Abstract

A novel configuration for phase locking two ring lasers with self-stabilized minimal exchange of power between them is presented. We show experimentally that losses introduced between the lasers are self compensated in order to maintain minimal power exchange between them. The experimental results are in good agreement with numerical results.

© 2012 OSA

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References

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  1. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer Verlag, 1984).
    [CrossRef]
  2. B. Wang, E. Mies, M. Minden, and A. Sanchez, “all-fiber 50 w coherently combined passive laser array,” Opt. Lett.34, 863–865 (2009).
    [CrossRef] [PubMed]
  3. F. Jeux, A. Desfarges-Berthelemot, V. Kermne, J. Guillot, and A. Barthelemy, “Passive coherent combining of lasers with phase-contrast filtering for enhanced efficiency,” App. Phys. B, 108, 1–7 (2012).
  4. M. Khajavikhan and J. Leger, “Modal analysis of path length sensitivity in superposition architectures for coherent laser beam combining,” IEEE Sel. Top. Quantum Electron.15, 281–290 (2009).
    [CrossRef]
  5. 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,” App. Phys. Lett.55, 816–818 (1989).
    [CrossRef]
  6. A. Ishaaya, N. Davidson, and A. Friesem, “Passive laser beam combining with intracavity interferometric combiners,” Sel. Top. Quantum Electron.15, 301–311 (2009).
    [CrossRef]
  7. 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).
  8. E. Ronen, M. Fridman, M. Nixon, A. A. Friesem, and N. Davidson, “Phase locking of lasers with intracavity polarization elements,” Opt. Lett.33, 2305–2307 (2008).
    [CrossRef] [PubMed]
  9. S. J. Augst, T. Y. Fan, and A. Sanchez, “Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers,” Opt. Lett.29, 474–476 (2004).
    [CrossRef] [PubMed]
  10. A. E. Siegman, Lasers (University Science Books, 1986).
  11. F. R. Faxvog, “Modes of a unidirectional ring laser,” Opt. Lett.5, 285–287 (1980).
    [CrossRef] [PubMed]
  12. J. A. Arnaud, “Degenerate optical cavities,” Appl. Opt.8, 189–195 (1969).
    [CrossRef] [PubMed]
  13. M. Nixon, M. Fridman, E. Ronen, I. Kanter, A.A Friesem, and N. Davidson, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett.106, 223–227 (2011).
    [CrossRef]
  14. J. Hohimer, G. Vawter, and D. Craft, “Unidirectional lasing in a ring semiconductor diode laser,” Appl. Phy. Lett.62, 1185–1187 (1993).
    [CrossRef]
  15. The attenuators are not optically flat so in addition to the absortion loss they add phase abberations to the donor mode which further reduces its overlap with the acceptor mode causing an additional loss that is not included in Fig. 3.
  16. L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A47, 4287–4296 (1993).
    [CrossRef] [PubMed]
  17. M. Fridman, V. Eckhouse, N. Davidson, and A. A. Friesem, “effect of quantum noise on coupled laser oscillators,” Phys. Rev. A77061803 (2008).
    [CrossRef]
  18. I. Kanter, Y. Aviad, I. Igor, E. Cohen, and M. Rosenblu, “An optical ultrafast random bit generator,” Nat. Phys.4, 58–61 (2010).
    [CrossRef]
  19. S. Schwartz, G. Feugnet, P. Bouyer, E. Lariontsev, A. Aspect, and J.-P. Pocholle, “Mode-coupling control in resonant devices: application to solid-state ring lasers,” Phys. Rev. Lett.97, 093902 (2006).
    [CrossRef] [PubMed]
  20. S. Schwartz, G. Feugnet, E. Lariontsev, and J.-P. Pocholle, “Oscillation regimes of a solid-state ring laser with active beat-note stabilization: From a chaotic device to a ring-laser gyroscope,” Phys. Rev. A76, 023807 (2007).
    [CrossRef]
  21. It should be noted that the usual solution for detuned coupled oscillators, where both oscillate with the mean frequency and the same intensity [16], does not yield a steady state solution for our coupled ring lasers. Experimentally there is always some finite breaking of symmetry between the two donor lasers that causes one of them to vansih.

