Abstract

The direct use of diode lasers for high-power applications in material processing is limited to applications with relatively low beam quality and power density requirements. To achieve high beam quality one must use single-mode diode lasers, however with the drawback of relatively low optical output powers from these components. To realize a high-power system while conserving the high beam quality of the individual emitters requires coherent coupling of the emitters. Such a power-scalable system consisting of 19 slave lasers that are injection locked by one master laser has been built and investigated, with low-power diode lasers used for system demonstration. The optical power of the 19 injection-locked lasers is coupled into polarization-maintaining single-mode fibers and geometrically superimposed by a lens array and a focusing lens. The phase of each emitter is controlled by a simple electronic phase-control loop. The coherence of each slave laser is stabilized by computer control of the laser current and guarantees a stable degree of coherence of the whole system of 0.7. An enhancement factor of 13.2 in peak power density compared with that which was achievable with the incoherent superposition of the diode lasers was observed.

© 1999 Optical Society of America

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References

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  1. S. O’Brien, A. Schoenfelder, R. J. Lang, “5-W cw diffraction-limited in-GaAs broad-area flared amplifier at 970 nm,” IEEE Photonics Technol. Lett. 9, 1217–1219 (1997).
    [CrossRef]
  2. M. Lurie, “Coherence and its effect on laser arrays,” in Surface Emitting Semiconductor Lasers and Arrays, G. A. Evans, ed. (Academic, Boston, Mass., 1993), pp. 435–443.
  3. G. L. Schuster, J. R. Andrews, “Coherent beam combining: optical loss effects on power scaling,” Appl. Opt. 34, 6801–6805 (1995).
    [CrossRef] [PubMed]
  4. D. Botez, “Monolithic phase-locked semiconductor laser arrays,” in Diode Laser Arrays, D. Botez, D. R. Scifres, eds. (Cambridge U. Press, Cambridge, 1994), pp. 1–67.
    [CrossRef]
  5. J. C. Ehlert, B. Cassarly, S. H. Chakmakjian, J. M. Finlan, K. M. Flood, R. G. Waarts, D. Nam, D. F. Welch, “Automated phase sensing and control of an external Talbot cavity laser with phase-contrast imaging,” Appl. Opt. 33, 5550–5556 (1994).
    [CrossRef] [PubMed]
  6. J. S. Osinski, D. Mehuys, D. F. Welch, R. G. Waarts, J. S. Major, K. M. Dzurko, R. J. Lang, “Phased array of high-power coherent, monolithic flared amplifier master oscillator power amplifiers,” Appl. Phys. Lett. 66, 556–558 (1995).
    [CrossRef]
  7. J. Levy, K. Roh, “Coherent array of 900 semiconductor laser amplifiers,” in Laser Diodes and Applications, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2382, 58–69 (1995).
    [CrossRef]
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    [CrossRef]
  10. R. J. Lang, A. Hardy, R. Parke, D. Mehuys, S. O’Brien, J. Major, D. Welch, “Numerical analysis of flared semiconductor laser amplifiers,” IEEE J. Quantum Electron. 29, 2044–2051 (1993).
    [CrossRef]
  11. R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J. Quantum Electron. 18, 976–983 (1982).
    [CrossRef]
  12. M. Pessa, J. Nappi, P. Savolainen, A. Ovtchinnikov, M. Toivonen, R. F. Murison, H. M. Asonen, “State-of-the-art aluminum-free 980-nm laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 161–168 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. W. M. Neubert, K. H. Kudielka, W. R. Leeb, A. L. Scholz, “Experimental demonstration of an optical phased array antenna for laser space communications,” Appl. Opt. 33, 3820–3830 (1994).
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    [CrossRef]

1997 (1)

S. O’Brien, A. Schoenfelder, R. J. Lang, “5-W cw diffraction-limited in-GaAs broad-area flared amplifier at 970 nm,” IEEE Photonics Technol. Lett. 9, 1217–1219 (1997).
[CrossRef]

