Abstract

The chimera state is the concurrent combination of synchronous and incoherent oscillations in a set of identical oscillators. In this study, we demonstrate the states for optical nanoresonators where the oscillators are designed based on a plasmonic dimer cavity. This resonator interchanges radiative energy with an active medium located at its hotspot, and therefore forms an amplitude-mediated oscillating system. Finite-difference time-domain (FDTD)-based numerical analysis of a circular array of the coupled oscillators reveals that regardless of identical nature, oscillator phase is not concordant over time for all members. The effect of coupling strength on the phase escape/synchronization of the oscillators is investigated for the plasmonic nanoresonator system. It is shown that for identical oscillators, which are placed symmetrically over the perimeter of a disc, the array can be divided to several subgroups of concurrent coherent and incoherent members. While the oscillator of each subgroup seems to be locked together, one member can escape from synchronization for a while and return to coherency, or it can sync with the other groups. The effect of coupling strength and number of oscillators on the phase-escape pace is studied for this system, and strong coupling is shown to force the array members to fully synchronize while weaker coupling causes chimera states in the array.

© 2018 Chinese Laser Press

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References

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    [Crossref]
  6. E. Omel’chenko, Y. L. Maistrenko, and P. A. Tass, “Chimera states: the natural link between coherence and incoherence,” Phys. Rev. Lett. 100, 044105 (2008).
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  8. S. Nkomo, M. R. Tinsley, and K. Showalter, “Chimera states in populations of nonlocally coupled chemical oscillators,” Phys. Rev. Lett. 110, 244102 (2013).
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  10. A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hövel, I. Omelchenko, and E. Schöll, “Experimental observation of chimeras in coupled-map lattices,” Nat. Phys. 8, 658–661 (2012).
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    [Crossref]
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    [Crossref]
  32. M. G. Blaber, M. D. Arnold, and M. J. Ford, “Search for the ideal plasmonic nanoshell: the effects of surface scattering and alternatives to gold and silver,” J. Phys. Chem. C 113, 3041–3045 (2009).
    [Crossref]
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    [Crossref]
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    [Crossref]

2017 (2)

J. Shena, J. Hizanidis, V. Kovanis, and G. P. Tsironis, “Turbulent chimeras in large semiconductor laser arrays,” Sci. Rep. 7, 42116 (2017).
[Crossref]

M. G. Clerc, M. A. Ferré, S. Coulibaly, R. G. Rojas, and M. Tlidi, “Chimera-like states in an array of coupled-waveguide resonators,” Opt. Lett. 42, 2906–2909 (2017).
[Crossref]

2016 (1)

J. Wojewoda, K. Czolczynski, Y. Maistrenko, and T. Kapitaniak, “The smallest chimera state for coupled pendula,” Sci. Rep. 6, 34329 (2016).
[Crossref]

2015 (2)

L. Larger, B. Penkovsky, and Y. Maistrenko, “Laser chimeras as a paradigm for multistable patterns in complex systems,” Nat. Commun. 6, 7752 (2015).
[Crossref]

M. J. Panaggio and D. M. Abrams, “Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators,” Nonlinearity 28, R67–R87 (2015).
[Crossref]

2014 (2)

G. C. Sethia and A. Sen, “Chimera states: the existence criteria revisited,” Phys. Rev. Lett. 112, 144101 (2014).
[Crossref]

E. Tognoli and J. S. Kelso, “The metastable brain,” Neuron 81, 35–48 (2014).
[Crossref]

2013 (5)

L. Larger, B. Penkovsky, and Y. Maistrenko, “Virtual chimera states for delayed-feedback systems,” Phys. Rev. Lett. 111, 054103 (2013).
[Crossref]

E. A. Martens, S. Thutupalli, A. Fourrière, and O. Hallatschek, “Chimera states in mechanical oscillator networks,” Proc. Natl Acad. Sci. U.S.A. 110, 10563–10567 (2013).
[Crossref]

O. E. Omel’chenko, “Coherence-incoherence patterns in a ring of non-locally coupled phase oscillators,” Nonlinearity 26, 2469–2498 (2013).
[Crossref]

