Abstract

A novel method for converting an array of out-of-phase lasers into one of in-phase lasers that can be tightly focused is presented. The method exploits second-harmonic generation and can be adapted for different laser arrays geometries. Experimental and calculated results, presented for negatively coupled lasers formed in a square, honeycomb, and triangular geometries are in good agreement.

© 2015 Chinese Laser Press

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References

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    [Crossref]
  2. M. Nixon, E. Ronen, A. A. Friesem, and N. Davidson, “Observing geometric frustration with thousands of coupled lasers,” Phys. Rev. Lett. 110, 184102 (2013).
    [Crossref]
  3. S. H. Strogatz, D. M. Abrams, A. McRobie, B. Eckhardt, and E. Ott, “Theoretical mechanics: crowd synchrony on the Millennium Bridge,” Nature 438, 43–44 (2005).
    [Crossref]
  4. L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
    [Crossref]
  5. S. H. Strogatz, “Exploring complex networks,” Nature 410, 268–276 (2001).
    [Crossref]
  6. M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106, 223901 (2011).
    [Crossref]
  7. D. J. Watts and S. H. Strogatz, “Collective dynamics of “small-world” networks,” Nature 393, 440–442 (1998).
    [Crossref]
  8. A. A. Ishaaya, N. Davidson, L. Shimshi, and A. A. Friesem, “Intracavity coherent addition of Gaussian beam distributions using a planar interferometric coupler,” Appl. Phys. Lett. 85, 2187–2189 (2004).
    [Crossref]
  9. W. Liang, N. Satyan, F. Aflatouni, A. Yariv, A. Kewitsch, G. Rakuljic, and H. Hashemi, “Coherent beam combining with multilevel optical phase-locked loops,” J. Opt. Soc. Am. B 24, 2930–2939 (2007).
    [Crossref]
  10. D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, P. Even, and D. Pureur, “Efficient coherent combining of widely tunable fiber lasers,” Opt. Express 11, 87–97 (2003).
    [Crossref]
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    [Crossref]
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    [Crossref]
  16. A. P. Napartovich, N. N. Elkin, D. V. Vysotsky, J. Kirch, and L. J. Mawst, “Two-dimensional antiguided vertical cavity surface emitting laser arrays with reflecting boundary,” IEEE J. Sel. Top. Quantum Electron. 19, 1700208 (2013).
    [Crossref]
  17. M. Fridman, M. Nixon, N. Davidson, and A. A. Friesem, “Passive phase locking of 25 fiber lasers,” Opt. Lett. 35, 1434–1436 (2010).
    [Crossref]
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  19. F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
    [Crossref]
  20. D. Mehuys, W. Streifer, R. G. Waarts, and D. F. Welch, “Modal analysis of linear Talbot-cavity semiconductor lasers,” Opt. Lett. 16, 823–825 (1991).
    [Crossref]
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    [Crossref]
  22. C. J. Corcoran and F. Durville, “Passive coherent combination of a diode laser array with 35 elements,” Opt. Express 22, 8420–8425 (2014).
    [Crossref]
  23. F. Jeux, A. Desfarges-Berthelemot, V. Kermène, and A. Barthelemy, “Efficient passive phasing of an array of 20 ring fiber lasers,” Laser Phys. Lett. 11, 095003 (2014).
    [Crossref]
  24. J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55, 334–336 (1989).
    [Crossref]
  25. R. H. Rediker, R. P. Schloss, and L. J. Van Ruyven, “Operation of individual diode lasers as a coherent ensemble controlled by a spatial filter within an external cavity,” Appl. Phys. Lett. 46, 133–135 (1985).
    [Crossref]
  26. W. J. Cassarly, J. C. Ehlert, J. M. Finlan, K. M. Flood, R. Waarts, D. Mehuys, D. Nam, and D. Welch, “Intracavity phase correction of an external Talbot cavity laser with the use of liquid crystals,” Opt. Lett. 17, 607–609 (1992).
    [Crossref]
  27. Y. Guan, P. Zhang, X. Xie, J. Zhou, and K. S. Wong, “Coherent beam combining with second-harmonic generation optimized with adaptive phase control,” IEEE J. Quantum Electron. 47, 348–353 (2011).
    [Crossref]
  28. R. W. Boyd, Nonlinear Optics (Academic, 2008).
  29. M. Sanagi, K. Yano, K. Fujimori, and S. Nogi, “Active phased array antenna radiating second harmonic output wave,” Electron. Comm. Jpn. Pt. II 89, 39–50 (2006).
    [Crossref]
  30. X. Li, H. Xiao, X.-L. Dong, Y.-X. Ma, and X.-J. Xu, “Coherent beam combining of two slab laser amplifiers and second-harmonic phase locking based on a multi-dithering technique,” Chin. Phys. Lett. 28, 094210 (2011).
    [Crossref]
  31. J. A. Arnaud, “Degenerate optical cavities,” Appl. Opt. 8, 189–195 (1969).
    [Crossref]
  32. M. Nixon, E. Ronen, M. Fridman, A. A. Friesem, and N. Davidson, “Phase locking large arrays of lasers via a single degenerate cavity,” in Frontiers in Optics 2011/Laser Science XXVII (Optical Society of America, 2011), paper FWR6.
  33. H. F. Talbot, “LXXVI. Facts relating to optical science. No. IV,” Philos. Mag. Ser. 3 9(56), 401–407 (1836).
  34. T. M. Baer and M. S. Keirstead, “Nd–YAG laser,” U.S. patent4,653,056 (Apr. 7, 1987).
  35. A. Caprara, J. L. Chilla, and L. A. Spinelli, “Intracavity frequency-converted optically-pumped semiconductor laser,” U.S. patent5,991,318 (Nov.23, 1999).
  36. T. Y. Fan, G. J. Dixon, and R. L. Byer, “Efficient GaAlAs diode-laser-pumped operation of Nd: YLF at 1.047  um with intracavity doubling to 523.6  nm,” Opt. Lett. 11, 204–206 (1986).
    [Crossref]