1995 (2)

J. S. Osinski, D. Mehuys, D. F. Welch, R. G. Waarts, J. S. Major, K. M. Dzurko, R. J. Lang, “Phased array of high-power coherent, monolithic flared amplifier master oscillator power amplifiers,” Appl. Phys. Lett. 66, 556–558 (1995).
[CrossRef]

G. L. Schuster, J. R. Andrews, “Coherent beam combining: optical loss effects on power scaling,” Appl. Opt. 34, 6801–6805 (1995).
[CrossRef] [PubMed]

1994 (2)

1993 (2)

M. Tempus, W. Lüthy, H. P. Weber, “Coherent recombination of laser beams with interferometrical phase control,” Appl. Phys. B 56, 79–83 (1993).
[CrossRef]

R. J. Lang, A. Hardy, R. Parke, D. Mehuys, S. O’Brien, J. Major, D. Welch, “Numerical analysis of flared semiconductor laser amplifiers,” IEEE J. Quantum Electron. 29, 2044–2051 (1993).
[CrossRef]

1992 (1)

1982 (1)

R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J. Quantum Electron. 18, 976–983 (1982).
[CrossRef]

1981 (1)

S. Kobayashi, T. Kimura, “Injection locking in AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 17, 681–689 (1981).
[CrossRef]

1974 (1)

D. E. N. Davies, S. Kingsley, “Method of phase-modulating signals in optical fibers: application to optical-telemetry systems,” Electron. Lett. 10, 21–22 (1974).
[CrossRef]

1965 (1)

Andrews, J. R.

Asonen, H. M.

M. Pessa, J. Nappi, P. Savolainen, A. Ovtchinnikov, M. Toivonen, R. F. Murison, H. M. Asonen, “State-of-the-art aluminum-free 980-nm laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 161–168 (1996).
[CrossRef]

Berger, L.

L. Berger, U. Brauch, A. Giesen, H. Hügel, H. Opower, M. Schubert, K. Wittig, “Coherent fiber coupling of laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 39–46 (1996).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1987), p. 503.

Botez, D.

D. Botez, “Monolithic phase-locked semiconductor laser arrays,” in Diode Laser Arrays, D. Botez, D. R. Scifres, eds. (Cambridge U. Press, Cambridge, 1994), pp. 1–67.
[CrossRef]

Brauch, U.

L. Berger, U. Brauch, A. Giesen, H. Hügel, H. Opower, M. Schubert, K. Wittig, “Coherent fiber coupling of laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 39–46 (1996).
[CrossRef]

Cassarly, B.

Chakmakjian, S. H.

Davies, D. E. N.

D. E. N. Davies, S. Kingsley, “Method of phase-modulating signals in optical fibers: application to optical-telemetry systems,” Electron. Lett. 10, 21–22 (1974).
[CrossRef]

Dzurko, K. M.

J. S. Osinski, D. Mehuys, D. F. Welch, R. G. Waarts, J. S. Major, K. M. Dzurko, R. J. Lang, “Phased array of high-power coherent, monolithic flared amplifier master oscillator power amplifiers,” Appl. Phys. Lett. 66, 556–558 (1995).
[CrossRef]

Ehlert, J. C.

Finlan, J. M.

Flood, K. M.

Frieden, B. R.

Giesen, A.

L. Berger, U. Brauch, A. Giesen, H. Hügel, H. Opower, M. Schubert, K. Wittig, “Coherent fiber coupling of laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 39–46 (1996).
[CrossRef]

Hardy, A.

R. J. Lang, A. Hardy, R. Parke, D. Mehuys, S. O’Brien, J. Major, D. Welch, “Numerical analysis of flared semiconductor laser amplifiers,” IEEE J. Quantum Electron. 29, 2044–2051 (1993).
[CrossRef]

Hügel, H.