N. Verschueren, U. Bortolozzo, M. G. Clerc, and S. Residori, “Spatiotemporal chaotic localized state in liquid crystal light valve experiments with optical feedback,” Phys. Rev. Lett. 110, 104101 (2013).
[Crossref]

S. Nkomo, M. R. Tinsley, and K. Showalter, “Chimera states in populations of nonlocally coupled chemical oscillators,” Phys. Rev. Lett. 110, 244102 (2013).
[Crossref]

2012 (2)

A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hövel, I. Omelchenko, and E. Schöll, “Experimental observation of chimeras in coupled-map lattices,” Nat. Phys. 8, 658–661 (2012).
[Crossref]

M. R. Tinsley, S. Nkomo, and K. Showalter, “Chimera and phase-cluster states in populations of coupled chemical oscillators,” Nat. Phys. 8, 662–665 (2012).
[Crossref]

2011 (2)

M. Wolfrum and E. Omel’chenko, “Chimera states are chaotic transients,” Phys. Rev. E 84, 015201 (2011).
[Crossref]

I. Omelchenko, Y. Maistrenko, P. Hövel, and E. Schöll, “Loss of coherence in dynamical networks: spatial chaos and chimera states,” Phys. Rev. Lett. 106, 234102 (2011).
[Crossref]

2010 (1)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref]

2009 (2)

E. Plum, V. Fedotov, P. Kuo, D. Tsai, and N. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17, 8548–8551 (2009).
[Crossref]

M. G. Blaber, M. D. Arnold, and M. J. Ford, “Search for the ideal plasmonic nanoshell: the effects of surface scattering and alternatives to gold and silver,” J. Phys. Chem. C 113, 3041–3045 (2009).
[Crossref]

2008 (6)

B. Willingham, D. Brandl, and P. Nordlander, “Plasmon hybridization in nanorod dimers,” Appl. Phys. B 93, 209–216 (2008).
[Crossref]

N. I. Zheludev, S. Prosvirnin, N. Papasimakis, and V. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[Crossref]

M. I. Stockman, “Spasers explained,” Nat. Photonics 2, 327–329 (2008).
[Crossref]

G. C. Sethia, A. Sen, and F. M. Atay, “Clustered chimera states in delay-coupled oscillator systems,” Phys. Rev. Lett. 100, 144102 (2008).
[Crossref]

E. Omel’chenko, Y. L. Maistrenko, and P. A. Tass, “Chimera states: the natural link between coherence and incoherence,” Phys. Rev. Lett. 100, 044105 (2008).
[Crossref]

D. M. Abrams, R. Mirollo, S. H. Strogatz, and D. A. Wiley, “Solvable model for chimera states of coupled oscillators,” Phys. Rev. Lett. 101, 084103 (2008).
[Crossref]

2007 (1)

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
[Crossref]

2006 (1)

P. K. Jain, S. Eustis, and M. A. El-Sayed, “Plasmon coupling in nanorod assemblies: optical absorption, discrete dipole approximation simulation, and exciton-coupling model,” J. Phys. Chem. B 110, 18243–18253 (2006).
[Crossref]

2004 (3)

S.-H. Chang and A. Taflove, “Finite-difference time-domain model of lasing action in a four-level two-electron atomic system,” Opt. Express 12, 3827–3833 (2004).
[Crossref]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[Crossref]

D. M. Abrams and S. H. Strogatz, “Chimera states for coupled oscillators,” Phys. Rev Lett. 93, 174102 (2004).
[Crossref]

2003 (1)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[Crossref]

Abrams, D. M.

M. J. Panaggio and D. M. Abrams, “Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators,” Nonlinearity 28, R67–R87 (2015).
[Crossref]

D. M. Abrams, R. Mirollo, S. H. Strogatz, and D. A. Wiley, “Solvable model for chimera states of coupled oscillators,” Phys. Rev. Lett. 101, 084103 (2008).
[Crossref]

D. M. Abrams and S. H. Strogatz, “Chimera states for coupled oscillators,” Phys. Rev Lett. 93, 174102 (2004).
[Crossref]

Arnold, M. D.

