev and M. A. Vorontsov, “Design of adaptive fiber optics collimator for free-space communication laser transceiver,” Proc. SPIE 5895, 58950R (2005).
    [CrossRef]
  25. T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, D. J. Nelson, and C. A. Lu, “Narrow linewidth coherent beam combining of optical fiber amplifier arrays,” Proc. SPIE 6451, 64511N (2007).
    [CrossRef]
  26. M. Aubailly and M. A. Vorontsov, “Imaging with an array of adaptive subapertures,” Opt. Lett. 33, 10-12 (2008).
    [CrossRef]

2008 (2)

2007 (2)

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, D. J. Nelson, and C. A. Lu, “Narrow linewidth coherent beam combining of optical fiber amplifier arrays,” Proc. SPIE 6451, 64511N (2007).
[CrossRef]

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

2006 (4)

P. Sprangle, J. Penano, and A. Ting, “Incoherent combining of high-power fiber lasers for long-range directed energy applications. Interim Rept. May-June 2006,” NRL/MR/6790-06-8963 (Naval Research Laboratory, 2006).

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]

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

2005 (3)

H. Bruesselbach, S. Wang, M. Minden, D. C. Jones, and M. Mangir, “Power-scalable phase-compensating fiber-array transceiver for laser communications through the atmosphere,” J. Opt. Soc. Am. B 22, 347-353 (2005).
[CrossRef]

M. A. Vorontsov, “Adaptive photonics phase-locked elements (APPLE): System architecture and wavefront control concept,” Proc. SPIE 5895, 589501 (2005).
[CrossRef]

L. A. Beresnev and M. A. Vorontsov, “Design of adaptive fiber optics collimator for free-space communication laser transceiver,” Proc. SPIE 5895, 58950R (2005).
[CrossRef]

2004 (1)

S. Serati, H. Masterson, and A. Linnenberger, “Beam combining using a phased array of phased arrays (PAPA),” in 2004 IEEE Aerospace Conference Proceedings (IEEE, 2004), Vol. 3, 1722-1729.

2003 (1)

B. D. Duncan, P. J. Bos, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42, 1038-1047 (2003).
[CrossRef]

2002 (2)

S. W. Sparrold, J. P. Mills, R. A. Paiva, T. D. Arndt, K. S. Ellis, and D. J. Knapp, “Beam steering optical arrangement using Risley prisms with surface contours for aberration correction,” U.S. patent 6,344,937 (5 February 2002).

P. F. McManamon and W. Thompson, “Phased array of phased arrays (PAPA) laser systems architecture,” in 2002 IEEE Aerospace Conference Proceedings (IEEE, 2002), Vol. 3, pp. 1465-1472.

2000 (1)

M. Minden, “Coherent coupling of a fiber amplifier array,” in Thirteenth Annual Solid State and Diode Laser Technology Review, SSDLTR 2000 Tech. Digest (Air Force Research Laboratory, 2000).

1996 (2)

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268-298 (1996).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

1992 (1)

1987 (1)

S. Thaniyavarn, “Wavelength-independent polarization converter,” U.S. patent 4,691,984 (8 September 1987).

1985 (1)

1980 (1)

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

1978 (1)

A. Labeyrie, “Coherent arrays,” in Proceedings of Conference on Optical Telescopes of the Future (ESO/CERN, 1978), pp. 375-385.

Anderegg, J.

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]

Angel, J. R. P.

Arndt, T. D.

S. W. Sparrold, J. P. Mills, R. A. Paiva, T. D. Arndt, K. S. Ellis, and D. J. Knapp, “Beam steering optical arrangement using Risley prisms with surface contours for aberration correction,” U.S. patent 6,344,937 (5 February 2002).

Aubailly, M.

Baker, J. T.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, D. J. Nelson, and C. A. Lu, “Narrow linewidth coherent beam combining of optical fiber amplifier arrays,” Proc. SPIE 6451, 64511N (2007).
[CrossRef]

Beckers, J. M.

Benham, V.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, D. J. Nelson, and C. A. Lu, “Narrow linewidth coherent beam combining of optical fiber amplifier arrays,” Proc. SPIE 6451, 64511N (2007).
[CrossRef]

Beresnev, L. A.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

L. A. Beresnev and M. A. Vorontsov, “Design of adaptive fiber optics collimator for free-space communication laser transceiver,” Proc. SPIE 5895, 58950R (2005).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

Bos, P. J.