L. Berger, U. Brauch, A. Giesen, H. Hügel, H. Opower, M. Schubert, K. Wittig, “Coherent fiber coupling of laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 39–46 (1996).
[CrossRef]

Kimura, T.

S. Kobayashi, T. Kimura, “Injection locking in AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 17, 681–689 (1981).
[CrossRef]

Kingsley, S.

D. E. N. Davies, S. Kingsley, “Method of phase-modulating signals in optical fibers: application to optical-telemetry systems,” Electron. Lett. 10, 21–22 (1974).
[CrossRef]

Kobayashi, S.

S. Kobayashi, T. Kimura, “Injection locking in AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 17, 681–689 (1981).
[CrossRef]

Kudielka, K. H.

Lang, R.

R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J. Quantum Electron. 18, 976–983 (1982).
[CrossRef]

Lang, R. J.

S. O’Brien, A. Schoenfelder, R. J. Lang, “5-W cw diffraction-limited in-GaAs broad-area flared amplifier at 970 nm,” IEEE Photonics Technol. Lett. 9, 1217–1219 (1997).
[CrossRef]

J. S. Osinski, D. Mehuys, D. F. Welch, R. G. Waarts, J. S. Major, K. M. Dzurko, R. J. Lang, “Phased array of high-power coherent, monolithic flared amplifier master oscillator power amplifiers,” Appl. Phys. Lett. 66, 556–558 (1995).
[CrossRef]

R. J. Lang, A. Hardy, R. Parke, D. Mehuys, S. O’Brien, J. Major, D. Welch, “Numerical analysis of flared semiconductor laser amplifiers,” IEEE J. Quantum Electron. 29, 2044–2051 (1993).
[CrossRef]

Leeb, W. R.

Levy, J.

J. Levy, K. Roh, “Coherent array of 900 semiconductor laser amplifiers,” in Laser Diodes and Applications, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2382, 58–69 (1995).
[CrossRef]

Lurie, M.

M. Lurie, “Coherence and its effect on laser arrays,” in Surface Emitting Semiconductor Lasers and Arrays, G. A. Evans, ed. (Academic, Boston, Mass., 1993), pp. 435–443.

Lüthy, W.

M. Tempus, W. Lüthy, H. P. Weber, “Coherent recombination of laser beams with interferometrical phase control,” Appl. Phys. B 56, 79–83 (1993).
[CrossRef]

Major, J.

R. J. Lang, A. Hardy, R. Parke, D. Mehuys, S. O’Brien, J. Major, D. Welch, “Numerical analysis of flared semiconductor laser amplifiers,” IEEE J. Quantum Electron. 29, 2044–2051 (1993).
[CrossRef]

Major, J. S.

J. S. Osinski, D. Mehuys, D. F. Welch, R. G. Waarts, J. S. Major, K. M. Dzurko, R. J. Lang, “Phased array of high-power coherent, monolithic flared amplifier master oscillator power amplifiers,” Appl. Phys. Lett. 66, 556–558 (1995).
[CrossRef]

Mehuys, D.

J. S. Osinski, D. Mehuys, D. F. Welch, R. G. Waarts, J. S. Major, K. M. Dzurko, R. J. Lang, “Phased array of high-power coherent, monolithic flared amplifier master oscillator power amplifiers,” Appl. Phys. Lett. 66, 556–558 (1995).
[CrossRef]

R. J. Lang, A. Hardy, R. Parke, D. Mehuys, S. O’Brien, J. Major, D. Welch, “Numerical analysis of flared semiconductor laser amplifiers,” IEEE J. Quantum Electron. 29, 2044–2051 (1993).
[CrossRef]

Murison, R. F.

M. Pessa, J. Nappi, P. Savolainen, A. Ovtchinnikov, M. Toivonen, R. F. Murison, H. M. Asonen, “State-of-the-art aluminum-free 980-nm laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 161–168 (1996).
[CrossRef]

Nakagawa, K.

Nam, D.

Nappi, J.