M. G. Blaber, M. D. Arnold, and M. J. Ford, “Search for the ideal plasmonic nanoshell: the effects of surface scattering and alternatives to gold and silver,” J. Phys. Chem. C 113, 3041–3045 (2009).
[Crossref]

Atay, F. M.

G. C. Sethia, A. Sen, and F. M. Atay, “Clustered chimera states in delay-coupled oscillator systems,” Phys. Rev. Lett. 100, 144102 (2008).
[Crossref]

Battogtokh, D.

Y. Kuramoto and D. Battogtokh, “Coexistence of coherence and incoherence in nonlocally coupled phase oscillators,” arXiv:cond-mat/0210694 (2002).

Bergman, D. J.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[Crossref]

Blaber, M. G.

M. G. Blaber, M. D. Arnold, and M. J. Ford, “Search for the ideal plasmonic nanoshell: the effects of surface scattering and alternatives to gold and silver,” J. Phys. Chem. C 113, 3041–3045 (2009).
[Crossref]

Bortolozzo, U.

N. Verschueren, U. Bortolozzo, M. G. Clerc, and S. Residori, “Spatiotemporal chaotic localized state in liquid crystal light valve experiments with optical feedback,” Phys. Rev. Lett. 110, 104101 (2013).
[Crossref]

Brandl, D.

B. Willingham, D. Brandl, and P. Nordlander, “Plasmon hybridization in nanorod dimers,” Appl. Phys. B 93, 209–216 (2008).
[Crossref]

Chang, S.-H.

Chettiar, U. K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref]

Clerc, M. G.

M. G. Clerc, M. A. Ferré, S. Coulibaly, R. G. Rojas, and M. Tlidi, “Chimera-like states in an array of coupled-waveguide resonators,” Opt. Lett. 42, 2906–2909 (2017).
[Crossref]

N. Verschueren, U. Bortolozzo, M. G. Clerc, and S. Residori, “Spatiotemporal chaotic localized state in liquid crystal light valve experiments with optical feedback,” Phys. Rev. Lett. 110, 104101 (2013).
[Crossref]

Coulibaly, S.

Czolczynski, K.

J. Wojewoda, K. Czolczynski, Y. Maistrenko, and T. Kapitaniak, “The smallest chimera state for coupled pendula,” Sci. Rep. 6, 34329 (2016).
[Crossref]

Drachev, V. P.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref]

El-Sayed, M. A.

P. K. Jain, S. Eustis, and M. A. El-Sayed, “Plasmon coupling in nanorod assemblies: optical absorption, discrete dipole approximation simulation, and exciton-coupling model,” J. Phys. Chem. B 110, 18243–18253 (2006).
[Crossref]

Eustis, S.

P. K. Jain, S. Eustis, and M. A. El-Sayed, “Plasmon coupling in nanorod assemblies: optical absorption, discrete dipole approximation simulation, and exciton-coupling model,” J. Phys. Chem. B 110, 18243–18253 (2006).
[Crossref]

Fedotov, V.

Ferré, M. A.

Ford, M. J.

M. G. Blaber, M. D. Arnold, and M. J. Ford, “Search for the ideal plasmonic nanoshell: the effects of surface scattering and alternatives to gold and silver,” J. Phys. Chem. C 113, 3041–3045 (2009).
[Crossref]

Fourrière, A.

E. A. Martens, S. Thutupalli, A. Fourrière, and O. Hallatschek, “Chimera states in mechanical oscillator networks,” Proc. Natl Acad. Sci. U.S.A. 110, 10563–10567 (2013).
[Crossref]

Hagerstrom, A. M.

A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hövel, I. Omelchenko, and E. Schöll, “Experimental observation of chimeras in coupled-map lattices,” Nat. Phys. 8, 658–661 (2012).
[Crossref]

Hallatschek, O.

E. A. Martens, S. Thutupalli, A. Fourrière, and O. Hallatschek, “Chimera states in mechanical oscillator networks,” Proc. Natl Acad. Sci. U.S.A. 110, 10563–10567 (2013).
[Crossref]

Hizanidis, J.

J. Shena, J. Hizanidis, V. Kovanis, and G. P. Tsironis, “Turbulent chimeras in large semiconductor laser arrays,” Sci. Rep. 7, 42116 (2017).
[Crossref]

Hövel, P.