2012 (1)

F. Jeux, A. Desfarges-Berthelemot, V. Kermne, J. Guillot, and A. Barthelemy, “Passive coherent combining of lasers with phase-contrast filtering for enhanced efficiency,” App. Phys. B, 108, 1–7 (2012).

2011 (2)

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).

M. Nixon, M. Fridman, E. Ronen, I. Kanter, A.A Friesem, and N. Davidson, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett.106, 223–227 (2011).
[CrossRef]

2010 (1)

I. Kanter, Y. Aviad, I. Igor, E. Cohen, and M. Rosenblu, “An optical ultrafast random bit generator,” Nat. Phys.4, 58–61 (2010).
[CrossRef]

2009 (3)

M. Khajavikhan and J. Leger, “Modal analysis of path length sensitivity in superposition architectures for coherent laser beam combining,” IEEE Sel. Top. Quantum Electron.15, 281–290 (2009).
[CrossRef]

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

A. Ishaaya, N. Davidson, and A. Friesem, “Passive laser beam combining with intracavity interferometric combiners,” Sel. Top. Quantum Electron.15, 301–311 (2009).
[CrossRef]

2008 (2)

E. Ronen, M. Fridman, M. Nixon, A. A. Friesem, and N. Davidson, “Phase locking of lasers with intracavity polarization elements,” Opt. Lett.33, 2305–2307 (2008).
[CrossRef] [PubMed]

M. Fridman, V. Eckhouse, N. Davidson, and A. A. Friesem, “effect of quantum noise on coupled laser oscillators,” Phys. Rev. A77061803 (2008).
[CrossRef]

2007 (1)

S. Schwartz, G. Feugnet, E. Lariontsev, and J.-P. Pocholle, “Oscillation regimes of a solid-state ring laser with active beat-note stabilization: From a chaotic device to a ring-laser gyroscope,” Phys. Rev. A76, 023807 (2007).
[CrossRef]

2006 (1)

S. Schwartz, G. Feugnet, P. Bouyer, E. Lariontsev, A. Aspect, and J.-P. Pocholle, “Mode-coupling control in resonant devices: application to solid-state ring lasers,” Phys. Rev. Lett.97, 093902 (2006).
[CrossRef] [PubMed]

2004 (1)

1993 (2)

J. Hohimer, G. Vawter, and D. Craft, “Unidirectional lasing in a ring semiconductor diode laser,” Appl. Phy. Lett.62, 1185–1187 (1993).
[CrossRef]

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A47, 4287–4296 (1993).
[CrossRef] [PubMed]

1989 (1)

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,” App. Phys. Lett.55, 816–818 (1989).
[CrossRef]

1980 (1)

1969 (1)

Arnaud, J. A.

Aspect, A.

S. Schwartz, G. Feugnet, P. Bouyer, E. Lariontsev, A. Aspect, and J.-P. Pocholle, “Mode-coupling control in resonant devices: application to solid-state ring lasers,” Phys. Rev. Lett.97, 093902 (2006).
[CrossRef] [PubMed]

Augst, S. J.

Aviad, Y.

I. Kanter, Y. Aviad, I. Igor, E. Cohen, and M. Rosenblu, “An optical ultrafast random bit generator,” Nat. Phys.4, 58–61 (2010).
[CrossRef]

Barthelemy, A.

F. Jeux, A. Desfarges-Berthelemot, V. Kermne, J. Guillot, and A. Barthelemy, “Passive coherent combining of lasers with phase-contrast filtering for enhanced efficiency,” App. Phys. B, 108, 1–7 (2012).

Bouyer, P.

S. Schwartz, G. Feugnet, P. Bouyer, E. Lariontsev, A. Aspect, and J.-P. Pocholle, “Mode-coupling control in resonant devices: application to solid-state ring lasers,” Phys. Rev. Lett.97, 093902 (2006).
[CrossRef] [PubMed]

Cohen, E.