M. Pessa, J. Nappi, P. Savolainen, A. Ovtchinnikov, M. Toivonen, R. F. Murison, H. M. Asonen, “State-of-the-art aluminum-free 980-nm laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 161–168 (1996).
[CrossRef]

Neubert, W. M.

O’Brien, S.

S. O’Brien, A. Schoenfelder, R. J. Lang, “5-W cw diffraction-limited in-GaAs broad-area flared amplifier at 970 nm,” IEEE Photonics Technol. Lett. 9, 1217–1219 (1997).
[CrossRef]

R. J. Lang, A. Hardy, R. Parke, D. Mehuys, S. O’Brien, J. Major, D. Welch, “Numerical analysis of flared semiconductor laser amplifiers,” IEEE J. Quantum Electron. 29, 2044–2051 (1993).
[CrossRef]

Ohtusu, M.

Opower, H.

L. Berger, U. Brauch, A. Giesen, H. Hügel, H. Opower, M. Schubert, K. Wittig, “Coherent fiber coupling of laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 39–46 (1996).
[CrossRef]

Osinski, J. S.

J. S. Osinski, D. Mehuys, D. F. Welch, R. G. Waarts, J. S. Major, K. M. Dzurko, R. J. Lang, “Phased array of high-power coherent, monolithic flared amplifier master oscillator power amplifiers,” Appl. Phys. Lett. 66, 556–558 (1995).
[CrossRef]

Ovtchinnikov, A.

M. Pessa, J. Nappi, P. Savolainen, A. Ovtchinnikov, M. Toivonen, R. F. Murison, H. M. Asonen, “State-of-the-art aluminum-free 980-nm laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 161–168 (1996).
[CrossRef]

Parke, R.

R. J. Lang, A. Hardy, R. Parke, D. Mehuys, S. O’Brien, J. Major, D. Welch, “Numerical analysis of flared semiconductor laser amplifiers,” IEEE J. Quantum Electron. 29, 2044–2051 (1993).
[CrossRef]

Pessa, M.

M. Pessa, J. Nappi, P. Savolainen, A. Ovtchinnikov, M. Toivonen, R. F. Murison, H. M. Asonen, “State-of-the-art aluminum-free 980-nm laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 161–168 (1996).
[CrossRef]

Roh, K.

J. Levy, K. Roh, “Coherent array of 900 semiconductor laser amplifiers,” in Laser Diodes and Applications, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2382, 58–69 (1995).
[CrossRef]

Savolainen, P.

M. Pessa, J. Nappi, P. Savolainen, A. Ovtchinnikov, M. Toivonen, R. F. Murison, H. M. Asonen, “State-of-the-art aluminum-free 980-nm laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 161–168 (1996).
[CrossRef]

Sayama, S.

Schoenfelder, A.

S. O’Brien, A. Schoenfelder, R. J. Lang, “5-W cw diffraction-limited in-GaAs broad-area flared amplifier at 970 nm,” IEEE Photonics Technol. Lett. 9, 1217–1219 (1997).
[CrossRef]

Scholz, A. L.

Schubert, M.

L. Berger, U. Brauch, A. Giesen, H. Hügel, H. Opower, M. Schubert, K. Wittig, “Coherent fiber coupling of laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 39–46 (1996).
[CrossRef]

Schuster, G. L.

Siegman, A. E.

A. E. Siegman, Lasers (Oxford U. Press, Oxford, 1986), p. 1134.

Tempus, M.

M. Tempus, W. Lüthy, H. P. Weber, “Coherent recombination of laser beams with interferometrical phase control,” Appl. Phys. B 56, 79–83 (1993).
[CrossRef]

Toivonen, M.

M. Pessa, J. Nappi, P. Savolainen, A. Ovtchinnikov, M. Toivonen, R. F. Murison, H. M. Asonen, “State-of-the-art aluminum-free 980-nm laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 161–168 (1996).
[CrossRef]

Waarts, R. G.