A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hövel, I. Omelchenko, and E. Schöll, “Experimental observation of chimeras in coupled-map lattices,” Nat. Phys. 8, 658–661 (2012).
[Crossref]

I. Omelchenko, Y. Maistrenko, P. Hövel, and E. Schöll, “Loss of coherence in dynamical networks: spatial chaos and chimera states,” Phys. Rev. Lett. 106, 234102 (2011).
[Crossref]

Jain, P. K.

P. K. Jain, S. Eustis, and M. A. El-Sayed, “Plasmon coupling in nanorod assemblies: optical absorption, discrete dipole approximation simulation, and exciton-coupling model,” J. Phys. Chem. B 110, 18243–18253 (2006).
[Crossref]

Kapitaniak, T.

J. Wojewoda, K. Czolczynski, Y. Maistrenko, and T. Kapitaniak, “The smallest chimera state for coupled pendula,” Sci. Rep. 6, 34329 (2016).
[Crossref]

Kelso, J. S.

E. Tognoli and J. S. Kelso, “The metastable brain,” Neuron 81, 35–48 (2014).
[Crossref]

Kildishev, A. V.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref]

Kovanis, V.

J. Shena, J. Hizanidis, V. Kovanis, and G. P. Tsironis, “Turbulent chimeras in large semiconductor laser arrays,” Sci. Rep. 7, 42116 (2017).
[Crossref]

Kuo, P.

Kuramoto, Y.

Y. Kuramoto and D. Battogtokh, “Coexistence of coherence and incoherence in nonlocally coupled phase oscillators,” arXiv:cond-mat/0210694 (2002).

Larger, L.

L. Larger, B. Penkovsky, and Y. Maistrenko, “Laser chimeras as a paradigm for multistable patterns in complex systems,” Nat. Commun. 6, 7752 (2015).
[Crossref]

L. Larger, B. Penkovsky, and Y. Maistrenko, “Virtual chimera states for delayed-feedback systems,” Phys. Rev. Lett. 111, 054103 (2013).
[Crossref]

Li, K.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[Crossref]

Linden, S.

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
[Crossref]

Maistrenko, Y.

J. Wojewoda, K. Czolczynski, Y. Maistrenko, and T. Kapitaniak, “The smallest chimera state for coupled pendula,” Sci. Rep. 6, 34329 (2016).
[Crossref]

L. Larger, B. Penkovsky, and Y. Maistrenko, “Laser chimeras as a paradigm for multistable patterns in complex systems,” Nat. Commun. 6, 7752 (2015).
[Crossref]

L. Larger, B. Penkovsky, and Y. Maistrenko, “Virtual chimera states for delayed-feedback systems,” Phys. Rev. Lett. 111, 054103 (2013).
[Crossref]

I. Omelchenko, Y. Maistrenko, P. Hövel, and E. Schöll, “Loss of coherence in dynamical networks: spatial chaos and chimera states,” Phys. Rev. Lett. 106, 234102 (2011).
[Crossref]

Maistrenko, Y. L.

E. Omel’chenko, Y. L. Maistrenko, and P. A. Tass, “Chimera states: the natural link between coherence and incoherence,” Phys. Rev. Lett. 100, 044105 (2008).
[Crossref]

Martens, E. A.

E. A. Martens, S. Thutupalli, A. Fourrière, and O. Hallatschek, “Chimera states in mechanical oscillator networks,” Proc. Natl Acad. Sci. U.S.A. 110, 10563–10567 (2013).
[Crossref]

Mirollo, R.

D. M. Abrams, R. Mirollo, S. H. Strogatz, and D. A. Wiley, “Solvable model for chimera states of coupled oscillators,” Phys. Rev. Lett. 101, 084103 (2008).
[Crossref]

Murphy, T. E.

A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hövel, I. Omelchenko, and E. Schöll, “Experimental observation of chimeras in coupled-map lattices,” Nat. Phys. 8, 658–661 (2012).
[Crossref]

Ni, X.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref]

Nkomo, S.

