Abstract

Coherent lasing of two lasers can be achieved passively by intracavity exchange of light between the lasers. Full coherence of the lasers typically implies synchronization in three parameters: frequency, phase, and polarization. Here we investigate a simple laser system in which exchange of light can cause a variety of states: full coherent lasing, only polarization-locked lasing, frequency-locked lasing without phase locking, and independent incoherent lasing. We demonstrate these states experimentally with evanescently coupled fiber lasers, and propose a simple model that offers a simple explanation for these intriguing observations.

© 2012 Optical Society of America

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References

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  1. E. Ronen and A. A. Ishayya, “Phase clusters induced by degeneracy in a phase locked fiber laser array,” IEEE J. Quantum Electron 47, 1526–15302011.
    [CrossRef]
  2. E. Ronen and A. A. Ishaaya, “Phase locking a fiber laser array via diffractive coupling,” Opt. Express 19, 1510–1515 (2011).
    [CrossRef]
  3. H. G. Winful and L. Rahman, “Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers,” Phys. Rev. Lett. 65, 1575–1578 (1990).
    [CrossRef]
  4. O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18, 037116 (2008).
    [CrossRef]
  5. Y. Aviad, I. Reidler, M. Zigzag, M. Rosenbluh, and I. Kanter, “Synchronization in small networks of time-delay coupled chaotic diode lasers,” Opt. Express 20, 4352–4359 (2012).
    [CrossRef]
  6. 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]
  7. M. Fridman, M. Nixon, E. Ronen, A. A. Friesem, and N. Davidson, “Phase locking of two coupled lasers with many longitudinal modes,” Opt. Lett. 35, 526–528 (2010).
    [CrossRef]
  8. M. Brunel, A. L. Floch, and F. Bretenaker, “Multiaxis laser eigenstates,” J. Opt. Soc. Am. B 13, 946–960 (1996).
    [CrossRef]
  9. 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]
  10. V. V. Likhanskii and A. P. Napartovich, “Radiation emitted by optically coupled lasers,” Sov. Phys. Usp. 33, 228–252(1990).
    [CrossRef]
  11. The fact that the system transmission does not depend on ΔL2 is true only for the linear model. In a real laser system, due to gain nonlinearites, the laser will actually prefer to lase in a wavelength that accumulates phase of kΔL2=κ2. But this effect will be secondary in importance to the requirement of kΔL3=0.
  12. O. Shnieder, B. Shulga, and A. Ishaaya, “Imposing spectral content when coherently combining laser channels,” to be published.

2012 (1)

2011 (2)

E. Ronen and A. A. Ishayya, “Phase clusters induced by degeneracy in a phase locked fiber laser array,” IEEE J. Quantum Electron 47, 1526–15302011.
[CrossRef]

E. Ronen and A. A. Ishaaya, “Phase locking a fiber laser array via diffractive coupling,” Opt. Express 19, 1510–1515 (2011).
[CrossRef]

2010 (1)

2008 (1)

O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18, 037116 (2008).
[CrossRef]

1996 (1)

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]

1991 (1)

1990 (2)

V. V. Likhanskii and A. P. Napartovich, “Radiation emitted by optically coupled lasers,” Sov. Phys. Usp. 33, 228–252(1990).
[CrossRef]

H. G. Winful and L. Rahman, “Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers,” Phys. Rev. Lett. 65, 1575–1578 (1990).
[CrossRef]

Aviad, Y.

Bretenaker, F.

Brunel, M.

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]

D’Huys, O.

O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18, 037116 (2008).
[CrossRef]

Danckaert, J.

O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18, 037116 (2008).
[CrossRef]

Davidson, N.

Erneux, T.

O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18, 037116 (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. A 47, 4287–4296 (1993).
[CrossRef]

Fischer, I.

O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18, 037116 (2008).
[CrossRef]

Floch, A. L.

Fridman, M.

Friesem, A. A.

Ishaaya, A.

O. Shnieder, B. Shulga, and A. Ishaaya, “Imposing spectral content when coherently combining laser channels,” to be published.

Ishaaya, A. A.

Ishayya, A. A.

E. Ronen and A. A. Ishayya, “Phase clusters induced by degeneracy in a phase locked fiber laser array,” IEEE J. Quantum Electron 47, 1526–15302011.
[CrossRef]

Kanter, I.

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]

Likhanskii, V. V.

V. V. Likhanskii and A. P. Napartovich, “Radiation emitted by optically coupled lasers,” Sov. Phys. Usp. 33, 228–252(1990).
[CrossRef]

Mehuys, D.