I. Kanter, Y. Aviad, I. Igor, E. Cohen, and M. Rosenblu, “An optical ultrafast random bit generator,” Nat. Phys.4, 58–61 (2010).
[CrossRef]

Colet, P.

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A47, 4287–4296 (1993).
[CrossRef] [PubMed]

Corcoran, C. J.

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

Craft, D.

J. Hohimer, G. Vawter, and D. Craft, “Unidirectional lasing in a ring semiconductor diode laser,” Appl. Phy. Lett.62, 1185–1187 (1993).
[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,” App. Phys. Lett.55, 816–818 (1989).
[CrossRef]

Davidson, N.

M. Nixon, M. Fridman, E. Ronen, I. Kanter, A.A Friesem, and N. Davidson, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett.106, 223–227 (2011).
[CrossRef]

A. Ishaaya, N. Davidson, and A. Friesem, “Passive laser beam combining with intracavity interferometric combiners,” Sel. Top. Quantum Electron.15, 301–311 (2009).
[CrossRef]

E. Ronen, M. Fridman, M. Nixon, A. A. Friesem, and N. Davidson, “Phase locking of lasers with intracavity polarization elements,” Opt. Lett.33, 2305–2307 (2008).
[CrossRef] [PubMed]

M. Fridman, V. Eckhouse, N. Davidson, and A. A. Friesem, “effect of quantum noise on coupled laser oscillators,” Phys. Rev. A77061803 (2008).
[CrossRef]

Desfarges-Berthelemot, A.

F. Jeux, A. Desfarges-Berthelemot, V. Kermne, J. Guillot, and A. Barthelemy, “Passive coherent combining of lasers with phase-contrast filtering for enhanced efficiency,” App. Phys. B, 108, 1–7 (2012).

Durville, F.

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

Eckhouse, V.

M. Fridman, V. Eckhouse, N. Davidson, and A. A. Friesem, “effect of quantum noise on coupled laser oscillators,” Phys. Rev. A77061803 (2008).
[CrossRef]

Fabiny, L.

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A47, 4287–4296 (1993).
[CrossRef] [PubMed]

Fan, T. Y.

Faxvog, F. R.

Feugnet, G.

S. Schwartz, G. Feugnet, E. Lariontsev, and J.-P. Pocholle, “Oscillation regimes of a solid-state ring laser with active beat-note stabilization: From a chaotic device to a ring-laser gyroscope,” Phys. Rev. A76, 023807 (2007).
[CrossRef]

S. Schwartz, G. Feugnet, P. Bouyer, E. Lariontsev, A. Aspect, and J.-P. Pocholle, “Mode-coupling control in resonant devices: application to solid-state ring lasers,” Phys. Rev. Lett.97, 093902 (2006).
[CrossRef] [PubMed]

Fridman, M.

M. Nixon, M. Fridman, E. Ronen, I. Kanter, A.A Friesem, and N. Davidson, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett.106, 223–227 (2011).
[CrossRef]

E. Ronen, M. Fridman, M. Nixon, A. A. Friesem, and N. Davidson, “Phase locking of lasers with intracavity polarization elements,” Opt. Lett.33, 2305–2307 (2008).
[CrossRef] [PubMed]

M. Fridman, V. Eckhouse, N. Davidson, and A. A. Friesem, “effect of quantum noise on coupled laser oscillators,” Phys. Rev. A77061803 (2008).
[CrossRef]

Friesem, A.

A. Ishaaya, N. Davidson, and A. Friesem, “Passive laser beam combining with intracavity interferometric combiners,” Sel. Top. Quantum Electron.15, 301–311 (2009).
[CrossRef]

Friesem, A. A.

E. Ronen, M. Fridman, M. Nixon, A. A. Friesem, and N. Davidson, “Phase locking of lasers with intracavity polarization elements,” Opt. Lett.33, 2305–2307 (2008).
[CrossRef] [PubMed]

M. Fridman, V. Eckhouse, N. Davidson, and A. A. Friesem, “effect of quantum noise on coupled laser oscillators,” Phys. Rev. A77061803 (2008).
[CrossRef]

Friesem, A.A

M. Nixon, M. Fridman, E. Ronen, I. Kanter, A.A Friesem, and N. Davidson, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett.106, 223–227 (2011).
[CrossRef]

Guillot, J.