S. Nkomo, M. R. Tinsley, and K. Showalter, “Chimera states in populations of nonlocally coupled chemical oscillators,” Phys. Rev. Lett. 110, 244102 (2013).
[Crossref]

M. R. Tinsley, S. Nkomo, and K. Showalter, “Chimera and phase-cluster states in populations of coupled chemical oscillators,” Nat. Phys. 8, 662–665 (2012).
[Crossref]

Nordlander, P.

B. Willingham, D. Brandl, and P. Nordlander, “Plasmon hybridization in nanorod dimers,” Appl. Phys. B 93, 209–216 (2008).
[Crossref]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[Crossref]

Omel’chenko, E.

M. Wolfrum and E. Omel’chenko, “Chimera states are chaotic transients,” Phys. Rev. E 84, 015201 (2011).
[Crossref]

E. Omel’chenko, Y. L. Maistrenko, and P. A. Tass, “Chimera states: the natural link between coherence and incoherence,” Phys. Rev. Lett. 100, 044105 (2008).
[Crossref]

Omel’chenko, O. E.

O. E. Omel’chenko, “Coherence-incoherence patterns in a ring of non-locally coupled phase oscillators,” Nonlinearity 26, 2469–2498 (2013).
[Crossref]

Omelchenko, I.

A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hövel, I. Omelchenko, and E. Schöll, “Experimental observation of chimeras in coupled-map lattices,” Nat. Phys. 8, 658–661 (2012).
[Crossref]

I. Omelchenko, Y. Maistrenko, P. Hövel, and E. Schöll, “Loss of coherence in dynamical networks: spatial chaos and chimera states,” Phys. Rev. Lett. 106, 234102 (2011).
[Crossref]

Oubre, C.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[Crossref]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998), Vol. 3.

Panaggio, M. J.

M. J. Panaggio and D. M. Abrams, “Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators,” Nonlinearity 28, R67–R87 (2015).
[Crossref]

Papasimakis, N.

N. I. Zheludev, S. Prosvirnin, N. Papasimakis, and V. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[Crossref]

Penkovsky, B.

L. Larger, B. Penkovsky, and Y. Maistrenko, “Laser chimeras as a paradigm for multistable patterns in complex systems,” Nat. Commun. 6, 7752 (2015).
[Crossref]

L. Larger, B. Penkovsky, and Y. Maistrenko, “Virtual chimera states for delayed-feedback systems,” Phys. Rev. Lett. 111, 054103 (2013).
[Crossref]

Plum, E.

Prodan, E.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[Crossref]

Prosvirnin, S.

N. I. Zheludev, S. Prosvirnin, N. Papasimakis, and V. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[Crossref]

Reif, F.

F. Reif, Fundamentals of Statistical and Thermal Physics (Waveland, 2009).

Residori, S.

N. Verschueren, U. Bortolozzo, M. G. Clerc, and S. Residori, “Spatiotemporal chaotic localized state in liquid crystal light valve experiments with optical feedback,” Phys. Rev. Lett. 110, 104101 (2013).
[Crossref]

Rojas, R. G.

Roy, R.

A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hövel, I. Omelchenko, and E. Schöll, “Experimental observation of chimeras in coupled-map lattices,” Nat. Phys. 8, 658–661 (2012).
[Crossref]

Schöll, E.

A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hövel, I. Omelchenko, and E. Schöll, “Experimental observation of chimeras in coupled-map lattices,” Nat. Phys. 8, 658–661 (2012).
[Crossref]

I. Omelchenko, Y. Maistrenko, P. Hövel, and E. Schöll, “Loss of coherence in dynamical networks: spatial chaos and chimera states,” Phys. Rev. Lett. 106, 234102 (2011).
[Crossref]

Sen, A.

G. C. Sethia and A. Sen, “Chimera states: the existence criteria revisited,” Phys. Rev. Lett. 112, 144101 (2014).
[Crossref]

G. C. Sethia, A. Sen, and F. M. Atay, “Clustered chimera states in delay-coupled oscillator systems,” Phys. Rev. Lett. 100, 144102 (2008).
[Crossref]

Sethia, G. C.