2014 (2)

C. J. Corcoran and F. Durville, “Passive coherent combination of a diode laser array with 35 elements,” Opt. Express 22, 8420–8425 (2014).
[Crossref]

F. Jeux, A. Desfarges-Berthelemot, V. Kermène, and A. Barthelemy, “Efficient passive phasing of an array of 20 ring fiber lasers,” Laser Phys. Lett. 11, 095003 (2014).
[Crossref]

2013 (2)

M. Nixon, E. Ronen, A. A. Friesem, and N. Davidson, “Observing geometric frustration with thousands of coupled lasers,” Phys. Rev. Lett. 110, 184102 (2013).
[Crossref]

A. P. Napartovich, N. N. Elkin, D. V. Vysotsky, J. Kirch, and L. J. Mawst, “Two-dimensional antiguided vertical cavity surface emitting laser arrays with reflecting boundary,” IEEE J. Sel. Top. Quantum Electron. 19, 1700208 (2013).
[Crossref]

2012 (1)

2011 (3)

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106, 223901 (2011).
[Crossref]

Y. Guan, P. Zhang, X. Xie, J. Zhou, and K. S. Wong, “Coherent beam combining with second-harmonic generation optimized with adaptive phase control,” IEEE J. Quantum Electron. 47, 348–353 (2011).
[Crossref]

X. Li, H. Xiao, X.-L. Dong, Y.-X. Ma, and X.-J. Xu, “Coherent beam combining of two slab laser amplifiers and second-harmonic phase locking based on a multi-dithering technique,” Chin. Phys. Lett. 28, 094210 (2011).
[Crossref]

2010 (1)

2007 (2)

I. Hassiaoui, N. Michel, M. Lecomte, O. Parillaud, M. Calligaro, and M. Kakowski, “In-phase coherent coupling of tapered lasers in an external Talbot cavity,” Proc. SPIE 6, 64850E (2007).

W. Liang, N. Satyan, F. Aflatouni, A. Yariv, A. Kewitsch, G. Rakuljic, and H. Hashemi, “Coherent beam combining with multilevel optical phase-locked loops,” J. Opt. Soc. Am. B 24, 2930–2939 (2007).
[Crossref]

2006 (1)

M. Sanagi, K. Yano, K. Fujimori, and S. Nogi, “Active phased array antenna radiating second harmonic output wave,” Electron. Comm. Jpn. Pt. II 89, 39–50 (2006).
[Crossref]

2005 (3)

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]

S. H. Strogatz, D. M. Abrams, A. McRobie, B. Eckhardt, and E. Ott, “Theoretical mechanics: crowd synchrony on the Millennium Bridge,” Nature 438, 43–44 (2005).
[Crossref]

J. A. Acebrón, R. Spigler, D. Matematica, R. Tre, L. S. L. Murialdo, L. Bonilla, C. Pérez Vicente, and F. Ritort, “The Kuramoto model: a simple paradigm for synchronization phenomena,” Rev. Mod. Phys. 77, 137–185 (2005).
[Crossref]

2004 (1)

A. A. Ishaaya, N. Davidson, L. Shimshi, and A. A. Friesem, “Intracavity coherent addition of Gaussian beam distributions using a planar interferometric coupler,” Appl. Phys. Lett. 85, 2187–2189 (2004).
[Crossref]

2003 (2)

2002 (1)

2001 (1)

S. H. Strogatz, “Exploring complex networks,” Nature 410, 268–276 (2001).
[Crossref]

1998 (1)

D. J. Watts and S. H. Strogatz, “Collective dynamics of “small-world” networks,” Nature 393, 440–442 (1998).
[Crossref]

1993 (1)

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[Crossref]

1992 (1)

1991 (2)

D. Mehuys, W. Streifer, R. G. Waarts, and D. F. Welch, “Modal analysis of linear Talbot-cavity semiconductor lasers,” Opt. Lett. 16, 823–825 (1991).
[Crossref]

D. Botez, M. Jansen, L. J. Mawst, G. Peterson, and T. J. Roth, “Watt-range, coherent, uniphase powers from phase-locked arrays of antiguided diode lasers,” Appl. Phys. Lett. 58, 2070–2072 (1991).
[Crossref]

1989 (2)

F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[Crossref]

J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55, 334–336 (1989).
[Crossref]

1987 (1)

A. Golubentsev, V. Likhanskii, and A. Napartovich, “Theory of phase locking of an array of lasers,” Zh. Eksp. Teor. Fiz. 93, 1199–1209 (1987).