F. Jeux, A. Desfarges-Berthelemot, V. Kermne, J. Guillot, and A. Barthelemy, “Passive coherent combining of lasers with phase-contrast filtering for enhanced efficiency,” App. Phys. B, 108, 1–7 (2012).

Hohimer, J.

J. Hohimer, G. Vawter, and D. Craft, “Unidirectional lasing in a ring semiconductor diode laser,” Appl. Phy. Lett.62, 1185–1187 (1993).
[CrossRef]

Igor, I.

I. Kanter, Y. Aviad, I. Igor, E. Cohen, and M. Rosenblu, “An optical ultrafast random bit generator,” Nat. Phys.4, 58–61 (2010).
[CrossRef]

Ishaaya, A.

A. Ishaaya, N. Davidson, and A. Friesem, “Passive laser beam combining with intracavity interferometric combiners,” Sel. Top. Quantum Electron.15, 301–311 (2009).
[CrossRef]

Jeux, F.

F. Jeux, A. Desfarges-Berthelemot, V. Kermne, J. Guillot, and A. Barthelemy, “Passive coherent combining of lasers with phase-contrast filtering for enhanced efficiency,” App. Phys. B, 108, 1–7 (2012).

Kanter, I.

M. Nixon, M. Fridman, E. Ronen, I. Kanter, A.A Friesem, and N. Davidson, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett.106, 223–227 (2011).
[CrossRef]

I. Kanter, Y. Aviad, I. Igor, E. Cohen, and M. Rosenblu, “An optical ultrafast random bit generator,” Nat. Phys.4, 58–61 (2010).
[CrossRef]

Kermne, V.

F. Jeux, A. Desfarges-Berthelemot, V. Kermne, J. Guillot, and A. Barthelemy, “Passive coherent combining of lasers with phase-contrast filtering for enhanced efficiency,” App. Phys. B, 108, 1–7 (2012).

Khajavikhan, M.

M. Khajavikhan and J. Leger, “Modal analysis of path length sensitivity in superposition architectures for coherent laser beam combining,” IEEE Sel. Top. Quantum Electron.15, 281–290 (2009).
[CrossRef]

Kuramoto, Y.

Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer Verlag, 1984).
[CrossRef]

Lariontsev, E.

S. Schwartz, G. Feugnet, E. Lariontsev, and J.-P. Pocholle, “Oscillation regimes of a solid-state ring laser with active beat-note stabilization: From a chaotic device to a ring-laser gyroscope,” Phys. Rev. A76, 023807 (2007).
[CrossRef]

S. Schwartz, G. Feugnet, P. Bouyer, E. Lariontsev, A. Aspect, and J.-P. Pocholle, “Mode-coupling control in resonant devices: application to solid-state ring lasers,” Phys. Rev. Lett.97, 093902 (2006).
[CrossRef] [PubMed]

Leger, J.

M. Khajavikhan and J. Leger, “Modal analysis of path length sensitivity in superposition architectures for coherent laser beam combining,” IEEE Sel. Top. Quantum Electron.15, 281–290 (2009).
[CrossRef]

Lenstra, D.

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A47, 4287–4296 (1993).
[CrossRef] [PubMed]

Mies, E.

Minden, M.

Nixon, M.

M. Nixon, M. Fridman, E. Ronen, I. Kanter, A.A Friesem, and N. Davidson, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett.106, 223–227 (2011).
[CrossRef]

E. Ronen, M. Fridman, M. Nixon, A. A. Friesem, and N. Davidson, “Phase locking of lasers with intracavity polarization elements,” Opt. Lett.33, 2305–2307 (2008).
[CrossRef] [PubMed]

Pocholle, J.-P.