G. C. Sethia and A. Sen, “Chimera states: the existence criteria revisited,” Phys. Rev. Lett. 112, 144101 (2014).
[Crossref]

G. C. Sethia, A. Sen, and F. M. Atay, “Clustered chimera states in delay-coupled oscillator systems,” Phys. Rev. Lett. 100, 144102 (2008).
[Crossref]

Shalaev, V. M.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref]

Shena, J.

J. Shena, J. Hizanidis, V. Kovanis, and G. P. Tsironis, “Turbulent chimeras in large semiconductor laser arrays,” Sci. Rep. 7, 42116 (2017).
[Crossref]

Showalter, K.

S. Nkomo, M. R. Tinsley, and K. Showalter, “Chimera states in populations of nonlocally coupled chemical oscillators,” Phys. Rev. Lett. 110, 244102 (2013).
[Crossref]

M. R. Tinsley, S. Nkomo, and K. Showalter, “Chimera and phase-cluster states in populations of coupled chemical oscillators,” Nat. Phys. 8, 662–665 (2012).
[Crossref]

Soukoulis, C. M.

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
[Crossref]

Stockman, M.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[Crossref]

Stockman, M. I.

M. I. Stockman, “Spasers explained,” Nat. Photonics 2, 327–329 (2008).
[Crossref]

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[Crossref]

Strogatz, S. H.

D. M. Abrams, R. Mirollo, S. H. Strogatz, and D. A. Wiley, “Solvable model for chimera states of coupled oscillators,” Phys. Rev. Lett. 101, 084103 (2008).
[Crossref]

D. M. Abrams and S. H. Strogatz, “Chimera states for coupled oscillators,” Phys. Rev Lett. 93, 174102 (2004).
[Crossref]

Taflove, A.

Tass, P. A.

E. Omel’chenko, Y. L. Maistrenko, and P. A. Tass, “Chimera states: the natural link between coherence and incoherence,” Phys. Rev. Lett. 100, 044105 (2008).
[Crossref]

Thutupalli, S.

E. A. Martens, S. Thutupalli, A. Fourrière, and O. Hallatschek, “Chimera states in mechanical oscillator networks,” Proc. Natl Acad. Sci. U.S.A. 110, 10563–10567 (2013).
[Crossref]

Tinsley, M. R.

S. Nkomo, M. R. Tinsley, and K. Showalter, “Chimera states in populations of nonlocally coupled chemical oscillators,” Phys. Rev. Lett. 110, 244102 (2013).
[Crossref]

M. R. Tinsley, S. Nkomo, and K. Showalter, “Chimera and phase-cluster states in populations of coupled chemical oscillators,” Nat. Phys. 8, 662–665 (2012).
[Crossref]

Tlidi, M.

Tognoli, E.

E. Tognoli and J. S. Kelso, “The metastable brain,” Neuron 81, 35–48 (2014).
[Crossref]

Tsai, D.

Tsironis, G. P.

J. Shena, J. Hizanidis, V. Kovanis, and G. P. Tsironis, “Turbulent chimeras in large semiconductor laser arrays,” Sci. Rep. 7, 42116 (2017).
[Crossref]

Verschueren, N.

N. Verschueren, U. Bortolozzo, M. G. Clerc, and S. Residori, “Spatiotemporal chaotic localized state in liquid crystal light valve experiments with optical feedback,” Phys. Rev. Lett. 110, 104101 (2013).
[Crossref]

Wegener, M.

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
[Crossref]

Wiley, D. A.

D. M. Abrams, R. Mirollo, S. H. Strogatz, and D. A. Wiley, “Solvable model for chimera states of coupled oscillators,” Phys. Rev. Lett. 101, 084103 (2008).
[Crossref]

Willingham, B.

B. Willingham, D. Brandl, and P. Nordlander, “Plasmon hybridization in nanorod dimers,” Appl. Phys. B 93, 209–216 (2008).
[Crossref]

Wojewoda, J.

J. Wojewoda, K. Czolczynski, Y. Maistrenko, and T. Kapitaniak, “The smallest chimera state for coupled pendula,” Sci. Rep. 6, 34329 (2016).
[Crossref]

Wolfrum, M.