1986 (1)

1985 (1)

R. H. Rediker, R. P. Schloss, and L. J. Van Ruyven, “Operation of individual diode lasers as a coherent ensemble controlled by a spatial filter within an external cavity,” Appl. Phys. Lett. 46, 133–135 (1985).
[Crossref]

1969 (1)

1836 (1)

H. F. Talbot, “LXXVI. Facts relating to optical science. No. IV,” Philos. Mag. Ser. 3 9(56), 401–407 (1836).

Abrams, D. M.

S. H. Strogatz, D. M. Abrams, A. McRobie, B. Eckhardt, and E. Ott, “Theoretical mechanics: crowd synchrony on the Millennium Bridge,” Nature 438, 43–44 (2005).
[Crossref]

Acebrón, J. A.

J. A. Acebrón, R. Spigler, D. Matematica, R. Tre, L. S. L. Murialdo, L. Bonilla, C. Pérez Vicente, and F. Ritort, “The Kuramoto model: a simple paradigm for synchronization phenomena,” Rev. Mod. Phys. 77, 137–185 (2005).
[Crossref]

Aflatouni, F.

Arnaud, J. A.

Baer, T. M.

T. M. Baer and M. S. Keirstead, “Nd–YAG laser,” U.S. patent4,653,056 (Apr. 7, 1987).

Barthelemy, A.

F. Jeux, A. Desfarges-Berthelemot, V. Kermène, and A. Barthelemy, “Efficient passive phasing of an array of 20 ring fiber lasers,” Laser Phys. Lett. 11, 095003 (2014).
[Crossref]

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, P. Even, and D. Pureur, “Efficient coherent combining of widely tunable fiber lasers,” Opt. Express 11, 87–97 (2003).
[Crossref]

Bonilla, L.

J. A. Acebrón, R. Spigler, D. Matematica, R. Tre, L. S. L. Murialdo, L. Bonilla, C. Pérez Vicente, and F. Ritort, “The Kuramoto model: a simple paradigm for synchronization phenomena,” Rev. Mod. Phys. 77, 137–185 (2005).
[Crossref]

Botez, D.

D. Botez, M. Jansen, L. J. Mawst, G. Peterson, and T. J. Roth, “Watt-range, coherent, uniphase powers from phase-locked arrays of antiguided diode lasers,” Appl. Phys. Lett. 58, 2070–2072 (1991).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2008).

Byer, R. L.

Calligaro, M.

I. Hassiaoui, N. Michel, M. Lecomte, O. Parillaud, M. Calligaro, and M. Kakowski, “In-phase coherent coupling of tapered lasers in an external Talbot cavity,” Proc. SPIE 6, 64850E (2007).

Caprara, A.

A. Caprara, J. L. Chilla, and L. A. Spinelli, “Intracavity frequency-converted optically-pumped semiconductor laser,” U.S. patent5,991,318 (Nov.23, 1999).

Cassarly, W. J.

Chilla, J. L.

A. Caprara, J. L. Chilla, and L. A. Spinelli, “Intracavity frequency-converted optically-pumped semiconductor laser,” U.S. patent5,991,318 (Nov.23, 1999).

Colet, P.

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[Crossref]

Corcoran, C. J.

C. J. Corcoran and F. Durville, “Passive coherent combination of a diode laser array with 35 elements,” Opt. Express 22, 8420–8425 (2014).
[Crossref]

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]

D’Amato, F. X.

F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[Crossref]

Davidson, N.

M. Nixon, E. Ronen, A. A. Friesem, and N. Davidson, “Observing geometric frustration with thousands of coupled lasers,” Phys. Rev. Lett. 110, 184102 (2013).
[Crossref]

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106, 223901 (2011).
[Crossref]

M. Fridman, M. Nixon, N. Davidson, and A. A. Friesem, “Passive phase locking of 25 fiber lasers,” Opt. Lett. 35, 1434–1436 (2010).
[Crossref]

A. A. Ishaaya, N. Davidson, L. Shimshi, and A. A. Friesem, “Intracavity coherent addition of Gaussian beam distributions using a planar interferometric coupler,” Appl. Phys. Lett. 85, 2187–2189 (2004).
[Crossref]

M. Nixon, E. Ronen, M. Fridman, A. A. Friesem, and N. Davidson, “Phase locking large arrays of lasers via a single degenerate cavity,” in Frontiers in Optics 2011/Laser Science XXVII (Optical Society of America, 2011), paper FWR6.

Desfarges-Berthelemot, A.

F. Jeux, A. Desfarges-Berthelemot, V. Kermène, and A. Barthelemy, “Efficient passive phasing of an array of 20 ring fiber lasers,” Laser Phys. Lett. 11, 095003 (2014).
[Crossref]

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, P. Even, and D. Pureur, “Efficient coherent combining of widely tunable fiber lasers,” Opt. Express 11, 87–97 (2003).
[Crossref]

Dixon, G. J.

Dong, X.-L.

X. Li, H. Xiao, X.-L. Dong, Y.-X. Ma, and X.-J. Xu, “Coherent beam combining of two slab laser amplifiers and second-harmonic phase locking based on a multi-dithering technique,” Chin. Phys. Lett. 28, 094210 (2011).
[Crossref]

Durville, F.

