Skip to main content
SpringerLink
Log in

Quantum Effects on Optical Properties of a Pair of Plasmonic Particles Separated by a Subnanometer Gap

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

The discrete source method is used to study the influence exerted by nonlocal screening on the optical properties of a linear cluster of nonspherical plasmonic nanoparticles separated by a subnanometer gap. It is shown that deformations of the particles and a reduction in the interparticle gap size lead to an enhanced nonlocal screening effect. It is found that an increase in both scattered and near field intensities is blocked by the nonlocal effect, and deformations of the particles can be used as an alternative to field intensity enhancement.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

Similar content being viewed by others

REFERENCES

  1. S. A. Maier, Nanoplasmonics: Theory and Applications (NGNORs Regulyarnaya i Khaoticheskaya Dinamika, Moscow, 2011) [in Russian].

  2. V. V. Klimov, Nanoplasmonics (Fizmatlit, Moscow, 2009) [in Russian].

    Google Scholar 

  3. H. Duan, A. I. Fernàndez-Domínguez, M. Bosman, S. A. Maier, and J. K. W. Yang, “Nanoplasmonics: Classical down to the nanometer scale,” Nano Lett. 12, 1683–1689 (2012).

    Article  Google Scholar 

  4. J. Kern, S. Großmann, N. V. Tarakina, T. Häcke, et al., “Atomic-scale confinement of resonant optical fields,” Nano Lett. 12, 5504–5509 (2012).

    Article  Google Scholar 

  5. V. R. Manfrinato, L. Zhang, D. Su, H. Dua, et al., “Resolution limits of electron-beam lithography toward the atomic scale,” Nano Lett. 13, 1555–1558 (2013).

    Article  Google Scholar 

  6. J. Mertens, A. L. Eiden, D. O. Sigle, F. Huang, et al., “Controlling subnanometer gaps in plasmonic dimers using graphene,” Nano Lett. 13, 5033–5038 (2013).

    Article  Google Scholar 

  7. F. J. J. García de Abajo, “Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides,” Phys. Chem. C 112, 17983–17987 (2008).

    Article  Google Scholar 

  8. G. Toscano, S. Raza, A. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express 20, 4176–4188 (2012).

    Article  Google Scholar 

  9. L. Stella, P. Zhang, F. J. García-Vidal, A. Rubio, and P. García-Gonzàlez, “Performance of nonlocal optics when applied to plasmonic nanostructures,” J. Phys. Chem. C 117, 8941–8949 (2013).

    Article  Google Scholar 

  10. C. Cirací, R. T. Hill, J. J. Mock, Y. Urzhumov, et al., “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).

    Article  Google Scholar 

  11. J. Bochterle, F. Neubrech, T. Nagao, and A. Pucci, “Angstrom-scale distance dependence of antenna-enhanced vibrational signals,” ACS Nano 6, 10917–10923 (2012).

    Article  Google Scholar 

  12. R. Fuchs and F. Claro, “Multipolar response of small metallic spheres: Nonlocal theory,” Phys. Rev. B 35, 3722–3727 (1987).

    Article  Google Scholar 

  13. J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).

    Article  Google Scholar 

  14. T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110, 263901 (2013).

  15. G. Toscano, J. Straubel, A. Kwiatkowski, C. Rockstuhl, et al., “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Natur. Commun. 6, Article No. 7132 (2015).

  16. M. Pelton and G. Bryant, Introduction to Metal-Nanoparticle Plasmonics (Wiley, New York, 2013).

    Google Scholar 

  17. S. Raza, S. I. Bozhevolnyi, M. Wubs, and A. N. Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys. Condens. Matter 27, 183204 (2015).

  18. R. Esteban, A. Zugarramurdi, P. Zhang, P. Nordlander, et al., “A classical treatment of optical tunneling in plasmonic gaps: Extending the quantum corrected model to practical situations,” Faraday Discuss. 178, 151–183 (2015).