M. Wolfrum and E. Omel’chenko, “Chimera states are chaotic transients,” Phys. Rev. E 84, 015201 (2011).
[Crossref]

Xiao, S.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref]

Yuan, H.-K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref]

Zheludev, N.

Zheludev, N. I.

N. I. Zheludev, S. Prosvirnin, N. Papasimakis, and V. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[Crossref]

Appl. Phys. B (1)

B. Willingham, D. Brandl, and P. Nordlander, “Plasmon hybridization in nanorod dimers,” Appl. Phys. B 93, 209–216 (2008).
[Crossref]

J. Phys. Chem. B (1)

P. K. Jain, S. Eustis, and M. A. El-Sayed, “Plasmon coupling in nanorod assemblies: optical absorption, discrete dipole approximation simulation, and exciton-coupling model,” J. Phys. Chem. B 110, 18243–18253 (2006).
[Crossref]

J. Phys. Chem. C (1)

M. G. Blaber, M. D. Arnold, and M. J. Ford, “Search for the ideal plasmonic nanoshell: the effects of surface scattering and alternatives to gold and silver,” J. Phys. Chem. C 113, 3041–3045 (2009).
[Crossref]

Nano Lett. (1)

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[Crossref]

Nat. Commun. (1)

L. Larger, B. Penkovsky, and Y. Maistrenko, “Laser chimeras as a paradigm for multistable patterns in complex systems,” Nat. Commun. 6, 7752 (2015).
[Crossref]

Nat. Photonics (2)

N. I. Zheludev, S. Prosvirnin, N. Papasimakis, and V. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[Crossref]

M. I. Stockman, “Spasers explained,” Nat. Photonics 2, 327–329 (2008).
[Crossref]

Nat. Phys. (2)

A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hövel, I. Omelchenko, and E. Schöll, “Experimental observation of chimeras in coupled-map lattices,” Nat. Phys. 8, 658–661 (2012).
[Crossref]

M. R. Tinsley, S. Nkomo, and K. Showalter, “Chimera and phase-cluster states in populations of coupled chemical oscillators,” Nat. Phys. 8, 662–665 (2012).
[Crossref]

Nature (1)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref]

Neuron (1)

E. Tognoli and J. S. Kelso, “The metastable brain,” Neuron 81, 35–48 (2014).
[Crossref]

Nonlinearity (2)

M. J. Panaggio and D. M. Abrams, “Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators,” Nonlinearity 28, R67–R87 (2015).
[Crossref]

O. E. Omel’chenko, “Coherence-incoherence patterns in a ring of non-locally coupled phase oscillators,” Nonlinearity 26, 2469–2498 (2013).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev Lett. (1)

D. M. Abrams and S. H. Strogatz, “Chimera states for coupled oscillators,” Phys. Rev Lett. 93, 174102 (2004).
[Crossref]

Phys. Rev. E (1)

M. Wolfrum and E. Omel’chenko, “Chimera states are chaotic transients,” Phys. Rev. E 84, 015201 (2011).
[Crossref]

Phys. Rev. Lett. (9)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[Crossref]

D. M. Abrams, R. Mirollo, S. H. Strogatz, and D. A. Wiley, “Solvable model for chimera states of coupled oscillators,” Phys. Rev. Lett. 101, 084103 (2008).
[Crossref]

N. Verschueren, U. Bortolozzo, M. G. Clerc, and S. Residori, “Spatiotemporal chaotic localized state in liquid crystal light valve experiments with optical feedback,” Phys. Rev. Lett. 110, 104101 (2013).
[Crossref]

G. C. Sethia, A. Sen, and F. M. Atay, “Clustered chimera states in delay-coupled oscillator systems,” Phys. Rev. Lett. 100, 144102 (2008).
[Crossref]

E. Omel’chenko, Y. L. Maistrenko, and P. A. Tass, “Chimera states: the natural link between coherence and incoherence,” Phys. Rev. Lett. 100, 044105 (2008).
[Crossref]

I. Omelchenko, Y. Maistrenko, P. Hövel, and E. Schöll, “Loss of coherence in dynamical networks: spatial chaos and chimera states,” Phys. Rev. Lett. 106, 234102 (2011).
[Crossref]