C. J. Corcoran and F. Durville, “Passive coherent combination of a diode laser array with 35 elements,” Opt. Express 22, 8420–8425 (2014).
[Crossref]

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]

Eckhardt, B.

S. H. Strogatz, D. M. Abrams, A. McRobie, B. Eckhardt, and E. Ott, “Theoretical mechanics: crowd synchrony on the Millennium Bridge,” Nature 438, 43–44 (2005).
[Crossref]

Ehlert, J. C.

Elkin, N. N.

A. P. Napartovich, N. N. Elkin, D. V. Vysotsky, J. Kirch, and L. J. Mawst, “Two-dimensional antiguided vertical cavity surface emitting laser arrays with reflecting boundary,” IEEE J. Sel. Top. Quantum Electron. 19, 1700208 (2013).
[Crossref]

Even, P.

Fabiny, L.

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[Crossref]

Fan, T. Y.

Finlan, J. M.

Flood, K. M.

Fridman, M.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106, 223901 (2011).
[Crossref]

M. Fridman, M. Nixon, N. Davidson, and A. A. Friesem, “Passive phase locking of 25 fiber lasers,” Opt. Lett. 35, 1434–1436 (2010).
[Crossref]

M. Nixon, E. Ronen, M. Fridman, A. A. Friesem, and N. Davidson, “Phase locking large arrays of lasers via a single degenerate cavity,” in Frontiers in Optics 2011/Laser Science XXVII (Optical Society of America, 2011), paper FWR6.

Friesem, A. A.

M. Nixon, E. Ronen, A. A. Friesem, and N. Davidson, “Observing geometric frustration with thousands of coupled lasers,” Phys. Rev. Lett. 110, 184102 (2013).
[Crossref]

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106, 223901 (2011).
[Crossref]

M. Fridman, M. Nixon, N. Davidson, and A. A. Friesem, “Passive phase locking of 25 fiber lasers,” Opt. Lett. 35, 1434–1436 (2010).
[Crossref]

A. A. Ishaaya, N. Davidson, L. Shimshi, and A. A. Friesem, “Intracavity coherent addition of Gaussian beam distributions using a planar interferometric coupler,” Appl. Phys. Lett. 85, 2187–2189 (2004).
[Crossref]

M. Nixon, E. Ronen, M. Fridman, A. A. Friesem, and N. Davidson, “Phase locking large arrays of lasers via a single degenerate cavity,” in Frontiers in Optics 2011/Laser Science XXVII (Optical Society of America, 2011), paper FWR6.

Fujimori, K.

M. Sanagi, K. Yano, K. Fujimori, and S. Nogi, “Active phased array antenna radiating second harmonic output wave,” Electron. Comm. Jpn. Pt. II 89, 39–50 (2006).
[Crossref]

Glova, A. F.

A. F. Glova, “Phase locking of optically coupled lasers,” Quantum Electron. 33, 283–306 (2003).
[Crossref]

Golubentsev, A.

A. Golubentsev, V. Likhanskii, and A. Napartovich, “Theory of phase locking of an array of lasers,” Zh. Eksp. Teor. Fiz. 93, 1199–1209 (1987).

Guan, Y.

Y. Guan, P. Zhang, X. Xie, J. Zhou, and K. S. Wong, “Coherent beam combining with second-harmonic generation optimized with adaptive phase control,” IEEE J. Quantum Electron. 47, 348–353 (2011).
[Crossref]

Hashemi, H.

Hassiaoui, I.

I. Hassiaoui, N. Michel, M. Lecomte, O. Parillaud, M. Calligaro, and M. Kakowski, “In-phase coherent coupling of tapered lasers in an external Talbot cavity,” Proc. SPIE 6, 64850E (2007).

Ishaaya, A. A.

E. Ronen and A. A. Ishaaya, “Frequency, phase, and polarization locking of evanescently coupled lasers,” J. Opt. Soc. Am. B 29, 1226–1230 (2012).
[Crossref]

A. A. Ishaaya, N. Davidson, L. Shimshi, and A. A. Friesem, “Intracavity coherent addition of Gaussian beam distributions using a planar interferometric coupler,” Appl. Phys. Lett. 85, 2187–2189 (2004).
[Crossref]

Jansen, M.

D. Botez, M. Jansen, L. J. Mawst, G. Peterson, and T. J. Roth, “Watt-range, coherent, uniphase powers from phase-locked arrays of antiguided diode lasers,” Appl. Phys. Lett. 58, 2070–2072 (1991).
[Crossref]

Jeux, F.

F. Jeux, A. Desfarges-Berthelemot, V. Kermène, and A. Barthelemy, “Efficient passive phasing of an array of 20 ring fiber lasers,” Laser Phys. Lett. 11, 095003 (2014).
[Crossref]

Kakowski, M.

I. Hassiaoui, N. Michel, M. Lecomte, O. Parillaud, M. Calligaro, and M. Kakowski, “In-phase coherent coupling of tapered lasers in an external Talbot cavity,” Proc. SPIE 6, 64850E (2007).

Kanter, I.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106, 223901 (2011).
[Crossref]

Keirstead, M. S.

T. M. Baer and M. S. Keirstead, “Nd–YAG laser,” U.S. patent4,653,056 (Apr. 7, 1987).

Kermene, V.

