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Discrete Source Method for the Study of Influence Nonlocality on Characteristics of the Plasmonic Nanolaser Resonators

Abstract

The discrete source method is generalized so as to investigate the nonlocal effects in multilayered particles on a substrate. The scheme for constructing an approximate solution and the corresponding numerical algorithm are described in detail. The developed approach is used to study the optical characteristics of 3D cavities of plasmonic nanolasers. It is shown that the amplitude of surface plasmon resonance and the amplification factor of the near-field intensity are reduced significantly when the nonlocal effects are taken into account. It is also shown that the amplification factor can be increased by more than twice by varying the material and thickness of the cavity shell and the direction of the incident wave.

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REFERENCES

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

    Google Scholar 

  2. A. Polman and H. A. Atwater, “Plasmonics: Optics at the nanoscale,” Mater. Today 8 (1), 56 (2005).

    Article  Google Scholar 

  3. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).

    Article  Google Scholar 

  4. M. I. Stockman, “Nanoplasmonic sensing and detection,” Science 348, 287–288 (2015).

    Article  Google Scholar 

  5. J. N. Anker, W. P. Hall, O. Lyandres, et al., “Biosensing with plasmonic nanosensors,” Nat. Mater 7, 442–453 (2008).

    Article  Google Scholar 

  6. D. Xu, X. Xiong, L. Wu, et al., “Quantum plasmonics: New opportunity in fundamental and applied photonics. Review,” Adv. Opt. Photonics 10 (4), 703–756 (2018).

    Article  Google Scholar 

  7. M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, et al., “Roadmap on plasmonics,” J. Opt. 20 (043001) (2018).

  8. R. F. Oulton, “Surface plasmon lasers: Sources of nanoscopic light. Review,” Mater. Today 15 (1–2), 26–34 (2012).

    Article  Google Scholar 

  9. M. Premaratne and M. Stockman, “Theory and technology of SPASERs: Review,” Adv. Opt. Photonics 9 (1), 79–128 (2017).

    Article  Google Scholar 

  10. V. I. Balykin, “Plasmonic nanolaser: Current state and prospects,” Phys. Usp. 61, 846–879 (2018).

    Article  Google Scholar 

  11. 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).

  12. H.-P. Solowan and C. Kryschi, “Facile design of a plasmonic nanolaser,” Condens. Mat. 2 (8), 1–7 (2017).

    Google Scholar 

  13. M. A. Noginov, G. Zhu, A. M. Belgrave, et al., “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1113 (2009).

    Article  Google Scholar 

  14. A. D. Phan, D. T. Nga, and N. A. Viet, “Theoretical model for plasmonic photothermal response of gold nanostructures solutions,” Opt. Commun. 410, 108–111 (2018).

    Article  Google Scholar 

  15. Y. Jeong, Y.-M. Kook, K. Lee, and W.-G. Koh, “Metal enhanced fluorescence (MEF) for biosensors: General approaches and a review of recent developments,” Biosensors Bioelectron. 111, 102–116 (2018).

    Article  Google Scholar 

  16. T. Dong, Y. Shi, H. Liu, F. Chen, et al., “Investigation on plasmonic responses in multilayered nanospheres including asymmetry and spatial nonlocal effects,” J. Phys. D: Appl. Phys. 50 (495302) (2017).

  17. A. I. Fernandez-Dominguez, A. Wiener, F. J. Garcia-Vidal, et al., “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett. 108 (106802) (2012).

  18. N. A. Mortensen, S. Raza, M. Wubs, et al., “A generalized nonlocal optical response theory for plasmonic nanostructures,” Nat. Commun. 5 (3809) (2014).

  19. G. Toscano, J. Straubel, A. Kwiatkowski, et al., “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Nat. Commun. 6 (7132) (2015).

  20. M. Barbry, P. Koval, F. Marchesin, et al., “Atomistic near-field nanoplasmonics: reaching atomic-scale resolution in nanooptics,” Nano Lett. 15 (3410) (2015).

  21. 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 

  22. Yu. A. Eremin and A. G. Sveshnikov, “Mathematical models in nanooptics and biophotonics based on the discrete sources method,” Comput. Math. Math. Phys. 47 (2), 262–279 (2007).

    MathSciNet  Article  Google Scholar 

  23. E. Ringe, B. Sharma, R.-I. Henry, et al., “Single nanoparticle plasmonics,” Phys. Chem. Chem. Phys. 15 (4110) (2013).

  24. 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).

    MathSciNet  Article  Google Scholar 

  25. Yu. A. Eremin and A. G. Sveshnikov, “Analysis method for the scattering properties of plasmonic particles on a substrate accounting for nonlocal effects,” Dokl. Math. 96 (3), 641–645 (2017).

    MathSciNet  Article  Google Scholar 

  26. C. Jerez-Hanckes and J.-C. Nedelec, “Asymptotics for Helmholtz and Maxwell solutions in 3-D open waveguides,” Research Report No. 2010-07 (Swiss Federal Inst. Technol., Zurich, 2010).

  27. N. Schmitt, C. Scheid, S. Lanteri, A. Moreau, and J. Viquerat, “A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account nonlocal dispersion effects,” J. Comput. Phys. 316, 396–415 (2016).

    MathSciNet  Article  Google Scholar 

  28. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1969).

    MATH  Google Scholar 

  29. D. Colton and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, New York, 1984).

    MATH  Google Scholar 

  30. www.refractiveindex.info.

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Correspondence to Yu. A. Eremin.

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Translated by I. Ruzanova

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Eremin, Y.A., Sveshnikov, A.G. Discrete Source Method for the Study of Influence Nonlocality on Characteristics of the Plasmonic Nanolaser Resonators. Comput. Math. and Math. Phys. 59, 2164–2172 (2019). https://doi.org/10.1134/S0965542519100063

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  • DOI: https://doi.org/10.1134/S0965542519100063

Keywords:

  • discrete source method
  • nanoplasmonics
  • quantum effect of nonlocality
  • plasmonic nanolaser (spaser)