S. Nkomo, M. R. Tinsley, and K. Showalter, “Chimera states in populations of nonlocally coupled chemical oscillators,” Phys. Rev. Lett. 110, 244102 (2013).
[Crossref]

L. Larger, B. Penkovsky, and Y. Maistrenko, “Virtual chimera states for delayed-feedback systems,” Phys. Rev. Lett. 111, 054103 (2013).
[Crossref]

G. C. Sethia and A. Sen, “Chimera states: the existence criteria revisited,” Phys. Rev. Lett. 112, 144101 (2014).
[Crossref]

Proc. Natl Acad. Sci. U.S.A. (1)

E. A. Martens, S. Thutupalli, A. Fourrière, and O. Hallatschek, “Chimera states in mechanical oscillator networks,” Proc. Natl Acad. Sci. U.S.A. 110, 10563–10567 (2013).
[Crossref]

Sci. Rep. (2)

J. Wojewoda, K. Czolczynski, Y. Maistrenko, and T. Kapitaniak, “The smallest chimera state for coupled pendula,” Sci. Rep. 6, 34329 (2016).
[Crossref]

J. Shena, J. Hizanidis, V. Kovanis, and G. P. Tsironis, “Turbulent chimeras in large semiconductor laser arrays,” Sci. Rep. 7, 42116 (2017).
[Crossref]

Science (1)

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
[Crossref]

Other (4)

FDTD Solutions (Lumerical, 2016).

F. Reif, Fundamentals of Statistical and Thermal Physics (Waveland, 2009).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998), Vol. 3.

Y. Kuramoto and D. Battogtokh, “Coexistence of coherence and incoherence in nonlocally coupled phase oscillators,” arXiv:cond-mat/0210694 (2002).

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Figures (5)

Fig. 1.
Fig. 1. Simplified model of electron interaction with photons in an active medium with a two-electron, four-energy-level atomic system.
Fig. 2.
Fig. 2. Plasmonic nano-oscillator. (a) Geometry and excitation illustration. (b) Electric field enhancement of the plasmonic dimer at the center of its gap with undoped InP. (c) Time profile of the electric field excitation. (d) Probed electric field at the dimer gap with doped InP. (e) Electron population density normalized to the density of active molecules in InP at the center of the plasmonic dimer.
Fig. 3.
Fig. 3. Array schematic and an example of full coherency in the oscillators. (a) Geometry of the array and the direction of incident plane wave electric field pulse (sketched not to the real scale). (b) Probed electric field at the center of oscillator 1, where the radius of the array r=27.5  nm. Inset shows the electric field at the center of all the oscillators with time. (c) Oscillation amplitude variation for different oscillators over time.
Fig. 4.
Fig. 4. Sampled amplitude and phase of oscillator electric fields at their gap for different array geometries with eight oscillators and different disc radii: (a), (b) r=27.5  nm, (c), (d) r=35  nm, (e), (f) r=70  nm, and (g), (h) r=140  nm.
Fig. 5.
Fig. 5. Sampled phase of oscillator electric fields at their gap for different array geometries with 16 oscillators and different disc radii: (a) r=54  nm, (b) r=68.7  nm, (c) r=137.3  nm, and (d) r=274.6  nm. These radii are selected to keep the inter-oscillator distances the same as those of the corresponding array in Fig. 4.

Equations (9)

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

d2P21/dt2+γ21dP21/dt+ω212P21=ζ21(N2N1)E,
d2P30/dt2+γ30dP30/dt+ω302P30=ζ30(N3N0)E.
dN3/dt=N3(1N2)/τ32N3(1N0)/τ30+dP30/dt·E/hω30,
dN2/dt=N3(1N2)/τ32N2(1N1)/τ21+dP21/dt·E/hω21,
dN1/dt=N2(1N1)/τ21N1(1N0)/τ10dP21/dt·E/hω21,
dN0/dt=N3(1N0)/τ30+N1(1N0)/τ10dP30/dt·E/hω30.
Ni/Nj=1/{1+α·exp[(EiEj)/kT]}.
φm(t)=ω30t+arctan{Σn=1:NIm[Emn(t)]/Σn=1:NRe[Emn(t)]},
φk=<Em(kΔt)ω30kΔt.

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