J. S. Osinski, D. Mehuys, D. F. Welch, R. G. Waarts, J. S. Major, K. M. Dzurko, R. J. Lang, “Phased array of high-power coherent, monolithic flared amplifier master oscillator power amplifiers,” Appl. Phys. Lett. 66, 556–558 (1995).
[CrossRef]

J. C. Ehlert, B. Cassarly, S. H. Chakmakjian, J. M. Finlan, K. M. Flood, R. G. Waarts, D. Nam, D. F. Welch, “Automated phase sensing and control of an external Talbot cavity laser with phase-contrast imaging,” Appl. Opt. 33, 5550–5556 (1994).
[CrossRef] [PubMed]

Wang, W.

Weber, H. P.

M. Tempus, W. Lüthy, H. P. Weber, “Coherent recombination of laser beams with interferometrical phase control,” Appl. Phys. B 56, 79–83 (1993).
[CrossRef]

Welch, D.

R. J. Lang, A. Hardy, R. Parke, D. Mehuys, S. O’Brien, J. Major, D. Welch, “Numerical analysis of flared semiconductor laser amplifiers,” IEEE J. Quantum Electron. 29, 2044–2051 (1993).
[CrossRef]

Welch, D. F.

J. S. Osinski, D. Mehuys, D. F. Welch, R. G. Waarts, J. S. Major, K. M. Dzurko, R. J. Lang, “Phased array of high-power coherent, monolithic flared amplifier master oscillator power amplifiers,” Appl. Phys. Lett. 66, 556–558 (1995).
[CrossRef]

J. C. Ehlert, B. Cassarly, S. H. Chakmakjian, J. M. Finlan, K. M. Flood, R. G. Waarts, D. Nam, D. F. Welch, “Automated phase sensing and control of an external Talbot cavity laser with phase-contrast imaging,” Appl. Opt. 33, 5550–5556 (1994).
[CrossRef] [PubMed]

Wittig, K.

L. Berger, U. Brauch, A. Giesen, H. Hügel, H. Opower, M. Schubert, K. Wittig, “Coherent fiber coupling of laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 39–46 (1996).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1987), p. 503.

Appl. Opt. (4)

Appl. Phys. B (1)

M. Tempus, W. Lüthy, H. P. Weber, “Coherent recombination of laser beams with interferometrical phase control,” Appl. Phys. B 56, 79–83 (1993).
[CrossRef]

Appl. Phys. Lett. (1)

J. S. Osinski, D. Mehuys, D. F. Welch, R. G. Waarts, J. S. Major, K. M. Dzurko, R. J. Lang, “Phased array of high-power coherent, monolithic flared amplifier master oscillator power amplifiers,” Appl. Phys. Lett. 66, 556–558 (1995).
[CrossRef]

Electron. Lett. (1)

D. E. N. Davies, S. Kingsley, “Method of phase-modulating signals in optical fibers: application to optical-telemetry systems,” Electron. Lett. 10, 21–22 (1974).
[CrossRef]

IEEE J. Quantum Electron. (3)

S. Kobayashi, T. Kimura, “Injection locking in AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 17, 681–689 (1981).
[CrossRef]

R. J. Lang, A. Hardy, R. Parke, D. Mehuys, S. O’Brien, J. Major, D. Welch, “Numerical analysis of flared semiconductor laser amplifiers,” IEEE J. Quantum Electron. 29, 2044–2051 (1993).
[CrossRef]

R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J. Quantum Electron. 18, 976–983 (1982).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

S. O’Brien, A. Schoenfelder, R. J. Lang, “5-W cw diffraction-limited in-GaAs broad-area flared amplifier at 970 nm,” IEEE Photonics Technol. Lett. 9, 1217–1219 (1997).
[CrossRef]

Opt. Lett. (1)

Other (7)

L. Berger, U. Brauch, A. Giesen, H. Hügel, H. Opower, M. Schubert, K. Wittig, “Coherent fiber coupling of laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 39–46 (1996).
[CrossRef]

M. Lurie, “Coherence and its effect on laser arrays,” in Surface Emitting Semiconductor Lasers and Arrays, G. A. Evans, ed. (Academic, Boston, Mass., 1993), pp. 435–443.