B. D. Duncan, P. J. Bos, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42, 1038-1047 (2003).
[CrossRef]

Brosnan, S.

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]

Bruesselbach, H.

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]

Colucci, D.

Corkum, D. L.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Dekany, R.

Dorschner, T. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Duncan, B. D.

B. D. Duncan, P. J. Bos, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42, 1038-1047 (2003).
[CrossRef]

Ellis, K. S.

S. W. Sparrold, J. P. Mills, R. A. Paiva, T. D. Arndt, K. S. Ellis, and D. J. Knapp, “Beam steering optical arrangement using Risley prisms with surface contours for aberration correction,” U.S. patent 6,344,937 (5 February 2002).

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]

Friedman, L. J.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Gapontsev, V. P.

V. P. Gapontsev, “New milestones in the development of super high power fiber lasers,” presented at the Photonics West, OE/LASE 2006, San Jose, Calif., January 21-26, 2006.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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]

Hege, E. K.

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]

Hobbs, D. S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Holz, M.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Jones, D. C.

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]

Knapp, D. J.

S. W. Sparrold, J. P. Mills, R. A. Paiva, T. D. Arndt, K. S. Ellis, and D. J. Knapp, “Beam steering optical arrangement using Risley prisms with surface contours for aberration correction,” U.S. patent 6,344,937 (5 February 2002).

Komine, H.

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]

Labeyrie, A.

A. Labeyrie, “Coherent arrays,” in Proceedings of Conference on Optical Telescopes of the Future (ESO/CERN, 1978), pp. 375-385.

Lachinova, S. L.

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]

Liberman, S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Linnenberger, A.

S. Serati, H. Masterson, and A. Linnenberger, “Beam combining using a phased array of phased arrays (PAPA),” in 2004 IEEE Aerospace Conference Proceedings (IEEE, 2004), Vol. 3, 1722-1729.

Liu, L.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

Lloyd-Hart, M.

Lu, C. A.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, D. J. Nelson, and C. A. Lu, “Narrow linewidth coherent beam combining of optical fiber amplifier arrays,” Proc. SPIE 6451, 64511N (2007).
[CrossRef]

Mangir, M.

Masterson, H.

S. Serati, H. Masterson, and A. Linnenberger, “Beam combining using a phased array of phased arrays (PAPA),” in 2004 IEEE Aerospace Conference Proceedings (IEEE, 2004), Vol. 3, 1722-1729.

McCarthy, D.

McCarthy, D. W.

McLeod, B.

McManamon, P. F.

P. F. McManamon and W. Thompson, “Phased array of phased arrays (PAPA) laser systems architecture,” in 2002 IEEE Aerospace Conference Proceedings (IEEE, 2002), Vol. 3, pp. 1465-1472.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Mills, J. P.

S. W. Sparrold, J. P. Mills, R. A. Paiva, T. D. Arndt, K. S. Ellis, and D. J. Knapp, “Beam steering optical arrangement using Risley prisms with surface contours for aberration correction,” U.S. patent 6,344,937 (5 February 2002).

Minden, M.

H. Bruesselbach, S. Wang, M. Minden, D. C. Jones, and M. Mangir, “Power-scalable phase-compensating fiber-array transceiver for laser communications through the atmosphere,” J. Opt. Soc. Am. B 22, 347-353 (2005).
[CrossRef]

M. Minden, “Coherent coupling of a fiber amplifier array,” in Thirteenth Annual Solid State and Diode Laser Technology Review, SSDLTR 2000 Tech. Digest (Air Force Research Laboratory, 2000).

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]

Nelson, D. J.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, D. J. Nelson, and C. A. Lu, “Narrow linewidth coherent beam combining of optical fiber amplifier arrays,” Proc. SPIE 6451, 64511N (2007).
[CrossRef]

Nguyen, H. Q.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Paiva, R. A.

S. W. Sparrold, J. P. Mills, R. A. Paiva, T. D. Arndt, K. S. Ellis, and D. J. Knapp, “Beam steering optical arrangement using Risley prisms with surface contours for aberration correction,” U.S. patent 6,344,937 (5 February 2002).