Kermène, V.

F. Jeux, A. Desfarges-Berthelemot, V. Kermène, and A. Barthelemy, “Efficient passive phasing of an array of 20 ring fiber lasers,” Laser Phys. Lett. 11, 095003 (2014).
[Crossref]

Kewitsch, A.

Kirch, J.

A. P. Napartovich, N. N. Elkin, D. V. Vysotsky, J. Kirch, and L. J. Mawst, “Two-dimensional antiguided vertical cavity surface emitting laser arrays with reflecting boundary,” IEEE J. Sel. Top. Quantum Electron. 19, 1700208 (2013).
[Crossref]

Lecomte, M.

I. Hassiaoui, N. Michel, M. Lecomte, O. Parillaud, M. Calligaro, and M. Kakowski, “In-phase coherent coupling of tapered lasers in an external Talbot cavity,” Proc. SPIE 6, 64850E (2007).

Lefort, L.

Leger, J. R.

J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55, 334–336 (1989).
[Crossref]

Lenstra, D.

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[Crossref]

Li, X.

X. Li, H. Xiao, X.-L. Dong, Y.-X. Ma, and X.-J. Xu, “Coherent beam combining of two slab laser amplifiers and second-harmonic phase locking based on a multi-dithering technique,” Chin. Phys. Lett. 28, 094210 (2011).
[Crossref]

Liang, W.

Likhanskii, V.

A. Golubentsev, V. Likhanskii, and A. Napartovich, “Theory of phase locking of an array of lasers,” Zh. Eksp. Teor. Fiz. 93, 1199–1209 (1987).

Ma, Y.-X.

X. Li, H. Xiao, X.-L. Dong, Y.-X. Ma, and X.-J. Xu, “Coherent beam combining of two slab laser amplifiers and second-harmonic phase locking based on a multi-dithering technique,” Chin. Phys. Lett. 28, 094210 (2011).
[Crossref]

Matematica, D.

J. A. Acebrón, R. Spigler, D. Matematica, R. Tre, L. S. L. Murialdo, L. Bonilla, C. Pérez Vicente, and F. Ritort, “The Kuramoto model: a simple paradigm for synchronization phenomena,” Rev. Mod. Phys. 77, 137–185 (2005).
[Crossref]

Mawst, L. J.

A. P. Napartovich, N. N. Elkin, D. V. Vysotsky, J. Kirch, and L. J. Mawst, “Two-dimensional antiguided vertical cavity surface emitting laser arrays with reflecting boundary,” IEEE J. Sel. Top. Quantum Electron. 19, 1700208 (2013).
[Crossref]

D. Botez, M. Jansen, L. J. Mawst, G. Peterson, and T. J. Roth, “Watt-range, coherent, uniphase powers from phase-locked arrays of antiguided diode lasers,” Appl. Phys. Lett. 58, 2070–2072 (1991).
[Crossref]

McRobie, A.

S. H. Strogatz, D. M. Abrams, A. McRobie, B. Eckhardt, and E. Ott, “Theoretical mechanics: crowd synchrony on the Millennium Bridge,” Nature 438, 43–44 (2005).
[Crossref]

Mehuys, D.

Michel, N.

I. Hassiaoui, N. Michel, M. Lecomte, O. Parillaud, M. Calligaro, and M. Kakowski, “In-phase coherent coupling of tapered lasers in an external Talbot cavity,” Proc. SPIE 6, 64850E (2007).

Murialdo, L. S. L.

J. A. Acebrón, R. Spigler, D. Matematica, R. Tre, L. S. L. Murialdo, L. Bonilla, C. Pérez Vicente, and F. Ritort, “The Kuramoto model: a simple paradigm for synchronization phenomena,” Rev. Mod. Phys. 77, 137–185 (2005).
[Crossref]

Nam, D.

Napartovich, A.

A. Golubentsev, V. Likhanskii, and A. Napartovich, “Theory of phase locking of an array of lasers,” Zh. Eksp. Teor. Fiz. 93, 1199–1209 (1987).

Napartovich, A. P.

A. P. Napartovich, N. N. Elkin, D. V. Vysotsky, J. Kirch, and L. J. Mawst, “Two-dimensional antiguided vertical cavity surface emitting laser arrays with reflecting boundary,” IEEE J. Sel. Top. Quantum Electron. 19, 1700208 (2013).
[Crossref]

Nixon, M.

M. Nixon, E. Ronen, A. A. Friesem, and N. Davidson, “Observing geometric frustration with thousands of coupled lasers,” Phys. Rev. Lett. 110, 184102 (2013).
[Crossref]

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106, 223901 (2011).
[Crossref]

M. Fridman, M. Nixon, N. Davidson, and A. A. Friesem, “Passive phase locking of 25 fiber lasers,” Opt. Lett. 35, 1434–1436 (2010).
[Crossref]

M. Nixon, E. Ronen, M. Fridman, A. A. Friesem, and N. Davidson, “Phase locking large arrays of lasers via a single degenerate cavity,” in Frontiers in Optics 2011/Laser Science XXVII (Optical Society of America, 2011), paper FWR6.

Nogi, S.

M. Sanagi, K. Yano, K. Fujimori, and S. Nogi, “Active phased array antenna radiating second harmonic output wave,” Electron. Comm. Jpn. Pt. II 89, 39–50 (2006).
[Crossref]

Ott, E.