D. Botez, “Monolithic phase-locked semiconductor laser arrays,” in Diode Laser Arrays, D. Botez, D. R. Scifres, eds. (Cambridge U. Press, Cambridge, 1994), pp. 1–67.
[CrossRef]

M. Pessa, J. Nappi, P. Savolainen, A. Ovtchinnikov, M. Toivonen, R. F. Murison, H. M. Asonen, “State-of-the-art aluminum-free 980-nm laser diodes,” in Laser Diodes and Applications II, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2682, 161–168 (1996).
[CrossRef]

A. E. Siegman, Lasers (Oxford U. Press, Oxford, 1986), p. 1134.

J. Levy, K. Roh, “Coherent array of 900 semiconductor laser amplifiers,” in Laser Diodes and Applications, K. J. Linden, P. R. Akkapeddi, eds., Proc. SPIE2382, 58–69 (1995).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1987), p. 503.

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Figures (10)

Fig. 1
Fig. 1

Schematic of system for coherent coupling of diode lasers by injection locking shown for three channels. The radiation of the slave lasers is coupled into polarization-maintaining single-mode fibers. The phase of the slave lasers is controlled by an electrical phase control loop.

Fig. 2
Fig. 2

Dependence of slave laser coherence on current. The lines illustrate the coherence control strategy. During a control sequence the current of the slave laser in question will be increased or decreased (depicted by an arrow) until the maximum coherence is reached.

Fig. 3
Fig. 3

Control loop for phase stabilization of one slave laser. The signal of the interferometric superposition of master and slave is used for detecting the phase difference between the lasers. The phase of the slave lasers is then modified by a piezoelectric disk with the fiber coiled around it. PI, proportional-integral.

Fig. 4
Fig. 4

Setup of the laser head in the experimental system. The fibers from the slave lasers are fixed relative to the lenses of the lens array. The collimated beams are focused by a single lens. A part of the slave radiation is superposed with the master radiation upon the photodiode array for phase detection.

Fig. 5
Fig. 5

Power-density distribution in the focal plane for two mutually coherent slave lasers. The calculation fits the measurements very well. The calculated degree of coherence is 0.9.

Fig. 6
Fig. 6

Measured degree of coherence between two slave lasers. After 10 min the coherence control loop was switched off.

Fig. 7
Fig. 7

Phase fluctuations between two lasers (a) without control, (b) with control but with high mechanical stress on the fibers, and (c) with control and only a laboratorylike load on the fiber.

Fig. 8
Fig. 8

Number of phase errors versus amount of phase error for measurement intervals of 2 s.

Fig. 9
Fig. 9

Power-density distribution for the superposition of the 19 slave-laser beams. Shown are (a) measured incoherent, (b) measured coherent, and (c) calculated coherent superposition. Identical scales are used for all three distributions. The power densities are normalized to the peak of the incoherent distribution of 4.4 kW/cm2.

Fig. 10
Fig. 10

Encircled power for (a), (b) the measured and (c)–(e) the calculated power-density distributions. The parameters for the calculations are given in Table 2.

Tables (2)

Tables Icon

Table 1 Measured Degree of Coherence of the Systema

Tables Icon

Table 2 Parameters for the Calculated Encircled Power Shown in Curves (c)–(e) of Fig. 10a

Equations (5)

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UsigtIt=2I01+cosΦit+ϕmot,
Φiti+ϕmoti=π/2
ΔΦt=arccosΔIt2I0-1.
Pr=A i,j Ii,jxi-x0, yj-y0, xi-x02+yj-y021/2<r.
Ex, y=γEcoh+1-γEincoh.

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