Napartovich, A. P.

V. V. Likhanskii and A. P. Napartovich, “Radiation emitted by optically coupled lasers,” Sov. Phys. Usp. 33, 228–252(1990).
[CrossRef]

Nixon, M.

Rahman, L.

H. G. Winful and L. Rahman, “Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers,” Phys. Rev. Lett. 65, 1575–1578 (1990).
[CrossRef]

Reidler, I.

Ronen, E.

Rosenbluh, M.

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]

Shnieder, O.

O. Shnieder, B. Shulga, and A. Ishaaya, “Imposing spectral content when coherently combining laser channels,” to be published.

Shulga, B.

O. Shnieder, B. Shulga, and A. Ishaaya, “Imposing spectral content when coherently combining laser channels,” to be published.

Streifer, W.

Vicente, R.

O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18, 037116 (2008).
[CrossRef]

Waarts, R. G.

Welch, D. F.

Winful, H. G.

H. G. Winful and L. Rahman, “Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers,” Phys. Rev. Lett. 65, 1575–1578 (1990).
[CrossRef]

Zigzag, M.

Chaos (1)

O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18, 037116 (2008).
[CrossRef]

IEEE J. Quantum Electron (1)

E. Ronen and A. A. Ishayya, “Phase clusters induced by degeneracy in a phase locked fiber laser array,” IEEE J. Quantum Electron 47, 1526–15302011.
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (2)

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. (1)

H. G. Winful and L. Rahman, “Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers,” Phys. Rev. Lett. 65, 1575–1578 (1990).
[CrossRef]

Sov. Phys. Usp. (1)

V. V. Likhanskii and A. P. Napartovich, “Radiation emitted by optically coupled lasers,” Sov. Phys. Usp. 33, 228–252(1990).
[CrossRef]

Other (2)

The fact that the system transmission does not depend on ΔL2 is true only for the linear model. In a real laser system, due to gain nonlinearites, the laser will actually prefer to lase in a wavelength that accumulates phase of kΔL2=κ2. But this effect will be secondary in importance to the requirement of kΔL3=0.

O. Shnieder, B. Shulga, and A. Ishaaya, “Imposing spectral content when coherently combining laser channels,” to be published.

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Figures (4)

Fig. 1.
Fig. 1.

Experimental configuration. Dashed lines, optional elements; P, polarizer.

Fig. 2.
Fig. 2.

Experimental results: the measured output far field intensity distribution for different output coupler positions (Z). (A) Z<zt2, (B) Z=zt2, (C) Z>zt2, and (D) a third laser is added, with the output coupler located at Z=zt2.

Fig. 3.
Fig. 3.

Measured RF beat spectrum of the lasers in the array for different system configurations. Red curve: the typical spectrum when the lasers are phased locked (when Z is different than 0.5Zt). Blue curve: spectrum when the lasers are not phased locked, (i.e., when the output coupler is positioned at 0.5Zt). Green curve: in the case of three lasers, the RF spectrum of the middle laser, which is not phased locked to the other lasers (when the output coupler is positioned at the 0.5Zt).

Fig. 4.
Fig. 4.

(A) The transmittance for a system of two lasers as a function of the position of the output coupler, for different lasing modes. Blue dotted line, in-phase supermode; green dot dashed line, anti-phase supermode; red continuous line, in-coherent lasing. (B) The system coherent transmittance for a system of three lasers, and the output coupler positioned at half-Talbot distance as a function of differences in the phase accumulation in channels two and three. As seen, only changes in the optical lengths of the latter decrease the system transmittance.

Equations (9)

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κ=e2πd2πω02i4zλ,
M¯¯=R¯¯eM¯¯(G)ei2kL0(eikΔLκκeikΔL),
V1,2={1±1};λ1,2=regei2kL0(1±κ).
TCoh=IfIi=(|MV¯¯|V¯)2=λ2.
TIn-Coh=IfIi=|M¯¯{10}|2+|M¯¯{01}|22.
{1iκ0iκ1iκ0iκ1}.
T1,2Coh=|M¯¯{1±11}|3=1+2κ2,
TI-Coh=|M¯¯{100}|+|M¯¯{010}|+|M¯¯{001}|3=1+1.33κ2.
{1iκeikΔL20iκeikΔL2e2ikΔL2iκeik(ΔL2+ΔL3)0iκeik(ΔL2+ΔL3)e2ikΔL3},

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