S. H. Strogatz, D. M. Abrams, A. McRobie, B. Eckhardt, and E. Ott, “Theoretical mechanics: crowd synchrony on the Millennium Bridge,” Nature 438, 43–44 (2005).
[Crossref]

Parillaud, O.

I. Hassiaoui, N. Michel, M. Lecomte, O. Parillaud, M. Calligaro, and M. Kakowski, “In-phase coherent coupling of tapered lasers in an external Talbot cavity,” Proc. SPIE 6, 64850E (2007).

Pérez Vicente, C.

J. A. Acebrón, R. Spigler, D. Matematica, R. Tre, L. S. L. Murialdo, L. Bonilla, C. Pérez Vicente, and F. Ritort, “The Kuramoto model: a simple paradigm for synchronization phenomena,” Rev. Mod. Phys. 77, 137–185 (2005).
[Crossref]

Peterson, G.

D. Botez, M. Jansen, L. J. Mawst, G. Peterson, and T. J. Roth, “Watt-range, coherent, uniphase powers from phase-locked arrays of antiguided diode lasers,” Appl. Phys. Lett. 58, 2070–2072 (1991).
[Crossref]

Pureur, D.

Rakuljic, G.

Rediker, R. H.

R. H. Rediker, R. P. Schloss, and L. J. Van Ruyven, “Operation of individual diode lasers as a coherent ensemble controlled by a spatial filter within an external cavity,” Appl. Phys. Lett. 46, 133–135 (1985).
[Crossref]

Ritort, F.

J. A. Acebrón, R. Spigler, D. Matematica, R. Tre, L. S. L. Murialdo, L. Bonilla, C. Pérez Vicente, and F. Ritort, “The Kuramoto model: a simple paradigm for synchronization phenomena,” Rev. Mod. Phys. 77, 137–185 (2005).
[Crossref]

Ronen, E.

M. Nixon, E. Ronen, A. A. Friesem, and N. Davidson, “Observing geometric frustration with thousands of coupled lasers,” Phys. Rev. Lett. 110, 184102 (2013).
[Crossref]

E. Ronen and A. A. Ishaaya, “Frequency, phase, and polarization locking of evanescently coupled lasers,” J. Opt. Soc. Am. B 29, 1226–1230 (2012).
[Crossref]

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106, 223901 (2011).
[Crossref]

M. Nixon, E. Ronen, M. Fridman, A. A. Friesem, and N. Davidson, “Phase locking large arrays of lasers via a single degenerate cavity,” in Frontiers in Optics 2011/Laser Science XXVII (Optical Society of America, 2011), paper FWR6.

Roth, T. J.

D. Botez, M. Jansen, L. J. Mawst, G. Peterson, and T. J. Roth, “Watt-range, coherent, uniphase powers from phase-locked arrays of antiguided diode lasers,” Appl. Phys. Lett. 58, 2070–2072 (1991).
[Crossref]

Roy, R.

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[Crossref]

Roychoudhuri, C.

F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[Crossref]

Sabourdy, D.

Saitou, T.

Sanagi, M.

M. Sanagi, K. Yano, K. Fujimori, and S. Nogi, “Active phased array antenna radiating second harmonic output wave,” Electron. Comm. Jpn. Pt. II 89, 39–50 (2006).
[Crossref]

Satyan, N.

Schloss, R. P.

R. H. Rediker, R. P. Schloss, and L. J. Van Ruyven, “Operation of individual diode lasers as a coherent ensemble controlled by a spatial filter within an external cavity,” Appl. Phys. Lett. 46, 133–135 (1985).
[Crossref]

Sekiguchi, T.

Shimshi, L.

A. A. Ishaaya, N. Davidson, L. Shimshi, and A. A. Friesem, “Intracavity coherent addition of Gaussian beam distributions using a planar interferometric coupler,” Appl. Phys. Lett. 85, 2187–2189 (2004).
[Crossref]

Shirakawa, A.

Siebert, E. T.

F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[Crossref]

Spigler, R.

J. A. Acebrón, R. Spigler, D. Matematica, R. Tre, L. S. L. Murialdo, L. Bonilla, C. Pérez Vicente, and F. Ritort, “The Kuramoto model: a simple paradigm for synchronization phenomena,” Rev. Mod. Phys. 77, 137–185 (2005).
[Crossref]

Spinelli, L. A.

A. Caprara, J. L. Chilla, and L. A. Spinelli, “Intracavity frequency-converted optically-pumped semiconductor laser,” U.S. patent5,991,318 (Nov.23, 1999).

Streifer, W.

Strogatz, S. H.

S. H. Strogatz, D. M. Abrams, A. McRobie, B. Eckhardt, and E. Ott, “Theoretical mechanics: crowd synchrony on the Millennium Bridge,” Nature 438, 43–44 (2005).
[Crossref]

S. H. Strogatz, “Exploring complex networks,” Nature 410, 268–276 (2001).
[Crossref]

D. J. Watts and S. H. Strogatz, “Collective dynamics of “small-world” networks,” Nature 393, 440–442 (1998).
[Crossref]

Talbot, H. F.