    Article  Google Scholar 

  19. W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, et al., “Quantum mechanical effects in plasmonic structures with subnanometre gaps: Review,” Natur. Commun. 7, Article No. 11495 (2016).

  20. K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, et al., “Revealing the quantum regime in tunneling plasmonics,” Nature 491, 574–577 (2012).

    Article  Google Scholar 

  21. E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics (Nauka, Moscow, 1978; Pergamon, Oxford, 1981).

  22. N. A. Mortensen, “Nonlocal formalism for nanoplasmonics: Phenomenological and semi-classical considerations,” Phot. Nanostr. 11, 303–316 (2013).

    Article  Google Scholar 

  23. M. Wubs and A. Mortensen, “Nonlocal response in plasmonic nanostructures,” Quantum Plasmonics, Ed. by S. I. Bozhevolnyi (Springer, Switzerland, 2017), pp. 279–302.

    Google Scholar 

  24. C. Tserkezis, W. Yan, W. Hsieh, G. Sun, et al., “On the origin of nonlocal dumping in plasmonic monomers and dimmers,” Int. J. Mod. Phys. B 31 (17400005) (2017).

  25. Yu. A. Eremin and A. G. Sveshnikov, “A computer technique for analyzing scattering problems by the discrete source method,” Comput. Math. Math. Phys. 40 (12), 1769–1783 (2000).

    MathSciNet  MATH  Google Scholar 

  26. Yu. A. Eremin and A. G. Sveshnikov, “Mathematical model taking into account nonlocal effects of plasmonic structures on the basis of the discrete source method,” Comput. Math. Math. Phys. 58 (4), 572–580 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  27. N. S. Bakhvalov, Numerical Methods: Analysis, Algebra, Ordinary Differential Equations (Nauka, Moscow, 1975; Mir, Moscow, 1977).

  28. V. V. Voevodin and Yu. A. Kuznetsov, Matrices and Computations (Nauka, Moscow, 1984) [in Russian].

    MATH  Google Scholar 

  29. R. G. Newton, Scattering Theory of Waves and Particles (McGraw Hill, New York, 1966).

    Google Scholar 

  30. www.refractiveindex.info.

  31. S. Raza, M. Wubs, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal study of ultimate plasmon hybridization,” Opt. Lett. 40 (5), 839–842 (2015).

    Article  Google Scholar 

  32. A. Cacciola, M. A. Iati, R. Saija, F. Borghese, et al., “Spectral shift between the near-field and far-field optoplasmonic response in gold nanospheres, nanoshells, homo- and hetero-dimers,” J. Quant. Spectrosc. Radiat. Transfer 195, 97–106 (2017).

    Article  Google Scholar 

  33. C. Tserkezis, N. A. Mortensen, and M. Wubs, “How nonlocal damping reduces plasmon-enhanced fluorescence in ultranarrow gaps,” Phys. Rev. B 96, 085413 (2017).

  34. E.-M. Roller, L. V. Besteiro, C. Pupp, L. K. Khorashad, et al., “Hotspot-mediated non-dissipative and ultrafast plasmon passage,” Nat. Phys. 13, 761–765 (2017).

    Article  Google Scholar 

  35. N. V. Grishina, Yu. A. Eremin, and A. G. Sveshnikov, “Analysis of plasmon resonances of closely located particles by the discrete sources method,” Opt. Spectrosc. 113 (4), 440–445 (2012).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991, Moscow, Russia

    Yu. A. Eremin & A. G. Sveshnikov

Authors
  1. Yu. A. Eremin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. G. Sveshnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. A. Eremin.

Additional information

Translated by I. Ruzanova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Eremin, Y.A., Sveshnikov, A.G. Quantum Effects on Optical Properties of a Pair of Plasmonic Particles Separated by a Subnanometer Gap. Comput. Math. and Math. Phys. 59, 112–120 (2019). https://doi.org/10.1134/S0965542519010081

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542519010081

Keywords:

Search

Navigation