Penano, J.

P. Sprangle, J. Penano, and A. Ting, “Incoherent combining of high-power fiber lasers for long-range directed energy applications. Interim Rept. May-June 2006,” NRL/MR/6790-06-8963 (Naval Research Laboratory, 2006).

Pilkington, D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, D. J. Nelson, and C. A. Lu, “Narrow linewidth coherent beam combining of optical fiber amplifier arrays,” Proc. SPIE 6451, 64511N (2007).
[CrossRef]

Polnau, E.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

Resler, D. P.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Sanchez, A. D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, D. J. Nelson, and C. A. Lu, “Narrow linewidth coherent beam combining of optical fiber amplifier arrays,” Proc. SPIE 6451, 64511N (2007).
[CrossRef]

Scott-Fleming, I.

Serati, S.

S. Serati, H. Masterson, and A. Linnenberger, “Beam combining using a phased array of phased arrays (PAPA),” in 2004 IEEE Aerospace Conference Proceedings (IEEE, 2004), Vol. 3, 1722-1729.

Sergan, V.

B. D. Duncan, P. J. Bos, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42, 1038-1047 (2003).
[CrossRef]

Sharp, R. C.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268-298 (1996).
[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.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, D. J. Nelson, and C. A. Lu, “Narrow linewidth coherent beam combining of optical fiber amplifier arrays,” Proc. SPIE 6451, 64511N (2007).
[CrossRef]

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

Sparrold, S. W.

S. W. Sparrold, J. P. Mills, R. A. Paiva, T. D. Arndt, K. S. Ellis, and D. J. Knapp, “Beam steering optical arrangement using Risley prisms with surface contours for aberration correction,” U.S. patent 6,344,937 (5 February 2002).

Sprangle, P.

P. Sprangle, J. Penano, and A. Ting, “Incoherent combining of high-power fiber lasers for long-range directed energy applications. Interim Rept. May-June 2006,” NRL/MR/6790-06-8963 (Naval Research Laboratory, 2006).

Strittmatter, P. A.

Thaniyavarn, S.

S. Thaniyavarn, “Wavelength-independent polarization converter,” U.S. patent 4,691,984 (8 September 1987).

Thompson, W.

P. F. McManamon and W. Thompson, “Phased array of phased arrays (PAPA) laser systems architecture,” in 2002 IEEE Aerospace Conference Proceedings (IEEE, 2002), Vol. 3, pp. 1465-1472.

Ting, A.

P. Sprangle, J. Penano, and A. Ting, “Incoherent combining of high-power fiber lasers for long-range directed energy applications. Interim Rept. May-June 2006,” NRL/MR/6790-06-8963 (Naval Research Laboratory, 2006).

Vorontsov, M. A.

S. L. Lachinova and M. A. Vorontsov, “Laser beam projection with adaptive array of fiber collimators. II. Analysis of atmospheric compensation efficiency,” J. Opt. Soc. Am. A 25, 1960-1973 (2008).
[CrossRef]

M. Aubailly and M. A. Vorontsov, “Imaging with an array of adaptive subapertures,” Opt. Lett. 33, 10-12 (2008).
[CrossRef]

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

M. A. Vorontsov, “Adaptive photonics phase-locked elements (APPLE): System architecture and wavefront control concept,” Proc. SPIE 5895, 589501 (2005).
[CrossRef]

L. A. Beresnev and M. A. Vorontsov, “Design of adaptive fiber optics collimator for free-space communication laser transceiver,” Proc. SPIE 5895, 58950R (2005).
[CrossRef]

Wang, S.

Watson, E. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268-298 (1996).
[CrossRef]

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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]

Weyrauch, T.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

Wickham, M.

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]

Wittman, D.

Wizinowich, P.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

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]

Appl. Opt. (2)

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

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

Opt. Eng. (1)

B. D. Duncan, P. J. Bos, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42, 1038-1047 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. IEEE (1)

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Proc. SPIE (6)

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

L. A. Beresnev and M. A. Vorontsov, “Design of adaptive fiber optics collimator for free-space communication laser transceiver,” Proc. SPIE 5895, 58950R (2005).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, D. J. Nelson, and C. A. Lu, “Narrow linewidth coherent beam combining of optical fiber amplifier arrays,” Proc. SPIE 6451, 64511N (2007).
[CrossRef]

M. A. Vorontsov, “Adaptive photonics phase-locked elements (APPLE): System architecture and wavefront control concept,” Proc. SPIE 5895, 589501 (2005).
[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]

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]

Other (12)

We assume that the coordinate vector r in Eqs. belongs to the target plane and all beamlets are projected onto the on-axis target plane without changes.