S. Schwartz, G. Feugnet, E. Lariontsev, and J.-P. Pocholle, “Oscillation regimes of a solid-state ring laser with active beat-note stabilization: From a chaotic device to a ring-laser gyroscope,” Phys. Rev. A76, 023807 (2007).
[CrossRef]

S. Schwartz, G. Feugnet, P. Bouyer, E. Lariontsev, A. Aspect, and J.-P. Pocholle, “Mode-coupling control in resonant devices: application to solid-state ring lasers,” Phys. Rev. Lett.97, 093902 (2006).
[CrossRef] [PubMed]

Ronen, E.

M. Nixon, M. Fridman, E. Ronen, I. Kanter, A.A Friesem, and N. Davidson, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett.106, 223–227 (2011).
[CrossRef]

E. Ronen, M. Fridman, M. Nixon, A. A. Friesem, and N. Davidson, “Phase locking of lasers with intracavity polarization elements,” Opt. Lett.33, 2305–2307 (2008).
[CrossRef] [PubMed]

Rosenblu, M.

I. Kanter, Y. Aviad, I. Igor, E. Cohen, and M. Rosenblu, “An optical ultrafast random bit generator,” Nat. Phys.4, 58–61 (2010).
[CrossRef]

Roy, R.

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A47, 4287–4296 (1993).
[CrossRef] [PubMed]

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,” App. Phys. Lett.55, 816–818 (1989).
[CrossRef]

Sanchez, A.

Schwartz, S.

S. Schwartz, G. Feugnet, E. Lariontsev, and J.-P. Pocholle, “Oscillation regimes of a solid-state ring laser with active beat-note stabilization: From a chaotic device to a ring-laser gyroscope,” Phys. Rev. A76, 023807 (2007).
[CrossRef]

S. Schwartz, G. Feugnet, P. Bouyer, E. Lariontsev, A. Aspect, and J.-P. Pocholle, “Mode-coupling control in resonant devices: application to solid-state ring lasers,” Phys. Rev. Lett.97, 093902 (2006).
[CrossRef] [PubMed]

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,” App. Phys. Lett.55, 816–818 (1989).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Vawter, G.

J. Hohimer, G. Vawter, and D. Craft, “Unidirectional lasing in a ring semiconductor diode laser,” Appl. Phy. Lett.62, 1185–1187 (1993).
[CrossRef]

Wang, B.

App. Phys. B (1)

F. Jeux, A. Desfarges-Berthelemot, V. Kermne, J. Guillot, and A. Barthelemy, “Passive coherent combining of lasers with phase-contrast filtering for enhanced efficiency,” App. Phys. B, 108, 1–7 (2012).

App. Phys. Lett. (1)

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,” App. Phys. Lett.55, 816–818 (1989).
[CrossRef]

Appl. Opt. (1)

Appl. Phy. Lett. (1)

J. Hohimer, G. Vawter, and D. Craft, “Unidirectional lasing in a ring semiconductor diode laser,” Appl. Phy. Lett.62, 1185–1187 (1993).
[CrossRef]

Appl. Phys. Lett. (1)

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

IEEE Sel. Top. Quantum Electron. (1)

M. Khajavikhan and J. Leger, “Modal analysis of path length sensitivity in superposition architectures for coherent laser beam combining,” IEEE Sel. Top. Quantum Electron.15, 281–290 (2009).
[CrossRef]

Nat. Phys. (1)

I. Kanter, Y. Aviad, I. Igor, E. Cohen, and M. Rosenblu, “An optical ultrafast random bit generator,” Nat. Phys.4, 58–61 (2010).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (3)

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A47, 4287–4296 (1993).
[CrossRef] [PubMed]

M. Fridman, V. Eckhouse, N. Davidson, and A. A. Friesem, “effect of quantum noise on coupled laser oscillators,” Phys. Rev. A77061803 (2008).
[CrossRef]

S. Schwartz, G. Feugnet, E. Lariontsev, and J.-P. Pocholle, “Oscillation regimes of a solid-state ring laser with active beat-note stabilization: From a chaotic device to a ring-laser gyroscope,” Phys. Rev. A76, 023807 (2007).
[CrossRef]

Phys. Rev. Lett. (2)

S. Schwartz, G. Feugnet, P. Bouyer, E. Lariontsev, A. Aspect, and J.-P. Pocholle, “Mode-coupling control in resonant devices: application to solid-state ring lasers,” Phys. Rev. Lett.97, 093902 (2006).
[CrossRef] [PubMed]