H. F. Talbot, “LXXVI. Facts relating to optical science. No. IV,” Philos. Mag. Ser. 3 9(56), 401–407 (1836).

Tre, R.

J. A. Acebrón, R. Spigler, D. Matematica, R. Tre, L. S. L. Murialdo, L. Bonilla, C. Pérez Vicente, and F. Ritort, “The Kuramoto model: a simple paradigm for synchronization phenomena,” Rev. Mod. Phys. 77, 137–185 (2005).
[Crossref]

Ueda, K.

Van Ruyven, L. J.

R. H. Rediker, R. P. Schloss, and L. J. Van Ruyven, “Operation of individual diode lasers as a coherent ensemble controlled by a spatial filter within an external cavity,” Appl. Phys. Lett. 46, 133–135 (1985).
[Crossref]

Vysotsky, D. V.

A. P. Napartovich, N. N. Elkin, D. V. Vysotsky, J. Kirch, and L. J. Mawst, “Two-dimensional antiguided vertical cavity surface emitting laser arrays with reflecting boundary,” IEEE J. Sel. Top. Quantum Electron. 19, 1700208 (2013).
[Crossref]

Waarts, R.

Waarts, R. G.

Watts, D. J.

D. J. Watts and S. H. Strogatz, “Collective dynamics of “small-world” networks,” Nature 393, 440–442 (1998).
[Crossref]

Welch, D.

Welch, D. F.

Wong, K. S.

Y. Guan, P. Zhang, X. Xie, J. Zhou, and K. S. Wong, “Coherent beam combining with second-harmonic generation optimized with adaptive phase control,” IEEE J. Quantum Electron. 47, 348–353 (2011).
[Crossref]

Xiao, H.

X. Li, H. Xiao, X.-L. Dong, Y.-X. Ma, and X.-J. Xu, “Coherent beam combining of two slab laser amplifiers and second-harmonic phase locking based on a multi-dithering technique,” Chin. Phys. Lett. 28, 094210 (2011).
[Crossref]

Xie, X.

Y. Guan, P. Zhang, X. Xie, J. Zhou, and K. S. Wong, “Coherent beam combining with second-harmonic generation optimized with adaptive phase control,” IEEE J. Quantum Electron. 47, 348–353 (2011).
[Crossref]

Xu, X.-J.

X. Li, H. Xiao, X.-L. Dong, Y.-X. Ma, and X.-J. Xu, “Coherent beam combining of two slab laser amplifiers and second-harmonic phase locking based on a multi-dithering technique,” Chin. Phys. Lett. 28, 094210 (2011).
[Crossref]

Yano, K.

M. Sanagi, K. Yano, K. Fujimori, and S. Nogi, “Active phased array antenna radiating second harmonic output wave,” Electron. Comm. Jpn. Pt. II 89, 39–50 (2006).
[Crossref]

Yariv, A.

Zhang, P.

Y. Guan, P. Zhang, X. Xie, J. Zhou, and K. S. Wong, “Coherent beam combining with second-harmonic generation optimized with adaptive phase control,” IEEE J. Quantum Electron. 47, 348–353 (2011).
[Crossref]

Zhou, J.

Y. Guan, P. Zhang, X. Xie, J. Zhou, and K. S. Wong, “Coherent beam combining with second-harmonic generation optimized with adaptive phase control,” IEEE J. Quantum Electron. 47, 348–353 (2011).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (6)

F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[Crossref]

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]

J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55, 334–336 (1989).
[Crossref]

R. H. Rediker, R. P. Schloss, and L. J. Van Ruyven, “Operation of individual diode lasers as a coherent ensemble controlled by a spatial filter within an external cavity,” Appl. Phys. Lett. 46, 133–135 (1985).
[Crossref]

A. A. Ishaaya, N. Davidson, L. Shimshi, and A. A. Friesem, “Intracavity coherent addition of Gaussian beam distributions using a planar interferometric coupler,” Appl. Phys. Lett. 85, 2187–2189 (2004).
[Crossref]

D. Botez, M. Jansen, L. J. Mawst, G. Peterson, and T. J. Roth, “Watt-range, coherent, uniphase powers from phase-locked arrays of antiguided diode lasers,” Appl. Phys. Lett. 58, 2070–2072 (1991).
[Crossref]

Chin. Phys. Lett. (1)

X. Li, H. Xiao, X.-L. Dong, Y.-X. Ma, and X.-J. Xu, “Coherent beam combining of two slab laser amplifiers and second-harmonic phase locking based on a multi-dithering technique,” Chin. Phys. Lett. 28, 094210 (2011).
[Crossref]

Electron. Comm. Jpn. Pt. II (1)

M. Sanagi, K. Yano, K. Fujimori, and S. Nogi, “Active phased array antenna radiating second harmonic output wave,” Electron. Comm. Jpn. Pt. II 89, 39–50 (2006).
[Crossref]

IEEE J. Quantum Electron. (1)

Y. Guan, P. Zhang, X. Xie, J. Zhou, and K. S. Wong, “Coherent beam combining with second-harmonic generation optimized with adaptive phase control,” IEEE J. Quantum Electron. 47, 348–353 (2011).
[Crossref]