S. Thaniyavarn, “Wavelength-independent polarization converter,” U.S. patent 4,691,984 (8 September 1987).

See http://www.eospace.com/.

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P. Sprangle, J. Penano, and A. Ting, “Incoherent combining of high-power fiber lasers for long-range directed energy applications. Interim Rept. May-June 2006,” NRL/MR/6790-06-8963 (Naval Research Laboratory, 2006).

A. Labeyrie, “Coherent arrays,” in Proceedings of Conference on Optical Telescopes of the Future (ESO/CERN, 1978), pp. 375-385.

M. Minden, “Coherent coupling of a fiber amplifier array,” in Thirteenth Annual Solid State and Diode Laser Technology Review, SSDLTR 2000 Tech. Digest (Air Force Research Laboratory, 2000).

V. P. Gapontsev, “New milestones in the development of super high power fiber lasers,” presented at the Photonics West, OE/LASE 2006, San Jose, Calif., January 21-26, 2006.

S. W. Sparrold, J. P. Mills, R. A. Paiva, T. D. Arndt, K. S. Ellis, and D. J. Knapp, “Beam steering optical arrangement using Risley prisms with surface contours for aberration correction,” U.S. patent 6,344,937 (5 February 2002).

P. F. McManamon and W. Thompson, “Phased array of phased arrays (PAPA) laser systems architecture,” in 2002 IEEE Aerospace Conference Proceedings (IEEE, 2002), Vol. 3, pp. 1465-1472.

S. Serati, H. Masterson, and A. Linnenberger, “Beam combining using a phased array of phased arrays (PAPA),” in 2004 IEEE Aerospace Conference Proceedings (IEEE, 2004), Vol. 3, 1722-1729.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagrams of a fiber-based conformal-beam projection system using either a single laser source (a) or an array of fiber-coupled laser sources (b). Both systems include wavefront correctors for adaptive compensation of atmospheric turbulence-induced phase aberrations.

Fig. 2
Fig. 2

Geometries of fiber-based conformal-beam director of aperture D (dashed circles) with (a) 3, (b) 7, (c) 19, and (d) 37 densely packed subapertures of diameter d (solid circles). The gray-scale images correspond to the Gaussian-shaped intensity distributions inside the subapertures.

Fig. 3
Fig. 3

Beam projection on a remote target at distance L in vacuum for a conformal beam with N sub densely packed phase-locked subapertures of diameter d = 2.22 a 0 , as in Fig. 2. The diffraction-limited on-axis target-plane intensity I T 0 ( 0 ) obtained with tip/tilt and piston control using an approximation of the optimal phase u F ( r ) is normalized by the intensity I T F ( 0 ) corresponding to u F ( r ) . The intensity at each subaperture is described by the Gaussian function of radius a 0 .

Fig. 4
Fig. 4

Effect of the subaperture fill factor f sub = a 0 a sub on the conformal-beam intensity distribution in the pupil plane (top row) and the target plane at L = 0.1 L dif (middle and bottom rows) for coherent phase-locked (middle row) and incoherent (bottom rows) beam directors with seven densely packed subapertures: f sub = 0.5 in (a), 0.89 in (b), and 1.2 in (c). The transmitted power-loss factor γ p = p out p 0 [Eq. (15)] versus f sub in (d). Points A, B, and C in (d) correspond to the fill factor values shown in (a), (b), and (c), respectively.

Fig. 5
Fig. 5

Optimization of the subaperture fill factor f sub for coherent [(a) and (c)] and incoherent [(b) and (d)] conformal-beam directors using the diffraction-limited on-axis target-plane intensity I T 0 ( 0 ) as a metric: (a) and (b), dependence of I T 0 ( 0 ) I M F ( 0 ) on f sub for L = 0.1 L dif and different numbers of subapertures N sub ; (c) and (d), dependence of the optimal subaperture fill factor f sub opt on the propagation distance L. The optimal fill factor value f sub opt is depicted by the dashed line in (a) for N sub = 37 and in (b) for N sub = 3 .