M. Nixon, M. Fridman, E. Ronen, I. Kanter, A.A Friesem, and N. Davidson, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett.106, 223–227 (2011).
[CrossRef]

Sel. Top. Quantum Electron. (1)

A. Ishaaya, N. Davidson, and A. Friesem, “Passive laser beam combining with intracavity interferometric combiners,” Sel. Top. Quantum Electron.15, 301–311 (2009).
[CrossRef]

Other (4)

The attenuators are not optically flat so in addition to the absortion loss they add phase abberations to the donor mode which further reduces its overlap with the acceptor mode causing an additional loss that is not included in Fig. 3.

A. E. Siegman, Lasers (University Science Books, 1986).

Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer Verlag, 1984).
[CrossRef]

It should be noted that the usual solution for detuned coupled oscillators, where both oscillate with the mean frequency and the same intensity [16], does not yield a steady state solution for our coupled ring lasers. Experimentally there is always some finite breaking of symmetry between the two donor lasers that causes one of them to vansih.

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Figures (5)

Fig. 1
Fig. 1

Basic configurations for coupled ring lasers. A: Single laser self-coupled by an auxiliary external mirror. B: Two coupled ring lasers. Blue solid line [green dashed line] indicates the lasing direction of the donor modes [acceptor modes]. Inset: experimental interference fringe pattern of light from the two acceptor modes with 80% fringe visibility indicating high level of phase locking. AM- auxiliary mirror; M- mirror; GM- gain medium; OC- output coupler;

Fig. 2
Fig. 2

Experimental arrangement for coupling two ring lasers, experimentally implementing the configuration of Fig. 1(B). Ap: two apertures defining laser 1 and 2; F1: lens, 30 cm focal length; F2: lens, 15 cm focal length; M: mirror; OC: 50% output coupler; GM: gain medium; At: calibrated optical attenuators; AM: auxiliary mirror, 94% reflectivity; solid (blue) line: propagation direction of the CCW donor mode; dashed (green) line: propagation direction of the CW acceptor mode. Insets: Detected intensity distributions of different modes; A: one donor mode of zero intensity, and the other of extremely low intensity (surrounded by circles). B: the two acceptor modes have nearly equal high intensities (surrounded by circles).

Fig. 3
Fig. 3

Power of the surviving donor mode as a function of the round trip external loss introduced by the optical attenuators. Blue dots: measured power emerging from the cavity. Red squares: measured power injected back into the cavity (after passing twice through the optical attenuators). Blue solid line and red dashed line: corresponding calculated results (when the lasers have nearly identical initial conditions).

Fig. 4
Fig. 4

Calculated field amplitudes and phase difference of relevant donor and acceptor modes as a function of time for a system of two ring lasers.A: Amplitudes of donor and acceptor modes.B: The phase difference between the surviving donor mode and its slaved acceptor mode. The detuning is 0.015 t c, the coupling κ is 0.15, τc = 10ns, τf = 230μs, γ = 1 and p = 2.

Fig. 5
Fig. 5

Calculated amplitudes of the four acceptor modes as function of time for two ring lasers each with two different frequencies. A 0 a and A 0 b: amplitudes of lasers a and b with a common frequency; A 1 a and A 2 b: amplitudes of lasers a and b each with different frequency. Only the two acceptor modes with common frequency survive. The amplitudes of all four donor modes reach zero (not shown).

Equations (4)

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

E ˙ d 1 / 2 = 1 t c ( ( g 1 / 2 γ ) E d 1 / 2 ) + i ω 1 / 2 E d 1 / 2 ,
E ˙ a 1 / 2 = 1 t c ( ( g 1 / 2 γ ) E a 1 / 2 + κ E d 2 / 1 ) + i ω 1 / 2 E a 1 / 2 ,
g ˙ 1 / 2 = p 1 t f ( g 1 / 2 ( I d 1 / 2 + I a 1 / 2 + 1 ) ,
A d 1 = η A a 2 sin ( Δ ϕ s s ) .

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