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

A. P. Napartovich, N. N. Elkin, D. V. Vysotsky, J. Kirch, and L. J. Mawst, “Two-dimensional antiguided vertical cavity surface emitting laser arrays with reflecting boundary,” IEEE J. Sel. Top. Quantum Electron. 19, 1700208 (2013).
[Crossref]

J. Opt. Soc. Am. B (2)

Laser Phys. Lett. (1)

F. Jeux, A. Desfarges-Berthelemot, V. Kermène, and A. Barthelemy, “Efficient passive phasing of an array of 20 ring fiber lasers,” Laser Phys. Lett. 11, 095003 (2014).
[Crossref]

Nature (3)

D. J. Watts and S. H. Strogatz, “Collective dynamics of “small-world” networks,” Nature 393, 440–442 (1998).
[Crossref]

S. H. Strogatz, D. M. Abrams, A. McRobie, B. Eckhardt, and E. Ott, “Theoretical mechanics: crowd synchrony on the Millennium Bridge,” Nature 438, 43–44 (2005).
[Crossref]

S. H. Strogatz, “Exploring complex networks,” Nature 410, 268–276 (2001).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Philos. Mag. Ser. 3 (1)

H. F. Talbot, “LXXVI. Facts relating to optical science. No. IV,” Philos. Mag. Ser. 3 9(56), 401–407 (1836).

Phys. Rev. A (1)

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[Crossref]

Phys. Rev. Lett. (2)

M. Nixon, E. Ronen, A. A. Friesem, and N. Davidson, “Observing geometric frustration with thousands of coupled lasers,” Phys. Rev. Lett. 110, 184102 (2013).
[Crossref]

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106, 223901 (2011).
[Crossref]

Proc. SPIE (1)

I. Hassiaoui, N. Michel, M. Lecomte, O. Parillaud, M. Calligaro, and M. Kakowski, “In-phase coherent coupling of tapered lasers in an external Talbot cavity,” Proc. SPIE 6, 64850E (2007).

Quantum Electron. (1)

A. F. Glova, “Phase locking of optically coupled lasers,” Quantum Electron. 33, 283–306 (2003).
[Crossref]

Rev. Mod. Phys. (1)

J. A. Acebrón, R. Spigler, D. Matematica, R. Tre, L. S. L. Murialdo, L. Bonilla, C. Pérez Vicente, and F. Ritort, “The Kuramoto model: a simple paradigm for synchronization phenomena,” Rev. Mod. Phys. 77, 137–185 (2005).
[Crossref]

Zh. Eksp. Teor. Fiz. (1)

A. Golubentsev, V. Likhanskii, and A. Napartovich, “Theory of phase locking of an array of lasers,” Zh. Eksp. Teor. Fiz. 93, 1199–1209 (1987).

Other (4)

T. M. Baer and M. S. Keirstead, “Nd–YAG laser,” U.S. patent4,653,056 (Apr. 7, 1987).

A. Caprara, J. L. Chilla, and L. A. Spinelli, “Intracavity frequency-converted optically-pumped semiconductor laser,” U.S. patent5,991,318 (Nov.23, 1999).

M. Nixon, E. Ronen, M. Fridman, A. A. Friesem, and N. Davidson, “Phase locking large arrays of lasers via a single degenerate cavity,” in Frontiers in Optics 2011/Laser Science XXVII (Optical Society of America, 2011), paper FWR6.

R. W. Boyd, Nonlinear Optics (Academic, 2008).

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Figures (5)

Fig. 1.
Fig. 1. Arrangement for obtaining an array of negatively coupled phase-locked lasers, forming first and second harmonics and their detection. It consists of three main parts: a degenerate cavity laser with an intra-cavity mask of holes so as to obtain a desired laser array geometry, a telescope with a KTP nonlinear crystal to obtain the second harmonics, and an arrangement to detect the near-field and far-field of the first and second harmonics.
Fig. 2.
Fig. 2. Two coupled lasers; (a) schematic illustration of phase shift doubling in the second harmonics, where an out-of-phase locking (π phase shift) in the first harmonics is converted into an in-phase locking (2π phase shift) in the second harmonics; (b) experimental intensity distributions for the near- and far- fields of first and second harmonics.
Fig. 3.
Fig. 3. Array of 334 coupled lasers formed in a square geometry; (a) schematic illustration of phase shift doubling in the second harmonics, where an out-of-phase locking (π phase shift) in the first harmonics is converted into an in-phase locking (2π phase shift) in the second harmonics; (b) experimental intensity distributions for the near- and far-fields of first and second harmonics.
Fig. 4.
Fig. 4. Array of 199 coupled lasers formed in a honeycomb geometry (a) schematic illustration of phase shift doubling in the second harmonics, where an out-of-phase locking (π phase shift) in the first harmonics is converted into an in-phase locking (2π phase shift) in the second harmonics; (b) experimental (left) and calculated (right) intensity distributions for the near- and far-fields of first and second harmonics.
Fig. 5.
Fig. 5. Array of 299 coupled lasers formed in triangular geometry, each laser with many longitudinal modes; (a) schematic illustration where summing of two longitudinal modes with vortex and antivortex phase distributions leads to an in-phase intensity distribution; (b) summing two longitudinal modes both with vortex phase distributions leads to antivortex phase distribution; (c) experimental (left) and calculated (right) intensity distributions for the near- and far-fields of first and second harmonics.

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