Fig. 6
Fig. 6

Effect of the conformal aperture fill factor f C = l d on the beam intensity distribution in the pupil plane (top row) and at the target plane (bottom row) for a coherent phase-locked beam director with seven subapertures for f C = 1.0 (a), 1.5 (b), and 2.0 (c). Also shown are the dependences of the normalized metric J PIB 0 P 0 on f C for b T = 0.5 b T 0 (d) and b T = b T 0 (e) for different N sub . The bucket size is indicated in (a)–(c) by the dashed circles of radius b T 0 . The subaperture fill factor f sub = 0.89 and L = 0.1 L dif .

Fig. 7
Fig. 7

Parameters κ (the PIB metric rate of decrease) and χ (PIB for the densely packed conformal aperture) versus the normalized bucket radius b T b T 0 for different numbers of subapertures N sub .

Equations (19)

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E j ( ρ j , t ) = e j ( t ) M ( ρ j ) A j ( ρ j , t ) e i ω 0 t ( j = 1 , , N sub ) ,
E ( r , z = 0 , t ) = e i ω 0 t j = 1 N sub e j ( t ) M ( ρ j ) A j ( ρ j , t ) = e i ω 0 t j = 1 N sub e j ( t ) A j out ( ρ j , t ) .
A j ( ρ j , t ) = A 0 ( ρ j ) = A 0 ( 0 ) exp ( ρ j 2 a 0 2 ) ,
I j ( ρ j , t ) = I 0 ( ρ j ) = I 0 ( 0 ) exp ( 2 ρ j 2 a 0 2 ) ,
A j out ( ρ j , t ) = M ( ρ j ) A 0 ( ρ j ) exp [ i φ j out ( ρ j , t ) + i Δ j out ( t ) ] ,
E T ( r , t ) = e i ω 0 t M ( r ) A 0 ( r ) j = 1 N sub e j ( t ) exp [ i φ j T ( r , t ) + i Δ j T ( t ) + i u j tilt ( r ) ] ,
φ j T ( r , t ) = φ j out ( r , t ) + φ j at ( r , t )
Δ j T ( t ) = Δ j out ( t ) + Δ j at ( t )
I T ( r , t ) = M ( r ) I 0 ( r ) { N sub + 2 j = 1 N sub m = 1 j 1 p j , m ( t ) cos [ φ j T ( r , t ) φ m T ( r , t ) + Δ j T ( t ) Δ m T ( t ) + u j tilt ( r ) u m tilt ( r ) ] } ,
Δ j T ( t ) = Δ j out ( t ) + Δ j at ( t ) + v j ( t ) .
Δ j out ( t ) = n l j ( t ) ω 0 c + n l j ( t ) Δ ω j ( t ) c = Δ j s ( t ) + Δ j f ( t ) ,
E j ( ρ j , t ) = e j ( t ) A j out ( ρ j , t ) exp [ i ω 0 t + i Δ f ( t ) ] ,
A j out ( ρ j , t ) = M ( ρ j ) A 0 ( ρ j ) exp [ i φ j out ( ρ j , t ) + i Δ j s ( t ) ] .
u j tilt ( ρ j ) = k ( α j ρ j ) ( j = 1 , , N sub ) ,
γ p = p out p 0 = 2 π A 0 2 ( 0 ) a 0 2 Ω j A 0 2 ( r r j ) d 2 r = [ 1 exp ( 2 f sub 2 ) ] ,
A out ( r ) = j = 1 N sub A j out ( ρ j ) = j = 1 N sub M ( ρ j ) A 0 ( ρ j ) exp [ i u j tilt ( ρ j ) + i u j p ] .
A j out ( ρ j ) = M ( ρ j ) A 0 ( ρ j ) exp [ i u j tilt ( ρ j ) + i Δ j f ] ( j = 1 , , N sub ) .
J PIB ( t ) = S b A ( r , z = L , t ) 2 d 2 r ,
J PIB ( t ) = j = 1 N sub S b A j ( r , z = L , t ) 2 d 2 r = j = 1 N sub p j PIB ( t ) .

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